Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications

高等学校計算数学学報 = Numerical mathematics

A gradient-enhanced computational homogenization procedure, that allows for the modelling of microstructural size effects, is proposed within a general non-linear framework. In this approach the macroscopic deformation gradient tensor and its gradient are imposed on a microstructural representative volume element (RVE). This enables us to incorporate the microstructural size and to account for non-uniform macroscopic deformation fields within the microstructural cell. Every microstructural constituent is modelled as a classical continuum and the RVE problem is formulated in terms of standard equilibrium and boundary conditions. From the solution of the microstructural boundary value problem, the macroscopic stress tensor and the higher-order stress tensor are derived based on an extension of the Hill-Mandel condition. This automatically delivers the microstructurally based constitutive response of the higher-order macro continuum and deals with the microstructural size in a natural way. Several examples illustrate the approach, particularly the microstructural size effects.

http://www.mate.tue.nl/mate/pdfs/2091.pdf

Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme

https://hal.archives-ouvertes.fr/hal-01389078/document

A computational approach to handle complex microstructure geometries

Multi-scale second-order computational homogenization of multi-phase materials : a nested finite element solution strategy

The present study is devoted to the generalization of the Nonuniform Transformation Field Analysis (NTFA), a model-reduction approach introduced by the authors. First, the local fields of internal variables are decomposed on a reduced basis of modes. Second, the effective (average) dissipation potential of the phases is replaced by accurate approximations. The reduced evolution equations of the models, in other words the homogenized constitutive relations, can be entirely expressed explicitly in terms of quantities which are pre-computed " off-line ". The example of creep of polycrystalline ice is used to assess the accuracy of the models. Their predictions, both the overall response and the local response, are shown to be in good agreement with full-field simulations with a significant speed-up.

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Model-reduction in micromechanics of polycrystalline materials

Multiscale identification and NTFA reduction of the elasto-viscoplastic polycrystalline behaviour of uranium dioxide (UO2) for wide range of loading conditions

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Computational micromechanics: a variational derivation of FFT-based schemes Pierre Suquet, Jean-Claude Michel

https://hal.archives-ouvertes.fr/hal-01901253/document

Computational micromechanics: a variational derivation of FFT-based schemes

The Nonuniform Transformation Field Analysis is a reduction technique introduced in the realm of Multiscale Problems in Nonlinear Solid Mechanics to achieve scale transition for materials exhibing a nonlinear behaviour. It is indeed well recognized that the nonlinearity introduces a strong coupling between the problems at the different scales which, in full rigor, remain coupled. To avoid the computational cost of the scale coupling, reduced models have been developed. To improve on the predictions of Transformation Field Analysis where the plastic strain field is assumed to be uniform in each domain, the authors have proposed another reduced model, called the Nonuniform Transformation Field Analysis, where the plastic strain fields follow shape functions which are not piecewise uniform. The model is presented for individual phases exhibiting an elastoviscoplastic behavior. A brief account on the reduction technique is given first. Then the time-integration of the model at the level of a macroscopic material point is performed by means of a numerical scheme. This reduced model is applied to structural problems. The implementation of the model in a Finite Element code is discussed. It is shown that the model predicts accurately the effective behavior of nonlinear composite materials with just a few internal variables. Another worth-noting feature of the method is that the local stress and strain fields can be determined simply by postprocessing the output of the structural (macroscopic) computation performed with the model.

https://hal.archives-ouvertes.fr/hal-00683857/document

Jean-Claude Michel

Papers

Model-reduction in micromechanics of polycrystalline materials

Multiscale identification and NTFA reduction of the elasto-viscoplastic polycrystalline behaviour of uranium dioxide (UO2) for wide range of loading conditions

Computational micromechanics: a variational derivation of FFT-based schemes

Plastic strain heterogeneity in composite materials and the nonuniform transformation field analysis