A non-local gradient-enhanced damage-plasticity formulation is proposed, which prevents the loss of well-posedness of the governing field equations in the post-critical damage regime. The non-locality of the formulation then manifests itself in terms of a non-local free energy contribution that penalizes the occurrence of damage gradients. A second penalty term is introduced to force the global damage field to coincide with the internal damage state variable at the Gauss point level. An enforcement of Karush–Kuhn–Tucker conditions on the global level can thus be avoided and classical local damage models may directly be incorporated and equipped with a non-local gradient enhancement. An important part of the present work is to investigate the efficiency and robustness of different algorithmic schemes to locally enforce the Karush–Kuhn–Tucker conditions in the multi-surface damage-plasticity setting. Response simulations for representative inhomogeneous boundary value problems are studied to assess the effectiveness of the gradient enhancement regarding stability and mesh objectivity.

A gradient-enhanced ductile damage model at finite strains is presented, and its parameters are identified so as to match the behaviour of DP800. Within the micromorphic framework, a multi-surface model coupling isotropic Lemaitre-type damage to von Mises plasticity with nonlinear isotropic hardening is developed. In analogy to the effective stress entering the yield criterion, an effective damage driving force—increasing with increasing plastic strains—entering the damage dissipation potential is proposed. After an outline of the basic model properties, the setup of the (micro)tensile experiment is discussed and the importance of including unloading for a parameter identification with a material model including damage is emphasised. Optimal parameters, based on an objective function including measured forces and the displacement field obtained from digital image correlation, are identified. The response of the proposed model is compared to a tensile experiment of a specimen with a different geometry as a first approach to validate the identified parameters.

An isotropic gradient-enhanced damage model is applied to shape optimisation in order to establish a computational optimal design framework in view of optimal damage distributions. The model is derived from a free Helmholtz energy density enriched by the damage gradient contribution. The Karush-Kuhn-Tucker conditions are solved on a global finite element level by means of a Fischer-Burmeister function. This approach eliminates the necessity of introducing a local variable, leaving only the global set of equations to be iteratively solved. The necessary steps for the numerical implementation in the sense of the finite element method are established. The underlying theory as well as the algorithmic treatment of shape optimisation are derived in the context of a variational framework. Based on a particular finite deformation constitutive model, representative numerical examples are discussed with a focus on and application to damage optimised designs.

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A gradient-enhanced damage formulation is coupled to isotropic plasticity in the framework of finite strains. Within the finite element method, an additional field variable representing nonlocal damage is introduced and linked to its local counterpart in order to allow a standard local formulation at the material point level. The onset of damage and plasticity is governed by damage and yield criteria respectively. This multisurface approach requires the determination of the two Lagrange multipliers. By using logarithmic strains, a formulation in principal axes in combination with a von Mises yield criterion is implemented. The damage functions are defined by means of exponential functions in order to avoid further constraints on the local damage variable. The model is able to capture a wide range of material responses, ranging from brittle to ductile damage and plasticitiy dominated behaviour. The mesh independence of the model is shown by means of representative finite element examples. Nonlocal damage variableClassical gradient-enhanced damage models require, in the context of finite elements, a global handling of the underlying Karush-Kuhn-Tucker (KKT) conditions, e.g. an active set method to determine on which nodes damage evolves. In this work, however, following approaches in [1,2], an additional scalar field variable φ representing nonlocal damage is introduced. Local and nonlocal damage is weakly linked via a penalty approach. The gradient-enhancement of the model can then be achieved by incorporating the gradient of the nonlocal damage variable. Hence, the free Helmholtz energy is additively combined of a local and nonlocal contribution