In this work, a new damage model for cohesive fracture is presented. The concept of damage driving mechanism is introduced, from which the damage evolution law is derived. Special attention is paid to non pure mode-I and mode-II fracture modes, such as mixed-mode fracture and mode-II fracture under compression. Conversely to the previous traction-based damage model (Alfaiate et al. 2023), where the damage variables are derived from uniaxial tensile and shear relationships, the damage variables are now obtained explicitly from reference traction-jump displacement relationships, leading to an integration of fracture mechanics concepts with a damage mechanics approach. In this way, it is possible to explicitly control the dissipation of energy. The model is aimed at the simulation of the behaviour of reinforced concrete structures under corrosion. Corrosion affects i) cracking, which is modelled with a discrete crack approach, ii) bond-slip degradation between steel and concrete, iii) the reduction of the sane cross section of the reinforcement steel and iv) spalling of the concrete cover. In this work some illustrative examples of the performance of the model are shown. In part II, examples of reinforced concrete structures with and without corrosion are presented.

In the present work, macro-mechanical modelling of reinforced concrete structures under corrosion is performed. A traction based damage model is adopted. A discrete crack approach is used to model the fracture behaviour of concrete. The bond-slip relation between reinforcement steel and concrete is continuously evolving under corrosion, as a function of corrosion level and stress state. This is a non trivial issue, which is dealt with taking into account a total approach. Other corrosion aspects considered in this work are the reduction of the sane cross section of the reinforcement steel as well as spalling of the concrete cover. Bending tests are performed to evaluate the influence of corrosion at structural level, namely the increase of deformation as well as the decrease of the strength of the structure, leading to premature failure. Furthermore, stirrup confinement, in association with spalling, and slippage of the anchorage zone are analyzed.

Materials engineered with an internal architecture in order to achieve unusual properties, so-called mechanical metamaterials, are a promising candidate in the ongoing quest for lightweight impact mitigation. During impact events, these materials are subject to high strain rates, and the forces occurring due to the deceleration of the impactor are transmitted in a non-uniform way. The prevailing research in the field of impact mitigation focuses largely on the global effects of architected materials, with less attention being paid to the internal mechanisms of these structured materials. While there have been recent studies on the distribution of forces throughout an impact event, less research is devoted to the transmission of forces and the distribution of energy dissipation. The objective of this study is to examine the transition from static deformation patterns to dynamic phenomena for different types and sizes of microstructure, and to understand both the force transmission through the patch and the energetic distributions in different strain rate regimes. To enable this investigation discretized — geometrically as well as materially — nonlinear Timoshenko-Ehrenfest beams are used in implicit and explicit finite element schemes. The transmitted force levels and energy dissipation are investigated for two auxetic architectures (one for each mechanism resulting in a negative Poisson's ratio) and one non-auxetic architecture. The dynamic force levels transmitted to the back face exhibit an initial peak of a similar magnitude for all investigated strain rates and stabilize to the static stress plateau for each architecture. While the global amount of potential energy remains largely unchanged for all investigated rates, the amount of dissipation and kinetic energy demonstrates a non-linear increase from static deformation to slow and high rate deformation. The phenomena observed in different architectures are highlighted, and the differences are explained and related back to the configurations of the lattices. Notably, the prevalent notion in literature asserting the superiority of negative Poisson's ratio materials for impact mitigation applications is not replicated in this study.

A three-dimensional mesoscopic viscoplasticity model for simulating rate-dependent plasticity and creep in unidirectional thermoplastic composites is presented. The constitutive model is a transversely isotropic extension of an isotropic finite strain viscoplasticity model for neat polymers. Rate-dependent plasticity and creep are described by a non-Newtonian flow rule where the viscosity of the material depends on an equivalent stress measure through an Eyring-type relation. In the present formulation, transverse isotropy is incorporated by defining the equivalent stress measure and flow rule as functions of transversely isotropic stress invariants. In addition, the Eyring-type viscosity function is extended with anisotropic pressure dependence. As a result of the formulation, plastic flow in fiber direction is effectively excluded and pressure dependence of the polymer matrix is accounted for. The re-orientation of the transversely isotropic plane during plastic deformations is incorporated in the constitutive equations, allowing for an accurate large deformation response. The formulation is fully implicit and a consistent linearization of the algorithmic constitutive equations is performed to derive the consistent tangent modulus. The performance of the mesoscopic constitutive model is assessed through a comparison with a micromechanical model for carbon/PEEK, with the original isotropic viscoplastic version for the polymer matrix and with hyperelastic fibers. The micromodel is first used to determine the material parameters of the mesoscale model with a few stress–strain curves. It is demonstrated that the mesoscale model gives a similar response to the micromodel under various loading conditions. Finally, the mesoscale model is validated against off-axis experiments on unidirectional thermoplastic composite plies.

