W. Lindqwister
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There is a strong link between a material’s microstructural features and its macroscopic physical properties. However, heterogeneities in real-world rock microstructures often result in strong cross-correlations between the microscopic features, making it difficult to evaluate the influence of individual characteristics. Minkowski functionals (MFs), a set of measures derived from integral geometry, have recently gained attention as a robust way to quantify microstructural features. Recent datasets include the computed MFs to study their influence, but typically lack variation in individual MFs and offer limited ability to isolate specific contributions. Therefore, we present a curated, open-source dataset1 of microstructures, including random packings with varying grain shapes and cemented configurations featuring complex void networks. For each microstructure, the corresponding MFs are computed alongside the results of Stokes flow simulations. The controlled variation in particle shape and packing fraction enables a broader range of MFs, allowing for targeted analysis of how specific microstructural features influence macroscopic properties. This dataset supports the development and validation of structure-property models.
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There is a strong link between a material’s microstructural features and its macroscopic physical properties. However, heterogeneities in real-world rock microstructures often result in strong cross-correlations between the microscopic features, making it difficult to evaluate the influence of individual characteristics. Minkowski functionals (MFs), a set of measures derived from integral geometry, have recently gained attention as a robust way to quantify microstructural features. Recent datasets include the computed MFs to study their influence, but typically lack variation in individual MFs and offer limited ability to isolate specific contributions. Therefore, we present a curated, open-source dataset1 of microstructures, including random packings with varying grain shapes and cemented configurations featuring complex void networks. For each microstructure, the corresponding MFs are computed alongside the results of Stokes flow simulations. The controlled variation in particle shape and packing fraction enables a broader range of MFs, allowing for targeted analysis of how specific microstructural features influence macroscopic properties. This dataset supports the development and validation of structure-property models.
Journal article
(2026)
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Winston Lindqwister, Mrinal Chaudhury, Sarah Schyck, Iuri Rocha, Kunal Masania, Martin Lesueur
As we move towards more sustainable and resilient materials, new opportunities for harnessing the next generation of biological materials will arise. Materials composed of living organisms have great potential in fulfilling this role as a self-healing, lightweight and sustainable structural material. Recent advances in 3D-printing using fungi-inoculated hydrogels opens the potential of additive manufacturing with fungi into optimized shapes. However, while this technique of 3D-printing fungi has great potential in a wide range of engineering applications, computational models do not yet exist to precisely engineer the strength of structures made from this material. Here we create a computational modeling scheme for 3D-printed mycelium structures, linking the growth of fungi to stiffness. We first model the growth of fungi through a diffusion model. We then convert the resultant density values into local stiffness, creating a computational representation of the varying elemental stiffness as a function of local mycelial density. We implement two Bayesian optimization-based topology optimization schemes to maximize the strength of cuboid 3D-printed structures while minimizing the input material cost. One maximizes the material specific stiffness while the other applies a constrained scheme for identifying a minimized mass for a target design stiffness. Both show a distinct tradeoff in print mass to stiffness, with results validated experimentally. These new insights provide important next steps in the effective harnessing of this class of emergent material, as well as its larger adoption for engineering applications.
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As we move towards more sustainable and resilient materials, new opportunities for harnessing the next generation of biological materials will arise. Materials composed of living organisms have great potential in fulfilling this role as a self-healing, lightweight and sustainable structural material. Recent advances in 3D-printing using fungi-inoculated hydrogels opens the potential of additive manufacturing with fungi into optimized shapes. However, while this technique of 3D-printing fungi has great potential in a wide range of engineering applications, computational models do not yet exist to precisely engineer the strength of structures made from this material. Here we create a computational modeling scheme for 3D-printed mycelium structures, linking the growth of fungi to stiffness. We first model the growth of fungi through a diffusion model. We then convert the resultant density values into local stiffness, creating a computational representation of the varying elemental stiffness as a function of local mycelial density. We implement two Bayesian optimization-based topology optimization schemes to maximize the strength of cuboid 3D-printed structures while minimizing the input material cost. One maximizes the material specific stiffness while the other applies a constrained scheme for identifying a minimized mass for a target design stiffness. Both show a distinct tradeoff in print mass to stiffness, with results validated experimentally. These new insights provide important next steps in the effective harnessing of this class of emergent material, as well as its larger adoption for engineering applications.
Porous media, ranging from bones to concrete and from batteries to architected lattices, pose difficult challenges in fully harnessing for engineering applications due to their complex and variable structures. Accurate and rapid assessment of their mechanical behavior is both challenging and essential, and traditional methods such as destructive testing and finite element analysis can be costly, computationally demanding, and time consuming. Machine learning (ML) offers a promising alternative for predicting mechanical behavior by leveraging data-driven correlations. However, with such structural complexity and diverse morphology among porous media, the question becomes how to effectively characterize these materials to provide robust feature spaces for ML that are descriptive, succinct, and easily interpreted. Here, we developed an automated methodology to determine porous material strength. This method uses scalar morphological descriptors, known as Minkowski functionals, to describe the porous space. From there, we conduct uniaxial compression experiments for generating material stress-strain curves, and then train an ML model to predict the curves using said morphological descriptors. This framework seeks to expedite the analysis and prediction of stress-strain behavior in porous materials and lay the groundwork for future models that can predict mechanical behaviors beyond compression.
...
