M.A. Bessa
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1
The thesis begins with an introduction to regression from a Bayesian perspective, establishing the connection between deterministic and probabilistic treatments, and covering models from linear to kernel and deep neural network regressions. This chapter provides the theoretical foundation for the remainder of the thesis by formalizing inference techniques, uncertainty quantification strategies, and model evaluation metrics.
Two core machine learning methods are developed to tackle the challenges of uncertainty estimation and multi-fidelity data fusion. First, a cooperative training scheme is proposed that combines a variance estimation neural network with a Bayesian mean neural network, enabling explicit disentanglement of aleatoric and epistemic uncertainties while improving mean prediction. The approach demonstrates strong scalability and generality across tasks and network architectures. Second, a practical multi-fidelity Bayesian learning framework is introduced, which fuses low- and high-fidelity data via a deterministic model, a transfer-learning module, and a Bayesian residual learner. This architecture balances expressiveness and computational efficiency, yielding robust predictions in both data-scarce and data-rich regimes.
To support data-driven mechanics, the proposed framework is extended to generalized constitutive modeling of history-dependent materials. A hierarchical learning scheme is developed that spans from single-fidelity deterministic networks to multi-fidelity Bayesian recurrent neural networks. This addresses two major limitations in data-driven modeling: the reliance on large, clean datasets and the lack of interpretability in neural network predictions.
Finally, the methodology is applied to the sustainable design of recycled composite polymers, where uncertainty arises from microstructural variability and the use of compatibilizers. Leveraging the cooperative training framework, both aleatoric and epistemic uncertainties are quantified, and a novel polymer design is optimized to achieve better expected performance and lower data variation.
Together, this thesis presents a unified and scalable framework for Bayesian learning under uncertainty and multi-fidelity conditions, with broad applicability in scientific computing, materials modeling, and sustainable engineering. The thesis concludes by summarizing key findings, discussing current limitations, and outlining future research directions. ...
The thesis begins with an introduction to regression from a Bayesian perspective, establishing the connection between deterministic and probabilistic treatments, and covering models from linear to kernel and deep neural network regressions. This chapter provides the theoretical foundation for the remainder of the thesis by formalizing inference techniques, uncertainty quantification strategies, and model evaluation metrics.
Two core machine learning methods are developed to tackle the challenges of uncertainty estimation and multi-fidelity data fusion. First, a cooperative training scheme is proposed that combines a variance estimation neural network with a Bayesian mean neural network, enabling explicit disentanglement of aleatoric and epistemic uncertainties while improving mean prediction. The approach demonstrates strong scalability and generality across tasks and network architectures. Second, a practical multi-fidelity Bayesian learning framework is introduced, which fuses low- and high-fidelity data via a deterministic model, a transfer-learning module, and a Bayesian residual learner. This architecture balances expressiveness and computational efficiency, yielding robust predictions in both data-scarce and data-rich regimes.
To support data-driven mechanics, the proposed framework is extended to generalized constitutive modeling of history-dependent materials. A hierarchical learning scheme is developed that spans from single-fidelity deterministic networks to multi-fidelity Bayesian recurrent neural networks. This addresses two major limitations in data-driven modeling: the reliance on large, clean datasets and the lack of interpretability in neural network predictions.
Finally, the methodology is applied to the sustainable design of recycled composite polymers, where uncertainty arises from microstructural variability and the use of compatibilizers. Leveraging the cooperative training framework, both aleatoric and epistemic uncertainties are quantified, and a novel polymer design is optimized to achieve better expected performance and lower data variation.
Together, this thesis presents a unified and scalable framework for Bayesian learning under uncertainty and multi-fidelity conditions, with broad applicability in scientific computing, materials modeling, and sustainable engineering. The thesis concludes by summarizing key findings, discussing current limitations, and outlining future research directions.
One particularly pressing challenge is performing fast mechanical simulations along multiple length scales in heterogeneous materials. To this end, the reduced order method known as Self-Consistent Clustering Analysis (SCA) has been proposed as an effective means of striking a balance between accuracy and efficiency. Underpinning this is SCA's ability to decompose a domain into clusters in a preliminary offline stage (learning), efficiently reducing the problem's degrees of freedom. It has been shown to be remarkably accurate in predicting plasticity without significantly degrading accuracy compared to other methods, such as the finite element method. However, the offline stage requires a quantity known as the Cluster Interaction Tensor (CIT) to be computed, whose computational complexity scales quadratically with the number of clusters, thus causing a bottleneck in the method. Additionally, the CIT is recomputed during the online stage (prediction) in the recently proposed extension called adaptive Self-consistent Clustering Analysis (ASCA), which further stresses the need to speed up their computation.
