Theoretical and computational aspects of an elastoplastic damage gradient non local model

FEM results of softening material problems are known to show a pathological mesh dependency. To avoid this problem, the mechanical behavior in each integration point must take into account the immediate vicinity. Models including the influence of neigbourhood give rise to non local formulation in the early 70th. Nowadays, numerous formulations have been proposed to ensure mesh independency in post peak zone. The majority of non local models have been initially developed for concrete or brittle materials and can’t be easily generalized to ductile elastoplasticity. However, the case of damaging ductile materials have been treated in some papers ([

1

], [

4

]).These models introduce simples higher gradient formulations, able to provide mesh independent FEM results. This paper proposes a non local elastoplastic model fully coupled to damage. A thermodynamically consistent formulation involving a scalar damage field and its first gradient in the Helmholtz free energy is used. The formulation is based on a classical material theory accounting for a strong damage-behavior coupling. The strong coupling to the elastic and isotropic and kinematic hardening modulus is based on the energy equivalence assumption [

2

]. The local damage evolution law depends on a non local variable associated to the damage driving force [

3

]. This variable is the solution of a non local condition solved in a coupled fashion with the standard equilibrium equation [

5

]. This gives rise to a new finite element with additional DOFs. The relevant numerical aspects related to the FEM development and material integration scheme are presented. The damage gradient model is coded using both UEL and UMAT subroutines of ABAQUS/standard. Comparison between the standard local and non local formulations are discussed.