Analysis of fractures in linear viscoelastic media using a generalized finite element method and the elastic–viscoelastic correspondence principle

Abstract

A methodology for an efficient analysis of 3-D fracture mechanics problems in linear viscoelastic media is presented. It combines the Elastic–Viscoelastic Correspondence Principle (EVCP), a Generalized Finite Element Method (GFEM), and an inverse Laplace transform (ILT) method to compute Energy Release Rate (ERR) and Crack Mouth Opening Displacement (CMOD) for viscoelastic fracture problems in the time domain. The method is denoted EVCP-GFEM-ILT and consists of solving a reference elastic problem in the Laplace domain using a quadratic p-hierarchical GFEM, computing quantities of interest in this domain, and transforming them to the time domain with the aid of a numerical ILT method. One of the key features of the method is that a single elastic solution is required, regardless of the time interval of the target viscoelastic problem. A detailed verification of the methodology against analytical and reference numerical solutions is performed. Problems subjected to either non-homogeneous Neumann or Dirichlet boundary conditions of increasing complexity are considered. Two ILT methods are studied and the one based on Fourier series is shown to deliver accurate results for all tested boundary conditions, as well as non-trivial viscoelastic material models. The computational cost of the method applied to a 3-D problem is compared with the one for Abaqus which solves the problem directly in the time domain using a FEM mesh with quarter-point elements. A fully 3-D mixed-mode fracture problem with a non-trivial viscoelastic material model is solved to highlight the applicability of the proposed methodology. Finally, a problem of practical interest is analyzed in order to show how the methodology proposed in this work can be applied to efficiently handle large-scale simulations.