To address this limitation, a data-driven surrogate model is proposed to compute the CIT efficiently. The behavior of the local CIT components is first analyzed, from which it is concluded that a surrogate model shall be developed to predict upper off-diagonal terms. This decision is made due to the bi-modal nature of certain components in the tensor and the quadratic scaling behavior of off-diagonal terms versus the linear scaling of diagonal ones. Following that, a sensitivity study shows how various magnitudes of noise affect the homogenized response's accuracy and convergence performance. Furthermore, it is shown that the solution accuracy and convergence behavior are degraded when the number of clusters is increased. With a proper understanding of the CIT's behavior and its function within SCA, the surrogate can be created.
The surrogate's feasibility is first shown using the ResNet-18 architecture, a CNN model derived from computer vision. It is demonstrated that ResNet-18 can make accurate predictions for a range of different microstructural parameters. This includes the number of clusters and samples in the dataset's distribution and out of distribution. Composite RVEs are used as out-of-distribution samples to test the robustness of the surrogate to realistic inputs. An attempt is made to improve the model's performance by training it on an unbalanced dataset, and although it improves the overall CIT prediction in specific regimes, the resulting stress-strain generalizability is degraded. Subsequently, a lighter version of ResNet-18, known as ResNet-lite, is tested and shown to give faster predictions than the baseline method. This, however, comes at a cost to the accuracy of the solution.
Additionally, deemed as a critical aspect of the study, the efficient generation of a large representative training dataset is discussed. A novel method for generating clustered microstructures efficiently using gradient noise is introduced. By leveraging datasets derived using this method, the surrogate can learn the fundamental interactions needed to make accurate predictions on realistic, out-of-distribution samples. The need for a large dataset is further emphasized using a dataset size sensitivity study. ...
One particularly pressing challenge is performing fast mechanical simulations along multiple length scales in heterogeneous materials. To this end, the reduced order method known as Self-Consistent Clustering Analysis (SCA) has been proposed as an effective means of striking a balance between accuracy and efficiency. Underpinning this is SCA's ability to decompose a domain into clusters in a preliminary offline stage (learning), efficiently reducing the problem's degrees of freedom. It has been shown to be remarkably accurate in predicting plasticity without significantly degrading accuracy compared to other methods, such as the finite element method. However, the offline stage requires a quantity known as the Cluster Interaction Tensor (CIT) to be computed, whose computational complexity scales quadratically with the number of clusters, thus causing a bottleneck in the method. Additionally, the CIT is recomputed during the online stage (prediction) in the recently proposed extension called adaptive Self-consistent Clustering Analysis (ASCA), which further stresses the need to speed up their computation.
To address this limitation, a data-driven surrogate model is proposed to compute the CIT efficiently. The behavior of the local CIT components is first analyzed, from which it is concluded that a surrogate model shall be developed to predict upper off-diagonal terms. This decision is made due to the bi-modal nature of certain components in the tensor and the quadratic scaling behavior of off-diagonal terms versus the linear scaling of diagonal ones. Following that, a sensitivity study shows how various magnitudes of noise affect the homogenized response's accuracy and convergence performance. Furthermore, it is shown that the solution accuracy and convergence behavior are degraded when the number of clusters is increased. With a proper understanding of the CIT's behavior and its function within SCA, the surrogate can be created.
The surrogate's feasibility is first shown using the ResNet-18 architecture, a CNN model derived from computer vision. It is demonstrated that ResNet-18 can make accurate predictions for a range of different microstructural parameters. This includes the number of clusters and samples in the dataset's distribution and out of distribution. Composite RVEs are used as out-of-distribution samples to test the robustness of the surrogate to realistic inputs. An attempt is made to improve the model's performance by training it on an unbalanced dataset, and although it improves the overall CIT prediction in specific regimes, the resulting stress-strain generalizability is degraded. Subsequently, a lighter version of ResNet-18, known as ResNet-lite, is tested and shown to give faster predictions than the baseline method. This, however, comes at a cost to the accuracy of the solution.
Additionally, deemed as a critical aspect of the study, the efficient generation of a large representative training dataset is discussed. A novel method for generating clustered microstructures efficiently using gradient noise is introduced. By leveraging datasets derived using this method, the surrogate can learn the fundamental interactions needed to make accurate predictions on realistic, out-of-distribution samples. The need for a large dataset is further emphasized using a dataset size sensitivity study.
In this study we present the development of a double cantilever beam (DCB) test according to ASTM D5528, setup to quantify the interlaminar fracture toughness (GI) of Ganoderma lucidum (G. lucidum) grown in between wood veneers. The data was evaluated using an analytical approach based on a decrease in the beams' compliance. The specimens were fabricated with the use of additive manufacturing, allowing precise control over the placement of the fungus and its provided nutrients. Its growth behaviour into the substrate was qualitatively assessed through optical microscopy and scanning electron microscopy (SEM), and its digestive ability on the surface by fourier-transform infrared spectroscopy (FTIR).
