Variational sensitivity analysis and shape optimisation applied to a non-local, ductile damage model

Shape optimisation is applied to an elasto-plastic material model with non-local, regularised damage. Geometries of the same volume are generated which behave better under the aspect of damage accumulation. The underlying material model is taken from published literature and enhanced to derive the sensitivities w.r.t the initial reference geometry. A variational approach, together with an enhanced kinematic concept to decouple geometrical and physical quantities, is utilised to derive these sensitivities. With the inclusion of plastic and damaging effects, the load history of the problem has to be taken into account as well. This introduces additional terms for the sensitivity analysis and requires certain adjustments within the numerical treatment. These gradient information can finally be applied in gradient-based optimisation techniques to efficiently solve the stated optimisation problem. The two discussed examples highlight the benefit of damage optimisation. In the first example, a geometry is reshaped to directly reduce the damage accumulation under certain load. In a second example, the results of a compliance based optimisation with the ductile damage material behaviour are compared to shapes resulting from optimisation problems considering elastic and elasto-plastic material behaviour.