The activation of fracture networks poses significant risks and raises safety concerns for projects involving such geological structures. Consequently, an accurate and efficient simulation strategy is essential for modeling highly fractured subsurface formations. While the extended finite element method (XFEM), coupled with the penalty method, effectively models slip-stick conditions along fracture surfaces and fracture propagation under compression, its efficiency declines when handling dense fracture networks. To address this challenge, a multiscale XFEM (MS-XFEM) approach is developed and presented. MS-XFEM approximates fine-scale displacement field by interpolating solutions on a coarser-scale mesh using algebraically constructed basis functions. All extra degrees of freedom (DOFs) are incorporated within the basis functions matrix, rendering the coarse-scale system a standard finite element-based system. In each propagation step, basis functions are algebraically and locally updated to capture fracture propagation. Through four proof-of-concept test cases, the accuracy and efficiency of MS-XFEM in simulating fractured geological formations are demonstrated, emphasizing its potential for real-world applications.

A yield function in the stress resultant space of geometrically exact beams based on the elastoplastic cross-sectional warping problem has been proposed by Herrnböck et al. (Comput Mech, 67(3):723–742, 2021). This plasticity framework has been extended with a hardening tensor to model the kinematic hardening effects in Herrnböck et al. (Comput Mech, 71(1):1–24, 2022). While this framework provides scaling for the yield surface in ideal plasticity, scaling in hardening plasticity has not yet been explored. This paper focuses on the numeric modelling of hardening beams and beam assemblies at different geometric scales. Discretization effects from the introduction of plasticity into the geometrically exact beam model are demonstrated. Furthermore, the effects of scaling are explored, and a method to mitigate undesirable effects in order to achieve a size-agnostic formulation is proposed. Consistent geometric scaling is demonstrated for two alternative scaling approaches of the yield function.

A numerical framework for simulating progressive failure under high-cycle fatigue loading is validated against experiments of composite quasi-isotropic open-hole laminates. Transverse matrix cracking and delamination are modeled with a mixed-mode fatigue cohesive zone model, covering crack initiation and propagation. Furthermore, XFEM is used for simulating transverse matrix cracks and splits at arbitrary locations. An adaptive cycle jump approach is employed for efficiently simulating high-cycle fatigue while accounting for local stress ratio variations in the presence of thermal residual stresses. The cycle jump scheme is integrated in the XFEM framework, where the local stress ratio is used to determine the insertion of cracks and to propagate fatigue damage. The fatigue cohesive zone model is based on S-N curves and requires static material properties and only a few fatigue parameters, calibrated on simple fracture testing specimens. The simulations demonstrate a good correspondence with experiments in terms of fatigue life and damage evolution.

A numerical framework for simulating progressive failure under high-cycle fatigue loading is validated against experiments of composite quasi-isotropic open-hole laminates. Transverse matrix cracking and delamination are modeled with a mixed-mode fatigue cohesive zone model, covering crack initiation and propagation. Furthermore, XFEM is used for simulating transverse matrix cracks and splits at arbitrary locations. An adaptive cycle jump approach is employed for efficiently simulating high-cycle fatigue while accounting for local stress ratio variations in the presence of thermal residual stresses. The cycle jump scheme is integrated in the XFEM framework, where the local stress ratio is used to determine the insertion of cracks and to propagate fatigue damage. The fatigue cohesive zone model is based on S-N curves and requires static material properties and only a few fatigue parameters, calibrated on simple fracture testing specimens. The simulations demonstrate a good correspondence with experiments in terms of fatigue life and damage evolution.