A mycelium-laden ink presented by Gantenbein et al. (2023) was reproduced with a 75% lower agar content to serve a stable source of mycelium on the DCB specimens [1]. A growth period between 3 and 4 weeks from the printed hydrogel was required for substantial mycelium-substrate binding, which stabilised after 4 weeks of growth. Furthermore, the provision of malt extract (ME) was required, but not needed to be higher than 5% of the ink's weight. The GI was in these conditions reported to be 1.83 J/m2 on hornbeam veneers, where a maximum value of 3.46 J/m2 was reached. Variable growth generated substantially different mechanical properties, which resulted in the lower GI of mycelium grown on beech and spruce samples, caused by the use of an older fungal inoculum of a different reference plate. A stronger binding on beech than spruce did suggest a more important role of the substrate chemistry than its density. The mycelium always showed cohesive failure, showing the low GI to not result from poor substrate adhesion, but rather from the mechanics of the hyphae network developed. Microscopy and FTIR evaluations showed the ability of G. lucidum to digest the hornbeam's lignin. The full depths of hornbeam and beech veneer substrates with 5 and 3 mm thickness were colonised, where vessel elements served as the main pathway for the hyphae.
This study was, to the best of our knowledge, the first to isolate the binding behaviour of a living mycelium in a mode-I loading condition. It thereby provides valuable new insights in the field of living MBC, and contributes to the further development of this advanced, eco-friendly, and living material. The setup can now be utilised to study the binding behaviour of different fungi on substrates of varying chemistry and porosity. Furthermore, aiming to elucidate the use of additive manufacturing in the composite production, this study opened up pathways into controlling the composite's properties in the future.
[1] Silvan Gantenbein et al. “Three-dimensional printing of mycelium hydrogels into living complex materials”. In: Nature Materials 22.1 (2023), pp. 128–134. ...
In this study we present the development of a double cantilever beam (DCB) test according to ASTM D5528, setup to quantify the interlaminar fracture toughness (GI) of Ganoderma lucidum (G. lucidum) grown in between wood veneers. The data was evaluated using an analytical approach based on a decrease in the beams' compliance. The specimens were fabricated with the use of additive manufacturing, allowing precise control over the placement of the fungus and its provided nutrients. Its growth behaviour into the substrate was qualitatively assessed through optical microscopy and scanning electron microscopy (SEM), and its digestive ability on the surface by fourier-transform infrared spectroscopy (FTIR).
A mycelium-laden ink presented by Gantenbein et al. (2023) was reproduced with a 75% lower agar content to serve a stable source of mycelium on the DCB specimens [1]. A growth period between 3 and 4 weeks from the printed hydrogel was required for substantial mycelium-substrate binding, which stabilised after 4 weeks of growth. Furthermore, the provision of malt extract (ME) was required, but not needed to be higher than 5% of the ink's weight. The GI was in these conditions reported to be 1.83 J/m2 on hornbeam veneers, where a maximum value of 3.46 J/m2 was reached. Variable growth generated substantially different mechanical properties, which resulted in the lower GI of mycelium grown on beech and spruce samples, caused by the use of an older fungal inoculum of a different reference plate. A stronger binding on beech than spruce did suggest a more important role of the substrate chemistry than its density. The mycelium always showed cohesive failure, showing the low GI to not result from poor substrate adhesion, but rather from the mechanics of the hyphae network developed. Microscopy and FTIR evaluations showed the ability of G. lucidum to digest the hornbeam's lignin. The full depths of hornbeam and beech veneer substrates with 5 and 3 mm thickness were colonised, where vessel elements served as the main pathway for the hyphae.
This study was, to the best of our knowledge, the first to isolate the binding behaviour of a living mycelium in a mode-I loading condition. It thereby provides valuable new insights in the field of living MBC, and contributes to the further development of this advanced, eco-friendly, and living material. The setup can now be utilised to study the binding behaviour of different fungi on substrates of varying chemistry and porosity. Furthermore, aiming to elucidate the use of additive manufacturing in the composite production, this study opened up pathways into controlling the composite's properties in the future.
[1] Silvan Gantenbein et al. “Three-dimensional printing of mycelium hydrogels into living complex materials”. In: Nature Materials 22.1 (2023), pp. 128–134.
evaluate the suitability of the Mandrel Peel test method for establishing a relationship between mandrel roller size and mixed mode fracture behavior. Comparative assessments were conducted between the multi-mandrel radii peel test and standardized tests, including DCB, ENF, and MMB tests. Experimental tests, fractography studies, and numerical validation were performed on UD GF/PP and UD CF/PPS composites.
The results show that the average fracture toughness values are slightly higher and more consistent for 2-ply peel arm specimens compared to 1-ply peel arm specimens. This is attributed to the microstructure (matrix and fiber distribution) at the interface and its influence on damage mechanism and fracture propagation behavior. The thickness of the ply also affects delamination propagation behavior and depends on the microstructure, with thicker plies exhibiting non-uniform fiber and matrix distribution. The experimental investigation reveals that the fracture toughness values increase as the mandrel
radius increases for UD GF/PP and UD CF/PPS composites with a 0|0 interface. The fracture toughness of CF/PPS peel specimens with a 0|90 interface shows limited variation
with respect to the mandrel radius. The relationship between mandrel radius and fracture toughness may not follow a linear trend, and it can depend on other factors such as material thickness, interface orientation, and fracture energy at pure loading modes. Comparative assessments between standardized tests and mandrel peel tests show similar trends in fracture toughness values with increasing mode mixture and mandrel roller radii.
