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Multiscale design of three‐dimensional nonlinear composites using an interface‐enriched generalized finite element method
Author(s) -
Brandyberry David R.,
Najafi Ahmad R.,
Geubelle Philippe H.
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6333
Subject(s) - homogenization (climate) , finite element method , materials science , nonlinear system , ellipsoid , inverse , constitutive equation , composite material , inverse method , matrix (chemical analysis) , mathematical analysis , structural engineering , mathematics , geometry , physics , engineering , biodiversity , ecology , quantum mechanics , astronomy , biology
Summary A computational framework is developed to model and optimize the nonlinear multiscale response of three‐dimensional particulate composites using an interface‐enriched generalized finite element method. The material nonlinearities are associated with interfacial debonding of inclusions from a surrounding matrix which is modeled using C −1 continuous enrichment functions and a cohesive failure model. Analytic material and shape sensitivities of the homogenized constitutive response are derived and used to drive a nonlinear inverse homogenization problem using gradient‐based optimization methods. Spherical and ellipsoidal particulate microstructures are designed to match a component of the homogenized stress‐strain response to a desired constructed macroscopic stress‐strain behavior.