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# Ben Vadala-Roth (UNC-CH), GMA Seminar

## April 3, 2017 @ 4:00 pm - 5:00 pm

**Title:** An Introduction to Incompressible Nonlinear Solid Mechanics

**Abstract:** This talk will survey the basics of Solid Mechanics and the Finite Element Method (FEM) for the numerical solution of the associated PDE’s. We will focus on Finite Strain theory, which examines large deformations of a continuum body. This, referred to as geometric nonlinearity, will be one source of the nonlinearity under consideration. In these cases, multiple reference frames must be considered and likewise multiple measures of stress become relevant. The other source of nonlinearity, material nonlinearity, arises when the constitutive model describing the relationship between stress and strain is a nonlinear one. Finally, when we make the assumption that deformations are locally volume preserving, or incompressible, we introduce a pressure variable which serves as a Lagrange multiplier to enforce the incompressibility constraint. We will approximately enforce this constraint in a way that resembles a penalty method and discuss issues of volumetric locking that arise due to over-constraining the discretized system.