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.

Shape optimisation is utilised to generate damage resistant structures. By means of a variational approach, the analytical gradients for an elasto‐plastic material model with regularised damage properties are derived. Due to the complexity of the underlying material model, the application of the variational approach requires additional handling of the history field. The gradients are then used for Sequential Quadratic Programming (SQP) which is applied to shape optimisation and thus generation of damage optimised geometries.

Sensitivity analysis is applied to a regularised non-local ductile damage model. A variational approach is utilised to derive the analytical gradients of different objectives with respect to either geometrical of material parameters. Due to the definition of the material model, enhanced algorithmic treatments are necessary to capture its history dependent nature within the sensitivity computation. The gradient information with respect to the geometrical parameters are used to derive damage tolerant geometries in shape optimisation using Sequential Quadratic Programming (SQP). The sensitivities with respect to the material parameters are used to analyse the response and impact of certain material parameters of the model during loading and unloading of a specimen.