Fractography analysis provides valuable insights into the fracture behavior of tested materials, and a correlation is identified between the failure modes observed in mixed-mode bending (MMB) tests and mandrel peel tests. The mandrel peel test enables establishing a relatively straight crack front during the delamination propagation, controlled by the mandrel’s kinematics, resulting in a more uniform distribution of strain energy across the specimen’s width, unlike standard tests.
The findings suggest that utilizing the multi-mandrel concept in assessing mixed-mode fracture toughness offers the possibility of extrapolating pure mode I and II fracture toughness values. This approach presents a viable tool for characterizing the fracture energy of composites with non-zero fiber-oriented interfaces that cannot be effectively assessed using classical tests. The results support the claim that mandrel roller size influences the degree of mode-mixity and suggests considering mandrel size when assessing mode-mixity in fracture phenomena.
Overall, this study provides valuable insights into the sensitivity of specimen configuration and testing parameters, the influence of mandrel roller size on mixed-mode fracture behavior, and the potential benefits of the mandrel peel test for delamination studies. By considering these findings, further advancements can be made in understanding and characterizing fracture properties in hybrid material systems.
Keywords: Delamination, fracture toughness, mixed-mode fracture, DCB, ENF,
MMB, Mandrel Peel test, thermoplastic composite, GF/PP, CF/PPS, Multi-
Mandrel Concept, peel arm, mandrel roller, mode mixity ...
evaluate the suitability of the Mandrel Peel test method for establishing a relationship between mandrel roller size and mixed mode fracture behavior. Comparative assessments were conducted between the multi-mandrel radii peel test and standardized tests, including DCB, ENF, and MMB tests. Experimental tests, fractography studies, and numerical validation were performed on UD GF/PP and UD CF/PPS composites.
The results show that the average fracture toughness values are slightly higher and more consistent for 2-ply peel arm specimens compared to 1-ply peel arm specimens. This is attributed to the microstructure (matrix and fiber distribution) at the interface and its influence on damage mechanism and fracture propagation behavior. The thickness of the ply also affects delamination propagation behavior and depends on the microstructure, with thicker plies exhibiting non-uniform fiber and matrix distribution. The experimental investigation reveals that the fracture toughness values increase as the mandrel
radius increases for UD GF/PP and UD CF/PPS composites with a 0|0 interface. The fracture toughness of CF/PPS peel specimens with a 0|90 interface shows limited variation
with respect to the mandrel radius. The relationship between mandrel radius and fracture toughness may not follow a linear trend, and it can depend on other factors such as material thickness, interface orientation, and fracture energy at pure loading modes. Comparative assessments between standardized tests and mandrel peel tests show similar trends in fracture toughness values with increasing mode mixture and mandrel roller radii.
Fractography analysis provides valuable insights into the fracture behavior of tested materials, and a correlation is identified between the failure modes observed in mixed-mode bending (MMB) tests and mandrel peel tests. The mandrel peel test enables establishing a relatively straight crack front during the delamination propagation, controlled by the mandrel’s kinematics, resulting in a more uniform distribution of strain energy across the specimen’s width, unlike standard tests.
The findings suggest that utilizing the multi-mandrel concept in assessing mixed-mode fracture toughness offers the possibility of extrapolating pure mode I and II fracture toughness values. This approach presents a viable tool for characterizing the fracture energy of composites with non-zero fiber-oriented interfaces that cannot be effectively assessed using classical tests. The results support the claim that mandrel roller size influences the degree of mode-mixity and suggests considering mandrel size when assessing mode-mixity in fracture phenomena.
Overall, this study provides valuable insights into the sensitivity of specimen configuration and testing parameters, the influence of mandrel roller size on mixed-mode fracture behavior, and the potential benefits of the mandrel peel test for delamination studies. By considering these findings, further advancements can be made in understanding and characterizing fracture properties in hybrid material systems.
Keywords: Delamination, fracture toughness, mixed-mode fracture, DCB, ENF,
MMB, Mandrel Peel test, thermoplastic composite, GF/PP, CF/PPS, Multi-
Mandrel Concept, peel arm, mandrel roller, mode mixity
Given the complexity of the models, this thesis proposes the use of Bayesian optimization to facilitate the material parameter calibration when provided with the experimental data. A two-step procedure is proposed where first the models are calibrated for yielding, and then for post yielding behavior (strain softening and orientational hardening).
The models are assessed considering different experimental tests, including standardized specimens with different radius of curvature. A simple modification is suggested to capture the strain hardening response at large deformations accurately. This work concludes that the model developed by Mikhalaf et al. is capable of accurately reproducing the experimental results obtained in the validation experiments of PCR-PP where as the modified Anand model is capable of accurately reproducing the experimental results of PCR-PE. ...
