Computational shape optimisation for a gradient-enhanced continuum damage model

Abstract

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 optimised geometries for ductile damaging materials

“…The basic idea of the model is to couple the local damage d to a global field variable ϕ to then regularise the global damage without the need to solve the underlying Karush-Kuhn Tucker conditions at global level, see eg. [2] and [3] where this is done. This allows an easy implementation in the finite-element context and is known as the micromorphic approach.…”

A large strain gradient-enhanced ductile damage model: finite element formulation, experiment and parameter identification

“…The nonlinear equations (19) are solved with an iterative Newton-Raphson scheme. A Taylor series expansion at iteration step i + 1, neglecting further higher-order terms, yields…”

“…However, this results in a cumbersome treatment of the Karush-Kuhn-Tucker conditions on global finite element level, e.g. by an active-set algorithm [34,35] or by nonlinear complementarity functions [19]. Gradient-enhanced or micromorphic theories [16,18] allow a more efficient implementation and were adopted in the field, see, e.g.…”

Numerical optimisation of damage in extrusion processes

“…While numerical optimisation of damage is applied to academic-type problems for structural optimisation in literature, compare [4][5][6], its application within industrial-like problems is only scarcely researched. In this work a framework around the commercial software Abaqus FEA [7] is proposed, which handles the contact problems and runs the simulations, enabling numerical optimisation of forming processes.…”