Computational micro-to-macro transitions of discretized microstructures undergoing small strains

By C. Miehé, Andreas Koch. 2002

585 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/96a27cf5ca3509df22a2e77777db651db51b143b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

3D stochastic bicontinuous microstructures: generation, topology and elasticity (2018, methodology): “We start by introducing the notion of a continuum with microstructure and computational micro-to-macro transition [65,66] as sketched in Fig.”
Scale transition and enforcement of RVE boundary conditions in second‐order computational homogenization (2008, methodology): “For the first-order computational homogenization theory, it has been concluded by a number of authors (for example, [9]) that periodic boundary conditions applied to the RVE lead to the best estimate of the overall response, as compared with the uniform traction boundary conditions (lowerbound estim”
Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models (2016, methodology): “The use of RVE-based theories in situations of practical interest relies almost exclusively on techniques of computational homogenization, based on finite element methods [30,57,64,77,78,79,80,81,82, 93,115,121].”
An assessment of the Gurson yield criterion by a computational multi‐scale approach (2009, methodology): “This is at variance with the treatment adopted by Miehe & Koch (2002) who used a Lagrange multiplier method to enforce the discrete space constraint.”
Computational homogenization of cellular materials (2014, unknown): “(24, 26, 27), see [47, 27], lead to the microscopic non–linear equations rewritten in the matrix form as fint(w) = CTλ , Cw = 0 , (29)”
Computational homogenization for the multi-scale analysis of multi-phase materials (2002, methodology): “…(1995); Ghosh et al. (1995, 1996) and further developed and improved in more recent works by Smit et al. (1998); Smit (1998); Miehe et al. (1999b); Miehe and Koch (2002); Michel et al. (1999); Feyel and Chaboche (2000); Terada and Kikuchi (2001); Ghosh et al. (2001); Kouznetsova et al. (2001a).”
Perturbation-based stochastic multi-scale computational homogenization method for the determination of the effective properties of composite materials with random properties (2016, methodology): “Details of the computational homogenization method for heterogeneous materials adopted in this work can be found in [5,30,31].”
Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method (2016, methodology): “During subsequent years, the FE2 computational technique has been further developed in the works of many authors [59, 69, 74, 75, 78, 105, 108, 123].”
Computational multiscale modelling of heterogeneous material layers (2009, methodology): “With these elements, the finite-element formulation which can be found in References [1] [18] [23] [29] [30] [34] [35] [37], the constitutive relation consists by a cohesive traction–separation law, which has traditionally been treated by a priori assumptions, as they were proposed by Xu and Needlem”