A comparative study of micromorphic gradient-extensions for anisotropic damage at finite strains

Modern inelastic material model formulations rely on the use of tensor-valued internal variables. When inelastic phenomena include softening, simulations of the former are prone to localization. Thus, an accurate regularization of the tensor-valued internal variables is essential to obtain physically correct results. Here, we focus on the regularization of anisotropic damage at finite strains. Thus, a flexible anisotropic damage model with isotropic, kinematic, and distortional hardening is equipped with three gradient-extensions using a full and two reduced regularizations of the damage tensor. Theoretical and numerical comparisons of the three gradient-extensions yield excellent agreement between the full and the reduced regularization based on a volumetric-deviatoric regularization using only two nonlocal degrees of freedom

Discrete Empirical Interpolation Method for nonlinear softening problems involving damage and plasticity

Accurate simulations are essential for engineering applications, and intricate continuum mechanical material models are constructed to achieve this goal. However, the increasing complexity of the material models and geometrical properties lead to a significant increase in computational effort. Model order reduction aims to implement efficient methods for accelerating the simulation process while preserving a high degree of accuracy. Numerous studies have already demonstrated the benefits of this method for linear elastic material modeling. However, in the present work, we investigate a two-surface gradient-extended damage-plasticity model. We conducted complex simulations with this model, demonstrating both damage behavior and softening. The POD-based discrete empirical interpolation method (DEIM) is introduced and implemented. To accomplish simulations with DEIM and softening behaviour, we propose the implementation of a reduced form of the arc-length method. Existing research on calculating models with both damage and softening behavior using the DEIM and arc-length method is limited. To validate the methods, two numerical examples are thoroughly investigated in this study: a plate with a hole and an asymmetrically notched specimen. The results show that the proposed methods can create a reduced order model with high accuracy and a significant speedup of the simulation. For both examples, the analysis is conducted in three steps: first, plasticity without damage is examined, followed by damage without plasticity, and finally, the combination of plasticity and damage is investigated.Comment: 44 pages, 28 figures, 2 tables, 3 algorithm

Theory and implementation of inelastic Constitutive Artificial Neural Networks

Nature has always been our inspiration in the research, design and development of materials and has driven us to gain a deep understanding of the mechanisms that characterize anisotropy and inelastic behavior. All this knowledge has been accumulated in the principles of thermodynamics. Deduced from these principles, the multiplicative decomposition combined with pseudo potentials are powerful and universal concepts. Simultaneously, the tremendous increase in computational performance enabled us to investigate and rethink our history-dependent material models to make the most of our predictions. Today, we have reached a point where materials and their models are becoming increasingly sophisticated. This raises the question: How do we find the best model that includes all inelastic effects to explain our complex data? Constitutive Artificial Neural Networks (CANN) may answer this question. Here, we extend the CANNs to inelastic materials (iCANN). Rigorous considerations of objectivity, rigid motion of the reference configuration, multiplicative decomposition and its inherent non-uniqueness, restrictions of energy and pseudo potential, and consistent evolution guide us towards the architecture of the iCANN satisfying thermodynamics per design. We combine feed-forward networks of the free energy and pseudo potential with a recurrent neural network approach to take time dependencies into account. We demonstrate that the iCANN is capable of autonomously discovering models for artificially generated data, the response of polymers for cyclic loading and the relaxation behavior of muscle data. As the design of the network is not limited to visco-elasticity, our vision is that the iCANN will reveal to us new ways to find the various inelastic phenomena hidden in the data and to understand their interaction. Our source code, data, and examples are available at doi.org/10.5281/zenodo.10066805Comment: 54 pages, 14 figures, 14 table

A gradient-extended anisotropic damage-plasticity model in the logarithmic strain space

Within this contribution, we discuss additional theoretical as well as numerical aspects of the material model developed in [1, 2], where a `two-surface' damage-plasticity model is proposed accounting for induced damage anisotropy by means of a second order damage tensor. The constitutive framework is stated in terms of logarithmic strain measures, while the total strain is additively decomposed into elastic and plastic parts. Moreover, a novel gradientextension based on the damage tensor's invariants is presented using the micromorphic approach introduced in [3]. Finally, going beyond the numerical examples presented in [1, 2], we study the model's ability to cure mesh-dependency in a three-dimensional setup

Mechanical modeling of the maturation process for tissue-engineered implants: application to biohybrid heart valves

The development of tissue-engineered cardiovascular implants can improve the lives of large segments of our society who suffer from cardiovascular diseases. Regenerative tissues are fabricated using a process called tissue maturation. Furthermore, it is highly challenging to produce cardiovascular regenerative implants with sufficient mechanical strength to withstand the loading conditions within the human body. Therefore, biohybrid implants for which the regenerative tissue is reinforced by standard reinforcement material (e.g. textile or 3d printed scaffold) can be an interesting solution. In silico models can significantly contribute to characterizing, designing, and optimizing biohybrid implants. The first step towards this goal is to develop a computational model for the maturation process of tissue-engineered implants. This paper focuses on the mechanical modeling of textile-reinforced tissue-engineered cardiovascular implants. First, we propose an energy-based approach to compute the collagen evolution during the maturation process. Then, we apply the concept of structural tensors to model the anisotropic behavior of the extracellular matrix and the textile scaffold. Next, the newly developed material model is embedded into a special solid-shell finite element formulation with reduced integration. Finally, we use our framework to compute two structural problems: a pressurized shell construct and a tubular-shaped heart valve. The results show the ability of the model to predict collagen growth in response to the boundary conditions applied during the maturation process. Consequently, we can predict the implant's mechanical response, such as the deformation and stresses of the implant.Comment: Preprint submitted to Elsevie

A novel gradient-extended anisotropic two-surface damage-plasticity model for finite deformations.

