Modeling fracture in viscoelastic materials using a modified incremental meshfree RPIM and DIC technique

Abstract

In the present work, fracture mechanics of linear viscoelastic materials is investigated numerically and experimentally. Herein, an effective and accurate meshfree method is developed to analyze fracture mechanics in viscoelastic problems. To this end, an incremental approach with higher-order finite difference (FD) schemes for analysis of viscoelastic materials in the time domain, along with an improved meshfree method based on the global weak formulation, i.e. the radial point interpolation method (RPIM), is employed. An accurate and efficient integration approach with minimum computational cost, i.e. the background decomposition method (BDM), is also used to compute the domain integrals. To evaluate the accuracy and efficiency of the proposed numerical method, first, two example problems are provided and the robustness of the presented method is assessed. Then, a non-contact full-field optical method, i.e. the digital image correlation technique, is utilized to investigate the viscoelastic fields of a polymer, polymethyl-methacrylate (PMMA), during crack propagation in mode I. Also, in order to properly model the fracture behavior of this material by the meshfree RPIM, the mechanical properties of the PMMA, including the Prony viscoelastic parameters, are obtained by an ASTM test method. Moreover, the obtained results from the DIC test and also the load-displacement curve of the cracked specimen are compared with the results of the proposed meshfree RPIM and a very close agreement is observed.