A consistent peridynamic formulation for arbitrary particle distributions

Abstract

Abstract The Peridynamic Petrov–Galerkin (PPG) method is a meshfree particle method based on the weak form of the peridynamic momentum equation. It can be applied to arbitrary constitutive laws from the classical continuum mechanics theory. With non-linear approximation functions the rank deficiency present in many nodally integrated discretization schemes is prevented. The consistency of trial functions is not sufficient for the convergence with irregular particle distributions. In this paper the consistency of the test space is examined and possible correction techniques are presented. The resulting variationally consistent PPG method is able to pass the patch test and to restore the optimal convergence rates. A correction of the test functions that preserves the linear trial function consistency allows the use of displacement–pressure–dilation formulations and exhibits stability and robustness for 3-D in the regime of non-linear elasticity. Besides, the direct nodal coupling with Finite Elements and the application of symmetry boundary conditions are enabled.