Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—theory

By Pedro Ponte Castañeda. 2002

389 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ac0e502d6b983f1d148d178ad0a8e75c8c3c5d76

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In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Ductile failure modeling (2016, background): “As shown by Rudnicki and Rice (1975), plastic nonnormality can play a significant role in promoting localization.”
On the effective behavior of nonlinear inelastic composites: I. Incremental variational principles (2007, background): “They also include estimates, which are exact to second-order in the contrast of the phases, obtained by taking a Taylor expansion of the potential (Ponte Castañeda, 1996, Ponte Castañeda, 2002).”
A Gurson-type criterion for porous ductile solids containing arbitrary ellipsoidal voids—I: Limit-analysis of some representative cell (2012, methodology): “Danas and Ponte-Castaneda (2008a,b) recently proposed an improved model based on results of some “second-order homogenization method” (Ponte-Castaneda, 2002; Idiart and PonteCastaneda, 2005); but the accuracy of this new proposal has not yet been assessed.”
Simulation of micromechanical behavior of polycrystals: finite elements versus fast Fourier transforms (2009, background): “…significant enhancements, such as the n-site implementation (Ahzi 1987, Canova et al 1992, Solas and Tomé 2001), or a second-order extension (Ponte Castañeda 2002, Liu and Ponte Castañeda 2004, Lebensohn et al 2007) for a realistic prediction of the intragranular heterogeneity of the stress…”
Homogenization of elasto-(visco) plastic composites based on an incremental variational principle (2012, methodology): “In particular, variational techniques for the MF homogenization of nonlinear elastic composites have been successfully developed (Ponte Castañeda, 1991, 1996, 2002).”
A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials (2017, methodology): “Physically nonlinear random microstructures have been addressed as well [76,94,95], involving the Taylor–Bishop–Hill estimates, several (generalized) self-consistent schemes and asymptotic methods [96].”