Gradient-based optimization strategies, such as topology optimization, rely on sensitivity information to iteratively update design parameters and optimize a performance measure. Advanced sensitivity analysis techniques, such as the adjoint method, leverage detailed knowledge of the system's governing equations. In the context of finite deformation contact mechanics, as considered here, both geometric nonlinearity and nonlinearity arising from the contact itself must be taken into account. When frictional sliding is present, the governing equations become path-dependent. In this contribution, we derive the sensitivity analysis within an adjoint framework, including consistent analytical linearization, for three of the most common contact constraint enforcement methods: the Lagrange multiplier method, the penalty method, and the augmented Lagrangian method. A state-of-the-art mortar finite element approach is used for the spatial discretization of contact and frictional sliding terms. Finally, we present numerical examples that demonstrate the capabilities of the newly developed sensitivity analysis strategies.     «

Gradient-based optimization strategies, such as topology optimization, rely on sensitivity information to iteratively update design parameters and optimize a performance measure. Advanced sensitivity analysis techniques, such as the adjoint method, leverage detailed knowledge of the system's governing equations. In the context of finite deformation contact mechanics, as considered here, both geometric nonlinearity and nonlinearity arising from the contact itself must be taken into account. When...     »