In this work we consider the hybrid Data-Driven Computational Mechanics (DDCM) approach, in which a smooth constitutive manifold is reconstructed to obtain a well-behaved nonlinear optimization problem (NLP) rather than the much harder discrete-continous NLP (DCNLP) of the direct DDCM approach. The key focus is on the addition of geometric inequality constraints to the hybrid DDCM formulation. Therein, the required constraint force leads to a contact problem in the form of a mathematical program with complementarity constraints (MPCC), a problem class that is still less complex than the DCNLP. For this MPCC we propose a heuristic quick-shot solution approach, which can produce verifiable solutions by solving up to four NLPs. We perform various numerical experiments on three different contact problems of increasing difficulty to demonstrate the potential and limitations of this approach.

翻译：本文研究了混合数据驱动计算力学（DDCM）方法，该方法通过重建光滑的本构流形，将问题转化为良好形态的非线性优化问题（NLP），而非直接DDCM方法中更为困难的离散连续非线性优化问题（DCNLP）。核心关注点在于将几何不等式约束引入混合DDCM框架中。在此框架下，所需约束力导致了一个带有互补约束的数学规划问题（MPCC）形式的接触问题，该问题类别仍较DCNLP简单。针对此MPCC，我们提出了一种启发式快速求解方法，通过最多求解四个NLP即可生成可验证的解。我们针对三个难度递增的不同接触问题进行了大量数值实验，以验证该方法的潜力与局限性。