Modelling mixed-mode fracture in poly( methylmethacrylate) using peridynamics

Peridynamics (Silling (2000)) is a non-local continuum theory that is particularly suited to handle discontinuities in the displacement field, such as those arising during fracture. Peridynamics prescribes that each material point interacts with all its neighbors contained in a sphere of given radius; this assumption introduces a characteristic length scale in the continuum description. In a nutshell, the interactions between material points depend on their relative distance; in the peridynamics fiamework this distance is called the "bond length". The equations of motion, holding at each material point, link the material point acceleration to the integral over the point neighborhood of a force density field, whose strength depend on bond-stretches, i.e. the ratio of the actual bond-length over the initial one. In these equations the displacement gradient does not appear, thus naturally allowing for discontinuities in the displacement field to occur. As to failure, the simplest possible damage description is provided by an interaction law prescribing the force to vanish when a critical bond-stretch threshold is crossed; this parameter can be related to the Mode I critical strain energy release rate. A single parameter is needed to describe failure, in principle under every possible loading condition. In this work the predictive abilities of peridynamics were checked against experimental results in the case of mixed-mode failure of brittle polymers. Pre-cracked poly(methylmethacrylate) (PMMA) samples were tested using different specimens, in order to obtain Mode I, Mixed-Mode and Mode II loading conditions. The material was assumed to behave according to a peridynamics brittle elastic material model; the parameters needed to calibrate the elastic behavior were determined from Mode I tests, as was the critical stretch. The peridynamics simulations of mixed-mode tests were able to catch the correct fracture initiation load and to provide a fair description of the crack path under different conditions. The peridynamics model was also able to qualitatively capture the typical "nail" shape assumed by the crack front during propagation. Copyright (C) 2016 The Authors. Published by Elsevier B.V