Given the complexity of the models, this thesis proposes the use of Bayesian optimization to facilitate the material parameter calibration when provided with the experimental data. A two-step procedure is proposed where first the models are calibrated for yielding, and then for post yielding behavior (strain softening and orientational hardening).
The models are assessed considering different experimental tests, including standardized specimens with different radius of curvature. A simple modification is suggested to capture the strain hardening response at large deformations accurately. This work concludes that the model developed by Mikhalaf et al. is capable of accurately reproducing the experimental results obtained in the validation experiments of PCR-PP where as the modified Anand model is capable of accurately reproducing the experimental results of PCR-PE.
However, the manufacturing and testing of bio-based composites is time and resource expensive. Moreover, exploring all natural fillers and fibres ratios is not feasible experimentally. Optimization and analytical models are two potential approaches that accelerate the search towards an optimal bio-based composite recipe when combined with bio-based materials research. A data-scarce Bayesian optimization model was already developed to research the composition of bio-based composites. The proof-of-concept program adjusts the natural materials’ weight ratios to optimize toward user-defined mechanical properties. The objective of this study is to experimentally investigate if the Bayesian Optimization model works by varying the objective functions and adapting the model according to the clients’ needs. By exploiting the machine learning model at an initial stage, the purpose is to test how the model reacts to different objective functions defined at high weight values and observe if the model can generate optimized recipes with better mechanical properties than the defined training set. For this study, four different fillers (calcite, lignocellulosic filler 1, lignocellulosic filler 2, waste-based filler) and two different fibres (flax, bamboo) are used, with calcite as the reference filler. A primary goal to be achieved by NPSP is to reduce or eliminate calcite as the primary filler due to its high density and brittle nature. Promising results have been obtained within two iterations of using the model for the different filler/fibre systems used.
Additionally, the thesis also investigates the rules of mixing for multi-component systems to develop analytical models that predict the mechanical properties of the composite. The Lewis-Nielsen model and the Cox -Krenchel theory have been used to compare theoretical values with experimental data points. The initial binary phase curve fitting followed by applying cascading to obtain ternary and quaternary phase mechanical properties provides approximate results for most recipes made. Finally, recommendations to improve both models have been covered, and a potential to combine both approaches has been shown. ...
However, the manufacturing and testing of bio-based composites is time and resource expensive. Moreover, exploring all natural fillers and fibres ratios is not feasible experimentally. Optimization and analytical models are two potential approaches that accelerate the search towards an optimal bio-based composite recipe when combined with bio-based materials research. A data-scarce Bayesian optimization model was already developed to research the composition of bio-based composites. The proof-of-concept program adjusts the natural materials’ weight ratios to optimize toward user-defined mechanical properties. The objective of this study is to experimentally investigate if the Bayesian Optimization model works by varying the objective functions and adapting the model according to the clients’ needs. By exploiting the machine learning model at an initial stage, the purpose is to test how the model reacts to different objective functions defined at high weight values and observe if the model can generate optimized recipes with better mechanical properties than the defined training set. For this study, four different fillers (calcite, lignocellulosic filler 1, lignocellulosic filler 2, waste-based filler) and two different fibres (flax, bamboo) are used, with calcite as the reference filler. A primary goal to be achieved by NPSP is to reduce or eliminate calcite as the primary filler due to its high density and brittle nature. Promising results have been obtained within two iterations of using the model for the different filler/fibre systems used.
Additionally, the thesis also investigates the rules of mixing for multi-component systems to develop analytical models that predict the mechanical properties of the composite. The Lewis-Nielsen model and the Cox -Krenchel theory have been used to compare theoretical values with experimental data points. The initial binary phase curve fitting followed by applying cascading to obtain ternary and quaternary phase mechanical properties provides approximate results for most recipes made. Finally, recommendations to improve both models have been covered, and a potential to combine both approaches has been shown.
Finite Element Model For Interfaces In Compatibilized Polymer Blends
A Comparative Study on the Mixed-Mode Response of Cohesive Zone Models Implemented With Small and Large Displacement Assumptions
A preliminary literature review showed that existing formulations for the large
deformation account for the nonlinearity by adjusting the assumptions. For example, Van den Bosch et al. (2007) proposed redefining the local basis at each integration point. In contrast, Reinoso and Paggi (2014) argued that this did not account for geometric nonlinearity and proposed including the first derivative of rotation vector in the finite element equation. However, the mixed-mode responses of the models were not characterized and validated thoroughly. Therefore, we studied the response from standardized mixed-mode tests to compare the large displacement formulation with the commonly used small-displacement formulation of the cohesive zone model.
The standardized tests used by Moreira et al. (2020) for characterizing the mixed-mode behavior of ductile interfaces inspired the tests used in this study. When implemented with the BK criteria, the mode partitioning method used by Moreira et al. (2020) results in a wider spread of the mean predicted mode ratio and the mean predicted fracture toughness. However, the corresponding mode ratio predictions are similar when the predicted fracture toughness is close to expected. Therefore, while the power-law is better for implementing the mode partitioning method, we can use the predictions from the mode partitioning method implemented with the power-law to find the BK parameter.