The storage of renewable hydrogen in salt caverns requires fast injection and production rates to cope with the imbalance between energy production and consumption. This raises concerns about the mechanical stability of salt caverns under such operational conditions. The use of appropriate constitutive models for salt mechanics is an important step in investigating this issue, therefore many constitutive models with several parameters have been presented in the literature. However, a robust calibration strategy to reliably determine which model and parameter set represents the given rock, based on stress–strain data sets, remains an unsolved challenge. In this paper, for the first time in the community, we present a multi-step strategy to determine a single parameter set based on many deformation data sets for salt rocks. Towards this end, we first develop a comprehensive constitutive model able to capture all relevant nonlinear deformation physics of transient, reverse, and steady-state creep. The determination of the single set of representative material parameters is then achieved by framing the calibration process as an optimization problem, for which the global Particle Swarm Optimization algorithm is employed. To allow for dynamic data integration, a multi-step calibration strategy is developed for a situation where experiments are included one at a time, as they become available. Additionally, due to the existing mild heterogeneity in the experimental rock samples, our optimization strategy is made flexible to allow for this slight heterogeneity. The devised optimization strategy, based on the multi-physics comprehensive constitutive modeling framework, results in a single set of representative material properties of all the deformation data sets. As a rigorous mathematical analysis for the presented method and the lack of relevant experimental data sets, we consider a wide range of synthetic experimental data sets, inspired by the existing sparse relevant data in the literature. The results of our performance analyses show that the proposed calibration strategy is robust. Moreover, the results become increasingly more accurate as more data sets become available.

Lightweight materials used for impact mitigation must be able to resist impact and absorb the maximum amount of energy from the impactor. Auxetic materials have the potential to achieve high resistance by drawing material into the impact zone and providing higher indentation and shear resistance. However, these materials must be artificially designed, and the large deformation dynamic effects of the created structures must be taken into consideration when deciding on a protection concept. Despite their promise, little attention has been given to understanding the working mechanisms of high-rate and finite deformation effects of architected auxetic lattice structures. This study compares the static and dynamic elastic properties of different auxetic structures with a honeycomb structure, a typical non-auxetic lattice, at equivalent mass and stiffness levels. In this study, we limit the investigation to elastic material behavior and do not consider contact between the beams of the lattices. It is demonstrated that the equivalent static and dynamic properties of individual lattices at an undeformed state are insufficient to explain the variations observed in impact situations. In particular, the initial Poisson's ratio does not determine the ability of a structure to resist impact. To gain a thorough comprehension of the overall behavior of these structures during localized, high rate compression, the evolution of the elastic tangent properties under compression and shear deformation was monitored, leading to a more profound understanding. Observations made in one configuration of stiffness and mass are replicated and analyzed in related configurations.

Corrosion in reinforced concrete is an important feature which can lead to increased deformation and cracking, as well as to premature failure. In the present work, macro-mechanical modelling of corrosion is performed, namely the degradation of bond–slip between concrete and steel. A mixed-mode damage model is adopted, in which the interaction between the bond–slip law and the stress acting in the neighbourhood of the concrete–steel bar interface is taken into account. Bond–slip degradation is modelled using an evolutionary bond–slip relationship, which depends on the level of corrosion. Different relevant loading cases are studied. Special attention is given to the evolution of corrosion in time, under constant load. This is done by adopting a Total Iterative Approach, in which the structure is reevaluated each time step, upon damage increase due to corrosion. Pullout tests are presented to illustrate the performance of the model. Bending tests are also performed to evaluate the influence of corrosion at structural level.

In this work, a recently proposed high-cycle fatigue cohesive zone model, which covers crack initiation and propagation with limited input parameters, is embedded in a robust and efficient numerical framework for simulating progressive failure in composite laminates under fatigue loading. The fatigue cohesive zone model is enhanced with an implicit time integration scheme of the fatigue damage variable which allows for larger cycle increments and more efficient analyses. The method is combined with an adaptive strategy for determining the cycle increment based on global convergence rates. Moreover, a consistent material tangent stiffness matrix has been derived by fully linearizing the underlying mixed-mode quasi-static model and the fatigue damage update. The enhanced fatigue cohesive zone model is used to describe matrix cracking and delamination in laminates. In order to allow for matrix cracks to initiate at arbitrary locations and to avoid complex and costly mesh generation, the phantom node version of the eXtended finite element method (XFEM) is employed. For the insertion of new crack segments, an XFEM fatigue crack insertion criterion is presented, which is consistent with the fatigue cohesive zone formulation. It is shown with numerical examples that the improved fatigue damage update enhances the accuracy, efficiency and robustness of the numerical simulations significantly. The numerical framework is applied to the simulation of progressive fatigue failure in an open-hole [±45]-laminate. It is demonstrated that the numerical model is capable of accurately and efficiently simulating the complete failure process from distributed damage to localized failure.

