UC Berkeley

A computational framework for assisting in the development of novel textiles is pre- sented. Electronic textiles are key in the rapidly growing field of wearable electronics for both consumer and military uses. Fabric actuators can be made with electrically function- alized fabrics that can be manipulated by externally applied electromagnetic fields when electric current is run through the yarns of the fabric. There are two main challenges to the modeling of electronic textiles: the discretization of the textile microstructure and the interaction between electromagnetic and mechanical fields.

The fully coupled mechanical, thermal, and electromagnetic behavior of a textile can be simulated in the context of quasistatic material property prediction and dynamic analysis of high speed impacts. Director-based beam formulations are used to discretize the fabric at the level of individual fibrils. Instead of solving Maxwell’s equations in full detail, a quasistatic approximation is used to solve the electric potential in the presence of a moving material medium. While this formulation alleviates the spatial and temporal discretization restrictions, the coupled problem is a Differential Algebraic Equation requiring special treat- ment. Diagonally Implicit Runge-Kutta methods using a monolithic Newton’s method solver are used to integrate the resulting nonlinear coupled systems in time. The finite element model is implemented using the open source package FEniCS. Contact integrals were added into the FEniCS framework so that multiphysics contact laws can be incorporated in the same framework, leveraging the code generation and automatic differentiation capabilities of FEniCS to produce the tangents needed by the implicit solution method.

The nonlinear deformation of a current-carrying elastic string is solved analytically. The computational model for a single fibril is validated using by comparison the static problem and verifying the convergence orders for higher-order finite element basis functions. The time stepping method for the fully coupled differential algebraic equation is verified using the convergence orders of the higher-order Runge-Kutta methods. The computational model is used to construct and determine the mechanical, thermal, and electrical properties of representative volume elements of textiles using dynamic relaxation to solve the decoupled fields in a static context. The dynamic deformation of a small electronic textile under various orientations of magnetic fields is solved. An electromagnetically-enhanced textile armor system impacted by a projectile is simulated.