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Reformulating Hyperelastic Materials with Peridynamic Modeling
Author(s) -
Xu Liyou,
He Xiaowei,
Chen Wei,
Li Sheng,
Wang Guoping
Publication year - 2018
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.13553
Subject(s) - hyperelastic material , peridynamics , strain energy density function , nonlinear system , strain energy , computer science , classification of discontinuities , parameterized complexity , function (biology) , elastic energy , classical mechanics , mathematical analysis , physics , continuum mechanics , finite element method , mathematics , algorithm , evolutionary biology , biology , quantum mechanics , thermodynamics
Peridynamics is a formulation of the classical elastic theory that is targeted at simulating deformable objects with discontinuities, especially fractures. Till now, there are few studies that have been focused on how to model general hyperelastic materials with peridynamics. In this paper, we target at proposing a general strain energy function of hyperelastic materials for peridynamics. To get an intuitive model that can be easily controlled, we formulate the strain energy density function as a function parameterized by the dilatation and bond stretches, which can be decomposed into multiple one‐dimensional functions independently. To account for nonlinear material behaviors, we also propose a set of nonlinear basis functions to help design a nonlinear strain energy function more easily. For an anisotropic material, we additionally introduce an anisotropic kernel to control the elastic behavior for each bond independently. Experiments show that our model is flexible enough to approximately regenerate various hyperelastic materials in classical elastic theory, including St. Venant‐Kirchhoff and Neo‐Hookean materials.