In quasi-brittle materials, such as reinforced concrete, localisation of initially diffuse cracking evolving in localised cracking patterns consists of a numerically challenging task. With conventional iterative methods, convergence of the numerical solution scheme to model crack localisation is often difficult to obtain. On the other hand, conventional total approaches, such as the Sequentially Linear Approach, although robust, fail to approximate properly the underlying material law. In the present work, a new model is introduced, designated the Total Iterative Approach, in which the internal damage variables are updated iteratively. It is found that this approach is robust, allows for the correct approximation of the material law and is a powerful tool for the analysis of softening behaviour. Some examples are presented to illustrate the performance of the model.

In fractured geological formations, as a result of the in-situ stress changes, fractures can propagate or slide. This phenomenon can be efficiently modeled by the extended finite element method (XFEM) when there are only a few fractures present. However, geological reservoirs contain many fractures which can also cross and are densely populated. Therefore, the classical XFEM is too expensive to be applied for the simulation of propagating fractures in geological formations. To reduce the costs, typically, homogenization or upscaling is used. However, they result in inaccurate solutions, since no separation of scales exists in this process. To resolve this challenge, in this work, a multiscale XFEM (MS-XFEM) for propagating fractures is developed and presented. In each time step, given the current geometries of the fractures, local XFEM-based basis functions are constructed or adaptively updated. The adaptive update takes place in certain regions where fracture geometries are changed due to propagation. Using these basis functions, a very efficient FEM-based coarse-scale system is developed since it has no extra degrees of freedom (DOFs). Once the coarse-scale system is solved, its solution is prolonged to the fine-scale original resolution using the basis functions. This approximate fine-scale solution is then used to estimate the group of growing fractures tips and their growing angles. This allows for exploiting the locality of the propagation process fully while solving a global system. To control the error, an iterative procedure is also developed. Proof-of-concept test cases are presented to study the developed MS-XFEM algorithm. It is shown that MS-XFEM results are capable of predicting the propagating paths for complicated fracture patterns. As such, MS-XFEM casts a promising method for field-scale applications.

Lattice models have been used to simulate mass transport to predict durability of cementitious materials. In particular, the use of dual lattice meshes allows for the coupling of fracture and transport processes, which commonly occur at the same time in these materials. Literature has shown good agreement between simulations and experimental results. Nevertheless, work regarding relevant computational aspects of the numerical model are scarce. In this study, a Voronoi-discretized lattice model is used to simulate unsaturated moisture transport in cement-base materials through the Richards equation. First, investigations regarding the choice of elemental volume approximation, time-stepping procedure and quadrature are evaluated. After validation of the approximations, simulated moisture transport in sound concrete was compared to experiments and mesh and time step sensitivity were discussed. A new approach to model capillary absorption of water in cracked concrete was also proposed and its advantages with respect to existing approaches are discussed by comparing to experimental measurements. The results confirm that the model can accurately predict the transport processes for the earlier stage of capillary absorption. Furthermore, moisture ingress in cracked concrete is simulated for different crack configurations and the use of different approaches is suggested accordingly. Finally, guidelines regarding the approximations used for optimization of the computations are presented.

Structural components in corrosive environments such as pipelines, bridges, aircrafts, and turbines are imposed to stress corrosion. A stress corrosion model for pit growth should a) accurately consider the electrochemistry of the corrosion process, b) properly deal with the moving interface between solid and electrolyte, and c) effectively incorporates the synergism between corrosion and mechanical field at the interface. In Part II, the influence of mechanical loading is added to the approach described in Part I. Part II investigates the model's capabilities of simulating stress corrosion via a set of numerical examples of corrosion pitting which include experimental validation and uncertainty quantification of model parameters and properties.

Adobe is a traditional masonry made of sundried earthen bricks and mud mortar. Despite a millennial history of buildings of architectural value, adobe still connotes a so called ‘not engineered’ construction type. Namely, the material and structural properties of adobe are still not entirely addressed, resulting in an equally uncertain normative framework for adobe buildings design. However, over the last ten years, a large research program has been conducted in the Netherlands to qualify the material and structural properties of this sustainable building technology. In this paper, a critical analysis of the current normative body for the material characterization of adobe is addressed. Guidelines, prescriptions and requirements related to test methods, materials selection and properties contained in the available building codes for adobe around the world are assessed. A critical normative review is performed using the most recent literature produced on adobe, with particular regards to the results of experimental tests and numerical simulations performed by the authors. On the basis of these findings, some issues have been identified in relation to the knowledge currently condensed in the norms for adobe. A series of programmatic guidelines is aimed at orienting future research on adobe as well as fostering the process of updating its current normative body.

