Coarse graining with control points: a cubic-Bézier based approach to modeling athermal fibrous materials

Abstract

Fibrous materials continue to be of central importance to modern life, including traditional materials, such as textiles and paper, modern materials, such as polymeric materials and glass fiber, and emerging materials, such as carbon nanotube yarns. Developing constitutive laws for the mechanical behavior of such materials can be challenging owing to the often non-periodic microstructure, resulting in fairly large and computationally intractable representative volume elements. Therefore, it is imperative to design novel coarse-grained models that can bridge the computational gap and capture accurate physics associated with the mechanical behavior of fibrous materials. In this work, cubic-Béziers are used to represent fiber-segments, allowing for up to C 2(curvature)-continuous representation of curved fibers. Equations of motion are derived in terms of the control points, which allow for minimization and time integration strategies with the Lagrangian and Hamiltonian formalism. This coarse-grained model promises faster and more accurate computational performance compared to discrete approaches.