Finite element method, Galerkin methods, Multigrid methods (Numerical analysis)
A one-dimensional set of nonlinear time-dependent partial differential equations developed by Acharya (2010) is studied to observe how differing levels of applied strain affect dislocation walls. The framework of this model consists of a convective and diffusive term which is used to develop a linear system of equations to test two methods of the finite element method. The linear system of partial differential equations is used to determine whether the standard or Discontinuous Galerkin method will be used. The Discontinuous Galerkin method is implemented to discretize the continuum model and the results of simulations involving zero and non-zero applied strain are computed. The evolution in time of functions for plastic deformation, dislocation density, and internal shear stress are plotted and discussed.
Breeden, Ja'Nya; Drake, Dow; and Puri, Saurabh, "Simulating Dislocation Densities with Finite Element Analysis" (2021). REU Final Reports. 23.