Abstract:

Recent advances in multifunctional materials are revolutionizing various fields, such as biomedicine, soft robotics and smart sensors. The ability to model and predict the behavior of these materials in different physical interactions is crucial. In this regard, multiphysics modeling is a valuable tool involving simulations in which multiple physical models or multiple simultaneous physical phenomena are present, and involves solving coupled systems of partial differential equations. In this work, a complete framework for modeling  multiphysics in materials based on the finite element method (FEM) is presented. The fundamental concepts of continuum mechanics and multiphysics coupling mechanisms, i.e., governing equations of mechanics, heat transfer and electromagnetism are explained and the capabilities of the FEM to discretize and solve these complex equations are highlighted, showing their application to address multiphysics challenges.

Three examples illustrate key computational elements in addressing relevant challenges, such as magneto-mechanical, electro-mechanical and thermo-electro-mechanical couplings. Emphasis is placed on the importance of taking into account the multiscale nature of these processes, from continuum-scale governing equations to particle- and pore-scale features, to accurately capture and understand the underlying mechanisms. The multiphysics models explore how magnetic fields influence the mechanical properties of magnetoactive materials, the interaction between electric fields and mechanical deformations in ferroelectric composites, and the interaction between thermal and electrical conductivity and mechanical loads in thermo-piezo-resistive materials, relevant for thermal management systems or smart actuators and sensors.