Universal Displacements in Inextensible Fiber-Reinforced Linear Elastic Solids

TL;DR

This paper characterizes universal displacements in anisotropic linear elastic solids reinforced with inextensible fibers, showing how internal constraints influence the set of displacements that can be maintained by boundary tractions.

Contribution

It provides a comprehensive characterization of universal displacements across symmetry classes in fiber-reinforced elastic solids, highlighting the impact of inextensible fibers on these displacements.

Findings

Inextensible fibers generally enlarge the set of universal displacements.

Universal displacements are characterized for each symmetry class with fiber reinforcement.

Presence of fibers affects the universality of displacements differently across symmetry classes.

Abstract

For a given class of materials, universal displacements are those displacements that can be maintained for any member of the class by applying only boundary tractions. In this paper we study universal displacements in compressible anisotropic linear elastic solids reinforced by a family of inextensible fibers. For each symmetry class and for a uniform distribution of straight fibers respecting the corresponding symmetry we characterize the respective universal displacements. A goal of this paper is to investigate how an internal constraint affects the set of universal displacements. We have observed that other than the triclinic and cubic solids in the other five classes (a fiber-reinforced solid with straight fibers cannot be isotropic) the presence of inextensible fibers enlarges the set of universal displacements.