Porous media, ranging from bones to concrete and from batteries to architected lattices, pose difficult challenges in fully harnessing for engineering applications due to their complex and variable structures. Accurate and rapid assessment of their mechanical behavior is both challenging and essential, and traditional methods such as destructive testing and finite element analysis can be costly, computationally demanding, and time consuming. Machine learning (ML) offers a promising alternative for predicting mechanical behavior by leveraging data-driven correlations. However, with such structural complexity and diverse morphology among porous media, the question becomes how to effectively characterize these materials to provide robust feature spaces for ML that are descriptive, succinct, and easily interpreted. Here, we developed an automated methodology to determine porous material strength. This method uses scalar morphological descriptors, known as Minkowski functionals, to describe the porous space. From there, we conduct uniaxial compression experiments for generating material stress-strain curves, and then train an ML model to predict the curves using said morphological descriptors. This framework seeks to expedite the analysis and prediction of stress-strain behavior in porous materials and lay the groundwork for future models that can predict mechanical behaviors beyond compression.
Through rocks and concrete, batteries, and bone, porous media represent a wide class of materials whose chemical makeup and reactivity directly impact their behavior at multiple scales. While various theoretical and computational models have been implemented to capture the chemical behavior of these systems, none have investigated how the very geometry of porous media, the structures that make these materials porous and define the interfaces between solids and fluids, affects these behaviors. Through this work, we explored Minkowski functionals-geometric morphometers that describe the spatial and topological features of a convex space-to investigate how microstructural morphology affects systemic chemical performance. Using a novel asynchronous cellular automaton known as a surface chemical reaction network (CRN) to model chemical behavior, linkages were found between Minkowski functionals and equilibrium constant, as well as properties related to the dynamics of the microstructure’s reaction quotient. These quantities, in turn, give insight into how morphology affects bulk porous media properties, such as Gibbs’ free energy.
...
Through rocks and concrete, batteries, and bone, porous media represent a wide class of materials whose chemical makeup and reactivity directly impact their behavior at multiple scales. While various theoretical and computational models have been implemented to capture the chemical behavior of these systems, none have investigated how the very geometry of porous media, the structures that make these materials porous and define the interfaces between solids and fluids, affects these behaviors. Through this work, we explored Minkowski functionals-geometric morphometers that describe the spatial and topological features of a convex space-to investigate how microstructural morphology affects systemic chemical performance. Using a novel asynchronous cellular automaton known as a surface chemical reaction network (CRN) to model chemical behavior, linkages were found between Minkowski functionals and equilibrium constant, as well as properties related to the dynamics of the microstructure’s reaction quotient. These quantities, in turn, give insight into how morphology affects bulk porous media properties, such as Gibbs’ free energy.
Learning latent hardening
Enhancing deep learning with domain knowledge for material inverse problems
Advancements in deep learning (DL) and machine learning (ML) have improved the ability to model complex, nonlinear relationships, such as those encountered in complex material inverse problems. However, the effectiveness of these methods often depends on large datasets, which are not always available. In this study, the incorporation of domain-specific knowledge of the mechanical behaviour of material microstructures is investigated to evaluate the effect on the predictive performance of the models in data-scarce scenarios. To overcome data limitations, a two-step framework, learning latent hardening (LLH), is proposed. In the first step of LLH, a deep neural network (DNN) is employed to reconstruct full stress–strain curves from randomly selected portions of the stress–strain curves to capture the latent mechanical response of a material based on key microstructural features. In the second step of LLH, the results of the reconstructed stress–strain curves are leveraged to predict key microstructural features of porous materials. The performance of six DL and/or ML models trained with and without domain knowledge are compared: convolutional neural networks (CNNs), DNN, extreme gradient boosting (XGBoost), K-nearest neighbours (KNN), long short-term memory (LSTM) and random forest (RF). The results from the models with domain-specific information consistently achieved higher 𝑅2 values compared to models without prior knowledge. When the models did not include domain knowledge, meaningful patterns in the model result, such as the link between stress–strain behaviour and underlying microstructural changes not being recognized, while those enhanced with domain knowledge insights showed better feature selection, in which they identified key stress–strain characteristics that are most relevant for predicting microstructure. These findings reveal the critical role domain-specific knowledge can provide in guiding DL models, further highlighting the need to combine domain expertise with data-driven approaches to achieve reliable and accurate outcomes in materials science and related fields.
...
Advancements in deep learning (DL) and machine learning (ML) have improved the ability to model complex, nonlinear relationships, such as those encountered in complex material inverse problems. However, the effectiveness of these methods often depends on large datasets, which are not always available. In this study, the incorporation of domain-specific knowledge of the mechanical behaviour of material microstructures is investigated to evaluate the effect on the predictive performance of the models in data-scarce scenarios. To overcome data limitations, a two-step framework, learning latent hardening (LLH), is proposed. In the first step of LLH, a deep neural network (DNN) is employed to reconstruct full stress–strain curves from randomly selected portions of the stress–strain curves to capture the latent mechanical response of a material based on key microstructural features. In the second step of LLH, the results of the reconstructed stress–strain curves are leveraged to predict key microstructural features of porous materials. The performance of six DL and/or ML models trained with and without domain knowledge are compared: convolutional neural networks (CNNs), DNN, extreme gradient boosting (XGBoost), K-nearest neighbours (KNN), long short-term memory (LSTM) and random forest (RF). The results from the models with domain-specific information consistently achieved higher 𝑅2 values compared to models without prior knowledge. When the models did not include domain knowledge, meaningful patterns in the model result, such as the link between stress–strain behaviour and underlying microstructural changes not being recognized, while those enhanced with domain knowledge insights showed better feature selection, in which they identified key stress–strain characteristics that are most relevant for predicting microstructure. These findings reveal the critical role domain-specific knowledge can provide in guiding DL models, further highlighting the need to combine domain expertise with data-driven approaches to achieve reliable and accurate outcomes in materials science and related fields.