A coupled FE–EFG approach for modelling crack growth in ductile materials

Abstract

A B S T R A C T In this work, a coupled finite element-element free Galerkin approach has been used to model crack growth in ductile materials under monotonic and cyclic loads. In this approach, a small discontinuous domain near crack is modelled by EFG method, whereas the rest of the domain is modelled by FEM to exploit the advantages of both the methods. A ramp function has been used in the transition region to maintain the continuity between FE and EFG domains. Two plasticity models (GTN and von-Mises) and three hardening rules (isotropic, kinematic and mixed) have been used to model the nonlinear material behaviour. Four different problems, i.e. single edge notched tension specimen, double edge notched tension specimen, compact tension specimen and three-point bend specimen, are solved under plane strain condition using J-R curve approach. Finally, a CT specimen problem is also solved by coupled approach using three hardening rules and two plasticity models under cyclic loading.A = void nucleation parameter a = initial crack length a J = degrees of freedom associated with Heaviside function a(x) = vector of unknown coefficients b = body force vector per unit volume b α K = degrees of freedom associated with asymptotic functions B = matrix of shape functions gradients D el = elastic constitutive matrix D ep = elasto-plastic constitutive matrix E = Young's modulus E = Green-Lagrange strain tensor f = void volume fraction f * = damage parameter G = matrix of derivatives of shape functions H = hardening modulus H(x) = Heaviside function I = second order unit tensor J cr = critical J-integral K mat = material tangent stiffness matrix K geo = geometric stiffness matrix K T = total tangent stiffness matrix m = order of basis function Correspondence: I. V. Singh.

Source codes and simulation data for the finite element implementation of the conventional and localizing gradient damage methods in ABAQUS

“…These sharp variations are incorporated into the displacement fields through enrichment functions. The discrete methods are namely extended FEM [2], [3], [4] extended IGA [5], EFGM [6] to name a few. On the other hand, the smeared methods use a continuous definition of a discontinuity.…”

A Mesh-Free Approach for Multiscale Modeling in Continuum–Granular Systems

“…The EFG method has been combined with other numerical tools in earlier studies. Most often, such as [27][28][29], the EFG method is combined with the finite element method in order to optimize domain meshing, improve computation efficiency and increase results accuracy. For example, Ullah et al [30] used the finite element method to mesh the continuum domain at the outset and converted part of the domain into EFG nodes where necessary.…”