Further, simulating the mixed-mode fracture tests with properties presented by
Moreira et al. (2020) showed that bulk materials with high modulus or stiffness, such as carbon fiber reinforced plastics, do not undergo nonlinear deformation to require the large deformation formulation. However, for bulk materials with lower modulus or stiffness, the responses of the two formulations in question are different. Additionally, for a given load case, a cohesive zone with anisotropic fracture properties experiences a different mode ratio when implemented with the large displacement formulation than the small displacement formulation. Moreover, more significant influence of the stronger mode on the load case results in greater difference between the mode ratio experienced at the interface. Nevertheless, the large displacement formulation is also applicable for stronger mode-II interfaces. However, a further investigation involving physical experiments is required to compare the response of the two formulations to the behavior of real material systems. ...
A preliminary literature review showed that existing formulations for the large
deformation account for the nonlinearity by adjusting the assumptions. For example, Van den Bosch et al. (2007) proposed redefining the local basis at each integration point. In contrast, Reinoso and Paggi (2014) argued that this did not account for geometric nonlinearity and proposed including the first derivative of rotation vector in the finite element equation. However, the mixed-mode responses of the models were not characterized and validated thoroughly. Therefore, we studied the response from standardized mixed-mode tests to compare the large displacement formulation with the commonly used small-displacement formulation of the cohesive zone model.
The standardized tests used by Moreira et al. (2020) for characterizing the mixed-mode behavior of ductile interfaces inspired the tests used in this study. When implemented with the BK criteria, the mode partitioning method used by Moreira et al. (2020) results in a wider spread of the mean predicted mode ratio and the mean predicted fracture toughness. However, the corresponding mode ratio predictions are similar when the predicted fracture toughness is close to expected. Therefore, while the power-law is better for implementing the mode partitioning method, we can use the predictions from the mode partitioning method implemented with the power-law to find the BK parameter.
Further, simulating the mixed-mode fracture tests with properties presented by
Moreira et al. (2020) showed that bulk materials with high modulus or stiffness, such as carbon fiber reinforced plastics, do not undergo nonlinear deformation to require the large deformation formulation. However, for bulk materials with lower modulus or stiffness, the responses of the two formulations in question are different. Additionally, for a given load case, a cohesive zone with anisotropic fracture properties experiences a different mode ratio when implemented with the large displacement formulation than the small displacement formulation. Moreover, more significant influence of the stronger mode on the load case results in greater difference between the mode ratio experienced at the interface. Nevertheless, the large displacement formulation is also applicable for stronger mode-II interfaces. However, a further investigation involving physical experiments is required to compare the response of the two formulations to the behavior of real material systems.
Conventional Topology Optimization (TO) enables the inverse design of nanophotonic structures by specifying the objective and constraints without a predefined topological concept. Yet, extreme scenarios such as the design of a lightsail pose challenges that require new solutions. Here, a convolutional neural network (CNN) based TO methodology is extended to optimize a two-dimensional photonic crystal used to design a lightsail that aims to reach the nearest star (Alpha Centauri) within 20 years by achieving 20% of the speed of light. The CNN-TO performance is compared to a more conventional method of moving asymptotes (MMA) based TO by optimizing a photonic crystal unit-cell for the 2016 Starshot Initiative parameters. The CNN-TO requires up to 40% fewer iterations than MMA-TO to reach better performance under different operational conditions. The generated design turned out to be easy to fabricate, allowing them to be produced with optical lithography. Additionally, a study regarding the design challenges of the lightsail has been performed, which resulted in an optimization considering the functionality of the sail. Additionally, the study showed the sensitivity of the resulting design to varying objectives and materials. Therefore, underlining the necessity of considering multiple operating conditions (e.g. laser alignment and cooling) within the design process. ...
Conventional Topology Optimization (TO) enables the inverse design of nanophotonic structures by specifying the objective and constraints without a predefined topological concept. Yet, extreme scenarios such as the design of a lightsail pose challenges that require new solutions. Here, a convolutional neural network (CNN) based TO methodology is extended to optimize a two-dimensional photonic crystal used to design a lightsail that aims to reach the nearest star (Alpha Centauri) within 20 years by achieving 20% of the speed of light. The CNN-TO performance is compared to a more conventional method of moving asymptotes (MMA) based TO by optimizing a photonic crystal unit-cell for the 2016 Starshot Initiative parameters. The CNN-TO requires up to 40% fewer iterations than MMA-TO to reach better performance under different operational conditions. The generated design turned out to be easy to fabricate, allowing them to be produced with optical lithography. Additionally, a study regarding the design challenges of the lightsail has been performed, which resulted in an optimization considering the functionality of the sail. Additionally, the study showed the sensitivity of the resulting design to varying objectives and materials. Therefore, underlining the necessity of considering multiple operating conditions (e.g. laser alignment and cooling) within the design process.
