? 2023 Elsevier B.V.Curvature dependence of gradient damage models is an often undesired side effect. It originates from a change of the orientation of the non-local gradient term. The resulting curvature dependence then implicitly affects the loading behaviour, the predicted fracture energy and also the damage distribution. Two extended approaches are presented here for curvature control and applied to a micromorphic gradient damage model and to a phase-field model for fracture. Both allow for a better control of the crack path and consider the Hessian of the non-local damage field by means of an additional micromorphic field, since curvature is connected to second derivatives. The first approach is based on an additional curvature-dependent potential within the Helmholtz energy and automatically fulfils the second law of thermodynamics. The second approach modifies the micro forces of the balance law that is responsible for the curvature dependence directly. Unlike the first approach, it allows to eliminate the curvature dependence completely. However, thermodynamic consistency has to be checked explicitly.
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