Data-Driven Finite Element Models of Passive Filamentary Networks

Abstract

A data-driven procedure is introduced to construct finite element models of heterogeneous systems for which an accurate microscopic description is available. A filter to define coarsened finite element nodal values is defined from the principal modes obtained by singular value decomposition of the microscopic data. The resulting finite element nodal values are subsequently used to reconstruct local linearization of the system behavior, defining drag and stiffness matrices for an overdamped system. The procedure is exemplified for an actin mesh described by Brownian dynamics and eight-node cuboid finite elements but is generally applicable with respect to both the microscopic model and the type of finite element approximation. In contrast to standard finite element formulations derived from hypotheses on assumed deformation behavior, the data-driven procedure introduced here is completely determined by the observed behavior be it obtained from simulations or experiment.