Two gradient plasticity theories discretized with the element-free Galerkin method Original Research Article

In this paper, the element-free Galerkin method is exploited to analyze gradient plasticity theories. The use of this discretization method has the advantage that higher-order continuity, which can be required for the plastic multiplier field, is provided for. In passing, we show that the regularization properties of the higher-order gradients are necessary, since, similar to finite element methods, a severe discretization sensitivity is encountered otherwise. The mesh-free discretization method is first applied to an established, stress-space gradient plasticity theory. Next, a strain-space gradient plasticity theory, which employs an implicit averaging of an invariant strain measure, is proposed and elaborated. This theory is insensitive to the order of the interpolation polynomials and, as a result, the convergence of the Newton–Raphson procedure is better. The performance of both gradient plasticity models is examined for the mesh-free discretization scheme. A comparative study is carried out for a one-dimensional bar in tension, while the influence of the discretization in biaxial compression is studied next, including that of the numerical parameters of the discretization scheme and that of the internal length scale contained in the gradient plasticity theories.