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Peridynamic integrals for strain invariants of homogeneous deformation
Author(s) -
Madenci Erdogan
Publication year - 2017
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201600242
Subject(s) - strain energy density function , hyperelastic material , isotropy , peridynamics , infinitesimal strain theory , force density , strain energy , jacobian matrix and determinant , energy density , finite strain theory , mathematical analysis , potential energy , hooke's law , classical mechanics , deformation (meteorology) , physics , mathematics , continuum mechanics , theoretical physics , finite element method , quantum mechanics , thermodynamics , meteorology
Abstract This study presents the peridynamic integrals. They enable the derivation of the peridynamic (nonlocal) form of the strain invariants. Therefore, the peridynamic form of the existing classical strain energy density functions can readily be constructed for linearly elastic and hyperelastic isotropic materials without any calibration. A general form of the force density vector is derived based on the strain energy density function that is expressed in terms of the first invariant of the right Cauchy‐Green strain tensor and the Jacobian. In the case of linear elastic response for isotropic materials, the peridynamic force density vector is derived based on the classical form of the strain energy density function for three‐ and two‐dimensional analysis. Also, a new form of the strain energy density function leads to a force density vector similar to that of bond‐based peridynamics. Numerical results concern the verification of the peridynamic predictions with these force density vectors by considering a rectangular plate under uniform stretch.