A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua

By F. Feyel. 2003

629 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/22ac9ed535bbb6546cfcfce80604db4e85038620

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In Computational Theory and Mathematics

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Coarse‐graining of multiscale crack propagation (2010, methodology): “A classic example of this type of method is the FE2 method [24, 25], where for each quadrature point in the coarse-scale finite element mesh, a fine-scale finite element mesh is used to compute the coarse-scale stress.”
Computational second-order homogenization of materials with effective anisotropic strain-gradient behavior (2020, methodology): “The approach is not restricted linear behaviors, and second-order computational homogenization has been extended to the nonlinear context through the FE(2) method in [35,36,22].”
Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm (2005, neutral): “In addition, the anisotropic observables are relevant in the context of theory, because they allow a comparison with the results of computer simulations [1] [2].”
Multiscale modeling of plasticity based on embedding the viscoplastic self-consistent formulation in implicit finite elements (2012, background): “In the general case of heterogeneous materials (of which a polycrystal is a particular case), these approaches are sometimes referred to as FE2 models (e.g. Feyel, 2003).”
Evaluation of generalized continuum substitution models for heterogeneous materials (2012, background): “…boundary conditions to be prescribed on a representative volume element in order to determine higher order effective properties can be applied to non–linear material response as done in Feyel (2003), Forest (1999), Geers et al. (2001), Kouznetsova et al. (2004b), and Trovalusci and Masiani (2003).”
A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality (2017, background): “First-order computational homogenization [97,99] assumes that the consecutive scales are separate; therefore, the macroscopic kinetic and kinematic quantities are obtained from a volume average of the micro-scale quantities of the RVE.”
Homogenization-based multiscale crack modelling: from micro diffusive damage to macro cracks (2011, methodology): “When implemented in a finite element (FE) framework, the method is known as an FE [5] scheme.”
Meta-modeling game for deriving theoretical-consistent, micro-structural-based traction-separation laws via deep reinforcement learning (2018, methodology): “…computational demand due to the large number of required representative elementary simulations, a trade-off that is widely known in FEM 2 [Feyel, 2003] and other homogenization-based multiscale methods, such as FEM-DEM [Sun et al., 2011b,a, Fish, 2013, Sun et al., 2013a, Wang and Sun,…”