A material model to deal with finite plasticity coupled with anisotropic damage will be presented. The presentation addresses mesh regularization problems and a novel approach for using gradient-extension in the context of damage. Since finite strains are considered, the strain measures chosen are logarithmic strains. To give the interested audience an idea of the behavior of the model, numerical examples are used for illustration

A thermo-coupled constitutive model for semi-crystalline polymers at finite strains: Application to varying degrees of crystallinity and temperatures

Thermoplastic materials are widely used for thermoforming and injection moulding processes, since their low density in combination with a high strength to mass ratio are interesting for various industrial applications. Semi-crystalline polymers make up a subcategory of thermoplastics, which partly crystallize after cool-down from the molten state. During the thermoforming process, residual stresses can arise, due to complex material behavior under different temperatures and strain rates. Therefore, computational models are needed to predict the material response and minimize production errors. This work presents a thermomechanically consistent phenomenological material formulation at finite strains, based on [1]. In order to account for the highly nonlinear material behavior, elasto-plastic and visco-elastic contributions are combined in the model formulation. To account for the crystalline regions, a hyperelastic-plastic framework is chosen, based on [2, 3]. Kinematic hardening of Arruda-Boyce form is incorporated in the formulation, as well as associated plastic flow. The material parameters depend on both, the temperature as well as the degree of crystallinity. A comparison to experiments with varying degrees of crystallinity and temperatures is presented, where a special blending technique ensures stable crystallinity conditions

Theory and numerics of gradient-extended damage coupled with plasticity

Numerical simulations for predicting damage and failure of materials and structures are of fundamental importance in many engineering disciplines, since they usually reduce the number of costly and time-consuming practical experiments and allow for deeper insights into processes that would otherwise not or only hardly be possible. The significance of such simulations depends to a large extent on the quality of the applied material models which are themselves constantly being further developed to take more and more phenomena and effects into account that occur in real materials. In this context, the coupled modeling of the complex material phenomena 'damage' and 'plasticity' can be mentioned as a challenging and practically relevant subject the scientific literature has been dealing with for quite some time already. There is still a pressing need for further research in this scientific field. The present cumulative dissertation aims at making a valuable contribution in this regard. It essentially represents a compilation of several published works of the author (and his coauthors) related to the topic. The overall goal is the development and investigation of novel gradient-extended damage-plasticity material models, both for the geometrically linear and nonlinear regime, which are based on a so-called 'two-surface' approach. The latter means that damage and plasticity are modeled as truly distinct (but coupled) dissipative mechanisms by taking separate damage loading and plastic yield criteria as well as loading / unloading conditions into consideration, respectively. Nonlinear Armstrong-Frederick kinematic hardening, nonlinear Voce isotropic hardening and nonlinear damage hardening are also accounted for by the models that can quite flexibly be adapted to various situations in which the considered real material shows either a (quasi-)brittle-type, ductile-type or possibly a mixed-type damaging behavior. The gradient-extension of damage (based on a micromorphic approach) is used to avoid pathological mesh sensitivity issues in finite element simulations that otherwise typically occur when using conventional models involving material softening behavior. After an introductory part with a literature overview and a more detailed clarification of the research-relevant questions, the thesis begins with two works that are concerned with a numerical comparison of two different and competing kind of formulations for large deformation plasticity: hypo- and hyperelastic-based plasticity formulations that rely upon an additive decomposition of the rate of deformation tensor or a multiplicative split of the deformation gradient. At this point, no damage is being considered, yet. The main purpose for the thesis is to clarify whether one of the two formulations should generally be preferred when it later comes to an extension of the geometrically linear gradient-enhanced damage-plasticity model to large deformations. Various simulations with single finite elements finally reveal that the results, which are obtained using the respective modeling approaches, can indeed significantly differ from each other under extreme conditions and that an incautious use of hypoelastic-based plasticity formulations can even lead to physically implausible model behavior. However, in more application-oriented structural simulations these problems are nearly insignificant and the results show a good agreement which suggests that, in principal, both formulations are well-suited for the development of new material models involving large plastic deformations. Afterwards, two works are presented that deal with the theory and numerics of two slightly different two-surface gradient-extended damage-plasticity models for the geometrically linear regime. Among other things, the following topics are discussed: the application of the micromorphic approach to achieve the gradient-extension of the models, the derivation of the strong and weak form of the underlying boundary value problem, the thermodynamically consistent derivation of the evolution equations, the models' implementation into finite element codes, the algorithmic handling of the discretized equations at the integration point level and the computation of the consistent tangent operators which are necessary to retain a quadratic rate of convergence of the Newton scheme at the global finite element level. The results of numerous structural simulations demonstrate the good practical performance and mesh regularizing properties of the models in finite element simulations involving material softening. In the last part of the thesis, the model formulation is extended for its application to geometrically nonlinear problems. For this, a hyperelastic-based plasticity framework is used which relies upon an additional multiplicative split of the plastic part of the deformation gradient in order to allow for the modeling of nonlinear Armstrong-Frederick kinematic hardening at large deformations and which utilizes exclusively symmetric internal variables. Besides the theory, also many numerically relevant topics are discussed, such as a suitable time integration scheme for the evolution equations that preserves both the plastic incompressibility and symmetry of the tensorial internal variables, or the implementation of the model formulation into finite element codes. Finally, the functionality of the geometrically nonlinear model is exemplified by a structural finite element simulation