In recent years, plain woven fabrics made of high-strength, lightweight fiber have been utilized in a variety of engineering applications ranging from ballistic shields (e.g., softbody armor, aircraft fuselage barriers) to high-performance flexible systems (e.g., parachutes, airbags, sails and geo-textiles). In particular, fabric materials with extremely high strength-to-weight ratio, such as Kevlar® and Zylon®, are rapidly becoming mainstays in ballistic impact and penetration technologies. The mechanical properties of fabric depend crucially on the underlying microstructure, which is determined by the material properties of the constituent yarns and the geometry of the fabric weave.

In this work, a multiscale model for fabric material is introduced. The model is based on the assumption that, at the continuum level, fabric behaves as a finitely deformable membrane. Moreover, the fabric is assumed to be composed of two families of continuously distributed yarns constrained at all time to occupy a common evolving surface in three-dimensional space. The two families may slide relative to one another on the surface, subject to their respective equation of motion. The constitutive law at the continuum-scale is derived from fine-scale consideration. On the fine-scale, the properties of the microstructure are accounted for by locally modeling the plain woven fabric as a pair of initially curved overlapping elasticae under periodic boundary conditions and subject to the constraint of non-penetration. A handshake process is developed to integrate the two levels of analysis. Making use of this process, a robust multiscale finite element-based algorithm is formulated and implemented to solve selected boundary- and initial-value problems.