Abstract

The paper addresses the problem of tensile and mixed‐mode cracking within the so‐called smeared crack approach. Because lack of point‐wise convergence on stresses is deemed as the main difficulty to be overcome in the discrete problem, a (stabilized) mixed formulation with continuous linear strain and displacement interpolations is used. The necessary convergence rate can be proved for such a formulation, at least in the linear problem. Two standard local isotropic Rankine damage models with strain‐softening, differing in the definition of the damage criteria, are used as discrete constitutive model. Numerical examples demonstrate the application of the proposed formulation using linear triangular P1P1 and bilinear quadrilateral Q1Q1 mixed elements. The results obtained do not suffer from spurious mesh‐bias dependence without the use of auxiliary tracking techniques.

Abstract

This paper deals with the question of strain localization associated with materials which exhibit softening due to tensile straining. A standard local isotropic Rankine damage model with strain-softening is used as exemplary constitutive model. Both the irreducible and mixed forms of the problem are examined and stability and solvability conditions are discussed. Lack of uniqueness and convergence difficulties related to the strong material nonlinearities involved are also treated. From this analysis, the issue of local discretization error in the pre-localization regime is deemed as the main difficulty to be overcome in the discrete problem. Focus is placed on low order finite elements with continuous strain and displacement fields (triangular P1P1 and quadrilateral Q1Q1), although the presented approach is very general. Numerical examples show that the resulting procedure is remarkably robust: it does not require the use of auxiliary tracking techniques and the results obtained do not suffer from spurious mesh-bias dependence.