A biologically-inspired mesh moving method for cyclic motions mesh fatigue

Moving boundaries and interfaces are commonly encountered in fluid flow simulations. For instance, fluid-structure interaction simulations require the formulation of the problem in moving and/or deformable domains, making the mesh distortion an issue of concern when it is required to guarantee the accuracy of the numerical model predictions. In addition, traditional elasticity-based mesh motion methods accumulate permanent mesh distortions when cyclic motions occur. In this work, we exploit a biologically-inspired framework for the mesh optimization at the same time it is moved to solve cyclic and nearly cyclic domain motions. Our work is in the framework introduced in Takizawa et al. (Comput Mech 65:1567-1591, 2020) under the name"low-distortion mesh moving method based on fiber-reinforced hyperelasticity and optimized zero-stress state". This mesh optimization/motion method is inspired by the mechanobiology of soft tissues, particularly those present in arterial walls, which feature an outstanding capacity to adapt to various mechanical stimuli through adaptive mechanisms such as growth and remodeling. This method adopts different reference configurations for each constituent, namely ground substance and fibers. Considering the optimization features of the adopted framework, it performs straightforwardly for cyclic motion with no cycle-to-cycle mesh distortion accumulation. Numerical experiments in both 2D and 3D using simplicial finite element meshes subjected to cyclic loads are reported. The results indicate that BIMO performance is better than the linear-elasticity mesh moving method in all test cases the two methods are compared.