A biologically-inspired mesh optimizer based on pseudo-material remodeling

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 domains, making the mesh distortion an issue of concern towards ensuring the accuracy of numerical model predictions. In this work, we propose a technique for the simultaneous mesh optimization and motion characterization. The mesh optimization/motion method introduced here is inspired by the mechanobiology of soft tissues, particularly those present in arterial walls, which feature an incredible capability to adapt to altered mechanical stimuli through adaptive mechanisms such as growth and remodeling. The proposed approach is in the framework of a low-distortion mesh moving method that is based on fiber-reinforced hyperelasticity and optimized zero-stress state. We adopt different reference configurations for the different constituents, namely ground substance and fibers. Hypothetical reference configurations are postulated for the different pieces of pseudo-material (the elements) as target shapes. Also, we modify the equilibrium equations using a volume-invariant strategy. Through the introduction of growth and remodeling adaptive processes we build an optimization algorithm which can attain an optimal configuration through a series of consecutive nonlinear optimizations steps. The remodeling mechanism allows to adapt the fiber deposition orientations, which become the driving force towards an homeostatic state, that is the optimal configuration. Also, a recruitment mechanism is introduced to selectively deal with initial highly distorted elements where high stresses develop due to the departure from the ideal configuration. We report 2D and 3D numerical experiments to show the application of this biologically-inspired mesh optimizer (BIMO) to simplicial finite element meshes. We also present additional numerical tests using BIMO as a mesh moving method. The results show that the proposed method performs satisfactorily, either as mesh optimizer and/or mesh motion strategy.