With the growing rise of LFTs, the research on their mechanical properties and their processing has grown as well. Injection molding method has been one of the most widely applied production method for LFTs processing. Research has shown that the mechanical edge offered by the LFT products obtained from injection molding is dependent on the lengths of the fibers in the final product. This makes it important to understand the breakage of fibers during processing.
This work addresses the breakage of fiber in injection molding by conducting a thorough review of the industrial, experimental and theoretical research done in the field. Following this, simulation approach has been undertaken to understand the fiber breakage in geometries which represent slightly complex shapes as compared to the conventionally used shapes. Based on the theoretical research, the state-of-the-art models have been reviewed and compared in their ability to produce reliable fiber breakage results.
The results showed the influence of rheology and geometry on fiber breakage in simulations, where shear rates led to higher fiber breakage and increasing viscosity led to a slight reduction in breakage. Further, the simulation study provided inconsistent results with variation in geometry, and a need for further fine tuning of simulation parameters was observed. The theoretical models applied in the study gave reliable results in terms of the trends of the fiber breakage, with a novel model, called Bechara model, showing acceptable and more time efficient results, in comparison with the currently applied commercial model, Phelps model. ...
With the growing rise of LFTs, the research on their mechanical properties and their processing has grown as well. Injection molding method has been one of the most widely applied production method for LFTs processing. Research has shown that the mechanical edge offered by the LFT products obtained from injection molding is dependent on the lengths of the fibers in the final product. This makes it important to understand the breakage of fibers during processing.
This work addresses the breakage of fiber in injection molding by conducting a thorough review of the industrial, experimental and theoretical research done in the field. Following this, simulation approach has been undertaken to understand the fiber breakage in geometries which represent slightly complex shapes as compared to the conventionally used shapes. Based on the theoretical research, the state-of-the-art models have been reviewed and compared in their ability to produce reliable fiber breakage results.
The results showed the influence of rheology and geometry on fiber breakage in simulations, where shear rates led to higher fiber breakage and increasing viscosity led to a slight reduction in breakage. Further, the simulation study provided inconsistent results with variation in geometry, and a need for further fine tuning of simulation parameters was observed. The theoretical models applied in the study gave reliable results in terms of the trends of the fiber breakage, with a novel model, called Bechara model, showing acceptable and more time efficient results, in comparison with the currently applied commercial model, Phelps model.
Inter-ply friction in unidirectional fiber-reinforced thermoplastics
With a focus on the influence of temperature
In this research, an extensive friction characterization with UD C/LM-PAEK is conducted at temperatures ranging from 300 to 365 ◦C. The neat matrix material has been studied with DSC and rheometry experiments. In general, a peak response can be seen during start-up in a friction characterization experiment. This peak, or overshoot, progresses towards a steady state friction response after a slip distance of several mm. Reducing the temperature showed similar effects to increasing the sliding velocity in a ply-ply slip system. The peak during start-up increases in magnitude while the steady state response remains approximately constant. Indications of flow induced crystallisation have been observed during friction characterization around the melting point of the material. The timetemperature-superposition principle has been applied to experimental friction data. This enabled to predict the duration of the transition of peak friction response towards a steady state. Several modelling efforts have been compared to the experimental data. The accuracy of the model predictions is similar between 315 and 365 ◦C. Influences of flow induced crystallisation impede the reliability of the specific models around and below the melting point.
The research lead to useful insights in the friction behaviour at relatively low temperatures. Further research is required on the field of flow induced crystallisation for a better understanding of its role in the friction response. Further study with other materials is needed to validate the application of the time-temperature-superposition principle to predict the speed of the transition of peak friction response towards steady state.
...
In this research, an extensive friction characterization with UD C/LM-PAEK is conducted at temperatures ranging from 300 to 365 ◦C. The neat matrix material has been studied with DSC and rheometry experiments. In general, a peak response can be seen during start-up in a friction characterization experiment. This peak, or overshoot, progresses towards a steady state friction response after a slip distance of several mm. Reducing the temperature showed similar effects to increasing the sliding velocity in a ply-ply slip system. The peak during start-up increases in magnitude while the steady state response remains approximately constant. Indications of flow induced crystallisation have been observed during friction characterization around the melting point of the material. The timetemperature-superposition principle has been applied to experimental friction data. This enabled to predict the duration of the transition of peak friction response towards a steady state. Several modelling efforts have been compared to the experimental data. The accuracy of the model predictions is similar between 315 and 365 ◦C. Influences of flow induced crystallisation impede the reliability of the specific models around and below the melting point.
The research lead to useful insights in the friction behaviour at relatively low temperatures. Further research is required on the field of flow induced crystallisation for a better understanding of its role in the friction response. Further study with other materials is needed to validate the application of the time-temperature-superposition principle to predict the speed of the transition of peak friction response towards steady state.
