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-continuous 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.

中文翻译：

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混合数据驱动计算力学中接触问题的公式化和启发式求解

在这项工作中，我们考虑混合数据驱动计算力学（DDCM）方法，其中重建平滑本构流形以获得表现良好的非线性优化问题（NLP），而不是困难得多的离散连续 NLP（DCNLP）直接 DDCM 方法。重点是在混合 DDCM 公式中添加几何不等式约束。其中，所需的约束力导致了具有互补约束的数学程序（MPCC）形式的接触问题，这是一个比 DCNLP 复杂度仍然较低的问题类别。对于此 MPCC，我们提出了一种启发式快速解决方案方法，该方法可以通过解决最多四个 NLP 来生成可验证的解决方案。我们对三个难度不断增加的不同接触问题进行了各种数值实验，以证明这种方法的潜力和局限性。