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.

中文翻译：

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梯度增强连续损伤模型的计算形状优化

将各向同性梯度增强损伤模型应用于形状优化，以建立针对最佳损伤分布的计算优化设计框架。该模型源自由损伤梯度贡献丰富的自由亥姆霍兹能量密度。Karush-Kuhn-Tucker 条件通过 Fischer-Burmeister 函数在全局有限元级别上求解。这种方法消除了引入局部变量的必要性，只留下全局方程组需要迭代求解。建立了有限元方法意义上的数值实现的必要步骤。形状优化的基础理论和算法处理是在变分框架的背景下得出的。基于特定的有限变形本构模型，