In order to accomplish this, a new kind of suspended microchannel resonator is introduced. The determination of these designs is strictly FEM based. The new resonator design, which is a doubly clamped beam, is made from pre-stressed silicon nitride which enables high Q-factors caused by an effect known as dissipation dilution. Dissipation dilution means diluting the energy losses of the system by increasing the stored energy which is increased by the initial stress in the silicon nitride. To increase this effect, the resonator is tapered towards the center. This is called strain engineering. Silicon nitride has been used in suspended microchannel resonators before but it did not result in higher Q-factors. Possibly due to clamping losses. The designs presented here offer a solution to that in the form of soft-clamping. This reduces the curvature near the boundaries to a minimum which means that the clamping losses are also reduced or eliminated. The combined effect of these features results in very high Q-factors as has already been reported for nanomechanical resonators. Through machine learning optimization it is possible to achieve 6E12 Hz in Qf product required for quantum mechanical experiments at room temperature and more than one order of magnitude improvement in mass sensitivity.
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In order to accomplish this, a new kind of suspended microchannel resonator is introduced. The determination of these designs is strictly FEM based. The new resonator design, which is a doubly clamped beam, is made from pre-stressed silicon nitride which enables high Q-factors caused by an effect known as dissipation dilution. Dissipation dilution means diluting the energy losses of the system by increasing the stored energy which is increased by the initial stress in the silicon nitride. To increase this effect, the resonator is tapered towards the center. This is called strain engineering. Silicon nitride has been used in suspended microchannel resonators before but it did not result in higher Q-factors. Possibly due to clamping losses. The designs presented here offer a solution to that in the form of soft-clamping. This reduces the curvature near the boundaries to a minimum which means that the clamping losses are also reduced or eliminated. The combined effect of these features results in very high Q-factors as has already been reported for nanomechanical resonators. Through machine learning optimization it is possible to achieve 6E12 Hz in Qf product required for quantum mechanical experiments at room temperature and more than one order of magnitude improvement in mass sensitivity.
A data-driven heuristic decision strategy for data-scarce optimization
With an application towards bio-based composites
graph for decades. The unknown material density is distributed within a domain,
a computational analysis predicts the response of that design and its derivative
with respect to the unknown, and this information is used by a chosen gradient
based optimization algorithm to find the next design iteration until it reaches an
optimum (local or global). Recently, however, a counterintuitive strategy was pro
posed which augments the computational graph by including a neural network in
between the response prediction (computational analysis) and the generation of a
new design (image). This shifts the optimization problem from its original space
to the weight space of the neural network. Yet, this indirect optimization process was shown elsewhere to outperform conventional topology optimization for a
large number of structural compliance problems – at least when choosing a particular convolutional neural network (part of a U-Net) and a particular optimizer
(L-BFGS). This investigation provides quantitative and qualitative arguments that
justify why these choices are successful, concluding that the line-search component of L-BFGS is key to traversing the reparameterized objective (loss) landscape
and quickly reaching good solutions in “flat” regions of the landscape. Importantly,
these topology optimization problems are not stochastic which make them different
from the majority of conventional deep learning applications, favoring the use of
line-search. Similarly, although to lesser extent, the approximation of the Hessian
provided by L-BFGS helps moving more effectively within the flat regions by rescaling the gradients, the quality of the approximation is less relevant. Together with
the deep image prior effect associated to deep learning, these arguments explain
the early success of the neural reparameterization strategy in topology optimization, in spite of the non-convex objective landscape distortion that they introduce
even for landscapes that were originally convex.
...
graph for decades. The unknown material density is distributed within a domain,
a computational analysis predicts the response of that design and its derivative
with respect to the unknown, and this information is used by a chosen gradient
based optimization algorithm to find the next design iteration until it reaches an
optimum (local or global). Recently, however, a counterintuitive strategy was pro
posed which augments the computational graph by including a neural network in
between the response prediction (computational analysis) and the generation of a
new design (image). This shifts the optimization problem from its original space
to the weight space of the neural network. Yet, this indirect optimization process was shown elsewhere to outperform conventional topology optimization for a
large number of structural compliance problems – at least when choosing a particular convolutional neural network (part of a U-Net) and a particular optimizer
(L-BFGS). This investigation provides quantitative and qualitative arguments that
justify why these choices are successful, concluding that the line-search component of L-BFGS is key to traversing the reparameterized objective (loss) landscape
and quickly reaching good solutions in “flat” regions of the landscape. Importantly,
these topology optimization problems are not stochastic which make them different
from the majority of conventional deep learning applications, favoring the use of
line-search. Similarly, although to lesser extent, the approximation of the Hessian
provided by L-BFGS helps moving more effectively within the flat regions by rescaling the gradients, the quality of the approximation is less relevant. Together with
the deep image prior effect associated to deep learning, these arguments explain
the early success of the neural reparameterization strategy in topology optimization, in spite of the non-convex objective landscape distortion that they introduce
even for landscapes that were originally convex.