An overview of coupled mechanical problems including contact phenomena solved by FEA

Abstract

Almost all mechanical systems operate under conditions of coupled mechanical problems, most often nonlinear. One of the primary sources of nonlinearity is the contact phenomenon, which is present in a large number of complex mechanical systems used, for example, in engineering and biomedicine. So far, no exact analytical methods exist for solving the response of bodies in contact in solid mechanics. To achieve this, the Finite Element Analysis (FEA) is employed, whose accuracy largely relies on properly chosen initial and boundary conditions, as well as the contact parameters, especially the contact stiffness. However, when the contact is coupled with other phenomena within the same mechanical problem, solving this task becomes far more complex. This is especially the case with engineering mechanical systems, where other phenomena, such as dynamics, impact, material elastoplastic characteristics, thermal strains, geometric nonlinearities, and multiple contacts, often appear as also nonlinear and can only be reduced to linear ones by introducing appropriate simplifications and assumptions. Nowadays, high accuracy in predicting the operating conditions and behavior of contemporary mechanical systems is also required. This leads to further complexity of models and simulations of the investigated complex mechanical systems. From the perspective of using validated approximate methods, such as FEA, the required knowledge of both the modeled systems and the modeling approaches is exceptionally high. To illustrate the problems that may arise when modeling such systems, as well as the approaches developed for solving complex mechanical problems with coupled nonlinear phenomena, including contact, this paper presents and discusses various case studies that the author has solved in previous years [1-4], as shown in Figure 1. An original approach in developing highly accurate and less time-consuming models for FEA based on controlled and precisely tailored models built from the bottom-up will be presented, meaning that FEA models are bottom-up developed to ensure accuracy, fidelity, and efficiency, and simultaneously adapted to the planned simulations from the very beginning.