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An implementation of the crystal plasticity theory in the context of the multiphase-field method provides a numerically efficient tracking of evolving grain boundaries, modeled as diffuse interfaces. In literature, several approaches exist for the implementation of the plastic material behavior within the diffuse interface, based on interpolation, homogenization, or the mechanical jump conditions. Among these, only the jump condition approach exhibits an intrinsic relationship to the sharp interface (SI) theory. Therefore, in the work at hand, the implementation of the crystal plasticity theory within the jump condition approach, referred to as phase-specific plastic fields approach (PSPFA), is discussed in detail. The PSPFA is compared to the interpolation approach, referred to as common plastic fields approach (CPFA), using three-dimensional benchmark simulations of a bicrystal set-up. The comparison reveals that the PSPFA and SI coincide convincingly regarding the accumulated plastic slip and the Mises stress. In contrast, a significant deviation of CPFA and SI is observed both quantitatively and qualitatively, not only within the diffuse interface region, but throughout the complete simulation domain. A variation of the interface width illustrates that this observation can be transferred to the normal components of the total strain, even for smaller interface widths. Consequently, a quantitative estimate of the plastic material behavior, which is crucial for the prediction of the dynamic behavior of grain boundaries, is only provided by the PSPFA. The application of the crystal plasticity in the context of PSPFA to more complex microstructures is illustrated with respect to a periodic honeycomb-structure and an octotuple. [ABSTRACT FROM AUTHOR]

This work investigates the capabilities of anisotropic theory-based, purely data-driven and hybrid approaches to model the homogenized constitutive behavior of cubic lattice metamaterials exhibiting large deformations and buckling phenomena. The effective material behavior is assumed as hyperelastic, anisotropic and finite deformations are considered. A highly flexible analytical approach proposed by Itskov (Int J Numer Methods Eng 50(8): 1777–1799, 2001) is taken into account, which ensures material objectivity and fulfillment of the material symmetry group conditions. Then, two non-intrusive data-driven approaches are proposed, which are built upon artificial neural networks and formulated such that they also fulfill the objectivity and material symmetry conditions. Finally, a hybrid approach combing the approach of Itskov (Int J Numer Methods Eng 50(8): 1777–1799, 2001) with artificial neural networks is formulated. Here, all four models are calibrated with simulation data of the homogenization of two cubic lattice metamaterials at finite deformations. The data-driven models are able to reproduce the calibration data very well and reproduce the manifestation of lattice instabilities. Furthermore, they achieve superior accuracy over the analytical model also in additional test scenarios. The introduced hyperelastic models are formulated as general as possible, such that they can not only be used for lattice structures, but for any anisotropic hyperelastic material. Further, access to the complete simulation data is provided through the public repository https://github.com/CPShub/sim-data. [ABSTRACT FROM AUTHOR]

A small strain plasticity model, based on the principles of continuum mechanics, is incorporated into a phase-field model for heterogeneous microstructures in polycrystalline and multiphase material systems (Nestler et al., Phys Rev 71:1-6, ). Thereby, the displacement field is computed by solving the local momentum balance dynamically (Spatschek et al., Phys Rev 75:1-14, ) using the finite difference method on a staggered grid. The elastic contribution is expressed as the linear approximation according to the Cauchy stress tensor. In order to calculate the plastic strain, the Prandtl-Reuss model is implemented consisting of an associated flow rule in combination with the von Mises yield criterion and a linear isotropic hardening approximation. Simulations are performed illustrating the evolution of the stress and plastic strain using a radial return mapping algorithm for single phase system and two phase microstructures. As an example for interface evolution coupling with elasto-plastic effects, we present crack propagation simulations in ductile material. [ABSTRACT FROM AUTHOR]

The constitutive response of porous materials is investigated computationally. For the solid phase elasto- plastic behavior of Green type is considered, i.e. an isotropic compressible yield criterion is assumed. A wide range of material parameters and porosities from 0.1 to 30 % are investigated by means of FEM simulations of periodic ensembles of spherical pores. The dilatation of the pores and of the compressible matrix are evaluated. It is found that a large part of the total dilatation is due to plastic volume changes of the solid phase. The asymptotic stress states of the simulations are compared to analytical predictions by Shen et al. (Comput Mater Sci 62:189-194, ). Based on the computational data, an effective constitutive law is proposed and verified by means of additional computations. A three-scale homogenization procedure for double porous materials is proposed that depends only on the micro- and mesoscale porosity and the yield stress of the solid phase. [ABSTRACT FROM AUTHOR]

As an anode material for lithium-ion batteries, amorphous silicon offers a significantly higher energy density than the graphite anodes currently used. Alloying reactions of lithium and silicon, however, induce large deformation and lead to volume changes up to 300%. We formulate a thermodynamically consistent continuum model for the chemo-elasto-plastic diffusion-deformation behavior of amorphous silicon and it’s alloy with lithium based on finite deformations. In this paper, two plasticity theories, i.e. a rate-independent theory with linear isotropic hardening and a rate-dependent one, are formulated to allow the evolution of plastic deformations and reduce occurring stresses. Using modern numerical techniques, such as higher order finite element methods as well as efficient space and time adaptive solution algorithms, the diffusion-deformation behavior resulting from both theories is compared. In order to further increase the computational efficiency, an automatic differentiation scheme is used, allowing for a significant speed up in assembling time as compared to an algorithmic linearization for the global finite element Newton scheme. Both plastic approaches lead to a more heterogeneous concentration distribution and to a change to tensile tangential Cauchy stresses at the particle surface at the end of one charging cycle. Different parameter studies show how an amplification of the plastic deformation is affected. Interestingly, an elliptical particle shows only plastic deformation at the smaller half axis. With the demonstrated efficiency of the applied methods, results after five charging cycles are also discussed and can provide indications for the performance of lithium-ion batteries in long term use. [ABSTRACT FROM AUTHOR]