Filipe X. C. Andrade

A Ductile Damage Nonlocal Model of Integral-type at Finite Strains: Formulation and Numerical Issues

This contribution is devoted to the formulation and numerical implementation of a ductile damage constitutive model enriched with a thermodynamically consistent nonlocal theory of integral type. In order to describe ductile deformation, the model takes finite strains into account. To model elasticity, a Hencky-like hyperelastic free energy potential coupled with nonlocal damage is adopted. The thermodynamic consistency of the model is ensured by applying the first and second thermodynamical principles in the global form and the dissipation inequality can be re-written in a local form by incorporating a nonlocal residual that accounts for energy exchanges between material points of the nonlocal medium. The thermodynamically consistent nonlocal model is compared with its associated classical formulation (in which nonlocality is merely incorporated by averaging the damage variable without resorting to thermodynamic potentials) where the thermodynamical admissibility of the classical formulation is demonstrated. Within the computational scheme, the nonlocal constitutive initial boundary value problem is discretized over pseudo-time where it is shown that well established numerical integration strategies can be straightforwardly extended to the nonlocal integral formulation. A modified Newton-Raphson solution strategy is adopted to solve the nonlinear complementarity problem and its numerical implementation, regarding the proposed nonlocal constitutive model, is presented in detail. The results of two-dimensional finite element analyses show that the model is able to eliminate the pathological mesh dependence inherently present under the softening regime if the local theory is considered.

Thermodynamical Framework for Ductile Damage and Plasticity

Many models employed for the prediction of plastic deformation rely exclusively on elastoplastic theories, disregarding significant effects of internal degradation [1]. Constitutive models based on the Continuum Damage Mechanics theory provide more realistic predictions since damage is taken into account as an internal variable. In the present contribution, Lemaire’s model for ductile damage [2] is questioned under the assumption of the principle of maximum inelastic dissipation [3]. The model is enhanced with a nonlocal formulation where the damage variable is spatially averaged by means of an integral operator [4]. Thermodynamical admissibility of the nonlocal model is checked by applying the global version of the Clausius‐Duhem inequality [5]. Results from numerical analysis show that the constitutive model is insensitive to spatial discretization.

Classical and Thermodynamically Consistent Non‐local Formulations for Ductile Damage: Comparison of Approaches

Non‐local theories have been commonly used as suitable localisation limiters for plasticity and damage in finite element analysis. Within the non‐local framework, two competitive formulations have emerged: the first one is the classical approach, where a previous local model is directly enhanced with a non‐local variable; the other one is fully supported on thermodynamical requirements. In this paper, we present two distinct classical non‐formulations for elasto‐plasticity coupled with damage where we chose damage and the energy release rate as non‐local variables. Within the thermodynamically motivated framework, a simultaneous averaging of both damage and its conjugated thermodynamic force is implied from the Clausius‐Duhem inequality. The three resulting models are assessed through numerical simulation with finite elements. The results show that the classical non‐local model with averaging of the energy release rate may not regularise the solution under certain circumstances. On the other hand, the other two formulations are able to effectively eliminate the pathological mesh dependency.