An orthotropic mesh corrected crack model

Abstract

This paper recovers the original spirit of the continuous crack approaches, where displacements jumps across the crack are smeared over the affected elements and the behaviour is established through a softening stress–(total) strain law, using standard finite element displacement interpolations and orthotropic local constitutive models. The paper focuses on the problem of shear locking observed in the discrete problem when orthotropic models are used. The solution for this drawback is found in the form of a mesh corrected crack model where the structure of the inelastic strain tensor is linked to the geometry of the cracked element. The discrete model is formulated as a non-symmetric orthotropic local damage constitutive model, in which the softening modulus is regularized according to the material fracture energy and the element size. The resulting formulation is easily implemented in standard non-linear FE codes and suitable for engineering applications. Numerical examples show that the results obtained using this crack model do not suffer from dependence on the mesh directional alignment, comparing very favourably with those obtained using related standard isotropic or orthotropic damage models.