Accurate assessment of the overall mechanical behavior of masonry, composed of bricks and mortar joints, remains challenging due to its inhomogeneous and orthotropic nature. In this study, the feasibility of various mean-field homogenization schemes for the three-dimensional orthotropic elastic properties of masonry is comprehensively investigated. Three kinds of masonry patterns are considered, including the stack bonded pattern, the running bonded pattern and the double-leaf Flemish bonded pattern that has received limited attention so far. Special attention is paid to the homogenization schemes which have not been applied to the masonry case, such as Lielens’ interpolative double inclusions (D-I) and the interaction direct derivative (IDD) schemes. After a comparison between the well-known mean-field homogenization schemes, an improved micro-mechanical model is proposed by combining the advantages of the IDD and D-I models. The validation of the proposed model is conducted through a comparison against experimental data from literature and numerical results obtained via finite element analyses (FEA). The results show that the proposed model can accurately evaluate the orthotropic elastic properties of the three masonry typologies for a wide range of stiffness ratios between brick and mortar, ranging from 1 to 1000. The proposed model also shows better performance than the classical schemes especially when the stiffness ratios between brick and mortar are higher than 10, which is of major importance for the application of mean-field homogenization based multiscale methods to the nonlinear analysis of masonry. Furthermore, the presented homogenization method can be of interest for other anisotropic materials, e.g., laminate materials.

Altering the state of the stress of the subsurface reservoirs can lead fractures to slip and extend their lengths (i.e., to propagate). This process can even be engineered, in many applications, e.g., enhanced geothermal systems. As such, accurate and efficient simulation of the mechanical deformation of the subsurface geological reservoirs, allowing for fracture propagation, is at the core of many geoscientific operational designs. Subsurface reservoirs entail many fractures at multiple scales. Implementation of 3D complex grids on these complex fractured systems, for mechanical deformation analyses, is extremely challenging. An alternative approach can be developed by using extended finite element methods (XFEM). XFEM allows for capturing the fractures effects on a conveniently-generated structured matrix mesh. The cracks are introduced by extra degrees of freedom (DOFs) on the nodes of the matrix rock mesh. For geoscientific applications, however, XFEM results in too many DOFs which are beyond the scope of simulators. Additionally, for propagating fractures, these DOFs need to be updated in response to the dynamic extension of the fractures in the domain. The propagation process not only adds to the sensitivity of the outputs to the accuracy of the estimated stress field, but also increases the size of the linear systems. In addition to these, matrix rocks are often highly heterogeneous, at high resolutions. In this work, we present a novel multiscale procedure for propagating fractures in heterogeneous geological reservoirs. For the first time in the community, we present the highly fractured systems at coarser resolutions via XFEM-based basis functions, which also account for the propagating effects. Fractures are allowed to extend their scale and the enriched basis functions are locally updated. Using these bases, the coarse scale system is obtained in which no extra DOFs due to fractures exist. This significantly reduces the computational complexity. As a significant step forward compared with our recently-published journal paper [Xu, Hajibeygi, Sluys, Journal of Computational Physics, 2021], in this conference contribution we allow the fractures to propagate. Specially, we introduce a local-global-based approach, in which fracture propagation is treated only at local stage; while the stress and deformation are modelled at global scale. In the search of convenient implementation, the procedure is presented algebraically. Through several test cases, we demonstrate the applicability of the method for complex fractured media. Specially we demonstrate that propagation can be modeled at local scale, while accurate stress and deformation fields are obtained at global scale.

Corrosion is a phenomenon observed in structural components in corrosive environments such as pipelines, bridges, aircrafts, turbines, etc. The computational model of corrosion should enjoy two features: a) accurately considering the electrochemistry of corrosion and b) properly dealing with the moving interface between solid and electrolyte. There are several approaches to model corrosion such as using FEM with mesh refinement algorithms, combining FEM and level-set method, employing finite volume methods, adopting peridynamic formulation, and utilizing phase field models. Because of its accuracy, lower computational cost, and robust dealing with multiple pit merging, the model which combines FEM with level-set method is selected to be more extensively assessed in this paper. Part I focuses on demonstrating the model's capabilities of simulating pitting corrosion through a set of numerical examples which include numerical solution verification, experimental validation, and uncertainty quantification of model parameters and properties.