Strain‐driven homogenization of inelastic microstructures and composites based on an incremental variational formulation

By C. Miehé. 2002

393 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/2762eaa626590a06b7006c2bf1c0b9c19c7eeeaa

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In Biomedical Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Variationally consistent modeling of finite strain plasticity theory with non-linear kinematic hardening (2010, neutral): “[17–19,13,9,20,21].”
On the implementation of rate-independent standard dissipative solids at finite strain – Variational constitutive updates (2010, methodology): “For models based on linearized kinematics, the reader is referred to [20].”
On the effective behavior of nonlinear inelastic composites: I. Incremental variational principles (2007, background): “The importance of these more recent variational principles in homogenization of nonlinear materials has also been recognized by Miehe (2002) and Miehe et al. (2002) who made several computational applications of these principles to finite strain plasticity of composites or polycrystals with…”
Towards variational constitutive updates for non-associative plasticity models at finite strain: models based on a volumetric-deviatoric split (2009, neutral): “[2–7].”
A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials (2017, methodology): “Alternatively, more efficient techniques are based on the Schur complement of the microscopic linearized system of equations (see [117,122] for more details on this procedure in combination with direct solvers).”
On multiscale FE analyses of heterogeneous structures: from homogenization to multigrid solvers (2007, methodology): “As shown in Miehe [15] and Miehe et al.”
A Vanishing Viscosity Approach to Quasistatic Evolution in Plasticity with Softening (2006, background): “Among the papers which are closest in spirit to our approach we quote [25], [26], [21], and [22].”
Novel boundary conditions for strain localization analyses in microstructural volume elements (2012, background): “Commonly applied RVE BCs are as follows: (i) linear displacement, (ii) periodic, and (iii) minimal kinematical, which are equivalent to uniform traction BCs [29].”
Quasistatic Evolution Problems for Linearly Elastic–Perfectly Plastic Materials (2004, neutral): “Appendix 37 References 40 1”
Homogenization of elasto-(visco) plastic composites based on an incremental variational principle (2012, background): “with JDðx; enþ1;Dp;NÞ 1⁄4 wðx; e; e; pÞ # wnðxÞ þ Dt/ ðx; _ p;pÞ: ð42Þ The local problem (40) can be restated into the following equivalent variational representation (Miehe, 2002; Lahellec and Suquet, 2007a):”
Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method (2016, methodology): “It is shown in literature that the Periodic boundary fluctuations provide a better apparent stiffness estimation for both periodic as well as random microstructures [52, 53, 74, 76, 97, 120, 126].”
Computational micro-to-macro transitions of discretized microstructures undergoing small strains (2002, methodology): “Numerical formulations for the analysis of representative cells of periodic composites in the small-strain format have recently been published in [3, 7, 11, 18] and [ 8 ], based on the discretization of composite microstructures in terms of the finite element method (FEM) or fast Fourier transforms.”