Methodological Aspects and Mesh Convergence in Numerical Analysis of Athermal Fiber Network Material Deformation

A balance between model complexity, accuracy, and computational cost is a central concern in numerical simulations. In particular, for stochastic fiber networks, the non-affine deformation of fibers, related non-linear geometric features due to large global deformation, and size effects can significantly affect the accuracy of the computer experiment outputs and increase the computational cost. In this work, we systematically investigate methodological aspects of fiber network simulations with a focus on the output accuracy and computational cost in models with cellular (Voronoi) and fibrous (Mikado) network architecture. We study both p and h-refinement of the discretizations in finite element solution procedure, with uniform and length-based adaptive h-refinement strategies. The analysis is conducted for linear elastic and viscoelastic constitutive behavior of the fibers, as well as for networks with initially straight and crimped fibers. With relative error as the determining criterion, we provide recommendations for mesh refinement, comment on the necessity of multiple realizations, and give an overview of associated computational cost that will serve as guidance toward minimizing the computational cost while maintaining a desired level of solution accuracy.