Peridynamic integrals for strain invariants of homogeneous deformation

Research output: Contribution to journalArticle

15 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1236-1251
Number of pages16
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume97
Issue number10
DOIs
StatePublished - Oct 2017

Keywords

  • Peridynamic
  • integrals
  • invariants
  • strain

ASJC Scopus subject areas

  • Computational Mechanics
  • Applied Mathematics

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