Colloquium: "Numerical approximation of prestrained plates"

Speaker: Diane Guignard, Texas A&M University

Abstract: We study the elastic behavior of prestrained plates relevant for instance in plastic deformation, natural growth of soft tissues or manufactured polymer gels. When actuated, the prestrained plates reduce their internal stresses by undergoing - possibly large - deformations. The mathematical model consists of a geometric nonlinear fourth order minimization problem with a nonlinear constraint. A discrete gradient flow is proposed to decrease the system energy and is coupled with discontinuous Galerkin finite elements for the plate deformation.

In this talk, we introduce the mathematical model and derive a reduced problem. We then describe the proposed numerical method along with several essential properties, such as convergence and control of the prestrain defect. We conclude with several insightful simulations which exhibit the great variety of shapes achievable with this technology.

Host: Renato Feres

Tea will be served @ 3:30pm in room 200.