Discrete-to-continuum modeling of spider silk fiber composites

Abstract

This work presents a discrete-to-continuum approach to the constitutive response of composite materials formed by embedding a network of spider silk fibers in a matrix material. A multiscale model that makes use of the virial stress concept of statistical mechanics is formulated, which accounts for hyperelastic constitutive equations of the component materials. The finite element implementation of the given constitutive equations is also carried out. Numerical simulations show the response of a silk composite formed by embedding a spider orb web in a matrix material, and illustrate the main features of the proposed model. In the presence of a weak matrix, the force–displacement response of a silk composite is compared with that deriving from an atomistic modeling of the spider orb web. A simulation of the response of a composite equipped with an elastomeric matrix is also discussed.