Optimization solvers and machine learning to enhance quasi-static unilateral contact simulations

This thesis focuses on computational methods to describe the mechanics of deformable bodies in unilateral contact. This field of research aims to develop numerical simulations that predict the mechanics that occur when a deformable body comes in contact with another deformable body, a rigid body or with itself. A diverse range of questions in this research domain remains open to this day. The goal of this thesis is to help answer two of them. The first part of this thesis investigates if optimization solvers can be exploited to predict the mechanics of a quasi-static, rate-independent deformable solid body when it experiences snap-back due to its contact with a rigid body. The second part of this thesis investigates if machine learning can be exploited to accelerate unilateral contact simulations. The first part of this thesis revolves around snap-back occurring due to unilateral contact. Snap-back occurs when (a part of) the energy stored in a quasi-static deformable body is suddenly released. Quasi-static deformable bodies in contact are particularly prone to experience snap-back. Conventional quasi-static simulations are not able to treat snap-back. A well-known remedy is to enhance the quasi-static simulation with an arc-length method. Another remedy is to perform a dynamical simulation instead of a quasi-static simulation. Both remedies come with their own advantages, disadvantages and limitations. To this purpose, the first part of this thesis investigates the capabilities of four optimization algorithms to describe the mechanics of a quasi-static, rate-independent deformable body when it experiences contact-induced snap-back. The presented investigation considers 2D and 3D scenarios, an elastic and elastoplastic mechanical model for the deformable body and different refinement levels to spatially discretize the deformable body. The machine learning algorithms under investigation in the second part of this thesis are neural networks. First, an existing neural network is investigated for its ability to replace the entire contact detection algorithm of the simulations. Second, a new neural network is proposed to replace only the most time-consuming tasks of the conventional contact detection algorithm. This hybrid strategy of only replacing a part of the existing algorithm and not interfering with the other part makes use of the speed of the neural network but also allows for the fact that neural networks are not perfect. The reason is that the final task of the conventional contact detection algorithm, which is responsible for the high accuracy, is the part that remains untouched. The proposed network is a multi-task neural network that simultaneously classifies and emulates functions. Because the network’s classifier and function emulator exchange information during each forward pass, its accuracy is sufficient for use in true contact simulations.