A finite strain thermo-mechanically coupled material model for semi-crystalline polymers

In this work, a thermo-mechanically coupled constitutive model for semicrystalline polymers is derived in a thermodynamically consistent manner. In general, the macroscopic material behaviour of this class of materials is dictated by the underlying microstructure, i.e. by the distribution and structure of crystalline regimes, which form up after cooling from the amorphous melt. In order to account for the latter, the total degree of crystallinity is incorporated as an internal variable and its evolution is prescribed by means of a non-isothermal crystallisation kinetics model. The numerically efficient and robust framework is characterised based on experimental data for Polyamide 6 and shows a promising potential to predict the hyperelastic, visco-plastic material behaviour at various temperature

A finite strain thermo-mechanically coupled material model for semi-crystalline polymers

In this work, a thermo-mechanically coupled constitutive model for semicrystalline polymers is derived in a thermodynamically consistent manner. In general, the macroscopic material behaviour of this class of materials is dictated by the underlying microstructure, i.e. by the distribution and structure of crystalline regimes, which form up after cooling from the amorphous melt. In order to account for the latter, the total degree of crystallinity is incorporated as an internal variable and its evolution is prescribed by means of a non-isothermal crystallisation kinetics model. The numerically efficient and robust framework is characterised based on experimental data for Polyamide 6 and shows a promising potential to predict the hyperelastic, visco-plastic material behaviour at various temperature

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 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

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 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

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

Mechanical investigations of the peltate leaf of Stephania japonica (Menispermaceae): Experiments and a continuum mechanical material model

Stephania japonica is a slender climbing plant with peltate, triangular-ovate leaves. Not many research efforts have been devoted to investigate the anatomy and the mechanical properties of this type of leaf shape. In this study, displacement driven tensile tests with three cycles on different displacement levels are performed on petioles, venation and intercostal areas of the Stephania japonica leaves. Furthermore, compression tests in longitudinal direction are performed on petioles. The mechanical experiments are combined with light microscopy and X-ray tomography. The experiments show, that these plant organs and tissues behave in the finite strain range in a viscoelastic manner. Based on the results of the light microscopy and X-ray tomography, the plant tissue can be considered as a matrix material reinforced by fibers. Therefore, a continuum mechanical anisotropic viscoelastic material model at finite deformations is proposed to model such behavior. The anisotropy is specified as the so-called transverse isotropy, where the behavior in the plane perpendicular to the fibers is assumed to be isotropic. The model is obtained by postulating a Helmholtz free energy, which is split additively into an elastic and an inelastic part. Both parts of the energy depend on structural tensors to account for the transversely isotropic material behavior. The evolution equations for the internal variables, e.g. inelastic deformations, are chosen in a physically meaningful way that always fulfills the second law of thermodynamics. The proposed model is calibrated against experimental data, and the material parameters are identified. The model can be used for finite element simulations of this type of leaf shape, which is left open for the future work

Theory and implementation of inelastic Constitutive Artificial Neural Networks: Source code and data

<p>This dataset contains the source code of the inelastic Constitutive Artificial Neural Network (iCANN) as well as the data for the examples from the publication:</p><p>Holthusen, H., Lamm, L., Brepols, T., Reese, S., & E. Kuhl.<i> Theory and implementation of inelastic Constitutive Artificial Neural Networks.</i></p><p>arXiv: <a href="https://doi.org/10.48550/arXiv.2311.06380">https://doi.org/10.48550/arXiv.2311.06380</a></p><p> </p><p><strong>01_Example01: </strong> Artificially generated data</p><p>This example investigates whether the iCANN is able to discover a model for the data generated by a continuum mechanical model.</p><p> </p><p><strong>02_Example02:</strong> Discovering a model for the polymer VHB 4910 subjected to cyclic loading</p><p>Here, we investigate the ability of iCANN to discover and learn a model for the material response of  VHB 4910 polymer subjected to cyclic loading at different stretch rates.</p><p>The experimental data are taken from the literature:</p><p>Hossain, M., Vu, D. K., & Steinmann, P. (2012). Experimental study and numerical modelling of VHB 4910 polymer. <i>Computational Materials Science</i>, <i>59</i>, 65-74.</p><p><a href="https://doi.org/10.1016/j.commatsci.2012.02.027">https://doi.org/10.1016/j.commatsci.2012.02.027</a></p><p> </p><p><strong>03_Example03: </strong>Discovering a model for passive skeletal muscle subjected to relaxation</p><p>In this example, we investigate whether the iCANN is able to discover a model for the material behavior of passive skeletal muscles. A total of five independent experiments are carried out in which the maximum applied compression stretch and the stretch rate are varied. In addition, the learning performance of the iCANN is investigated. Training is first carried out in each of the five experiments and then in each of four of the five experiments.</p><p>The experimental data are taken from the literature:</p><p>Van Loocke, M., Lyons, C. G., & Simms, C. K. (2008). Viscoelastic properties of passive skeletal muscle in compression: stress-relaxation behaviour and constitutive modelling. <i>Journal of biomechanics</i>, <i>41</i>(7), 1555-1566.</p><p><a href="https://doi.org/10.1016/j.jbiomech.2008.02.007">https://doi.org/10.1016/j.jbiomech.2008.02.007</a></p><p> </p><p><strong>python_requirements.txt: </strong>File containing a list of installed Python modules used to implement the iCANN</p&gt