A Discontinuous Galerkin Method for Strain Gradient Plasticity.

Abstract

This dissertation presents a formulation of incompatibility based strain gradient plasticity utilizing discontinuous Galerkin finite element methods. Foundations of the classical theory of plasticity are laid out including a discussion of computational implementation and a series of numerical examples. A gradient plasticity constitutive theory is developed based on micromechanical arguments emanating from dislocation theory generalized into a continuum, tensorial treatment. The variational statement of the gradient plasticity equations utilizes concepts from discontinuous Galerkin methods to account for the continuity requirements dictated by the theory. Implementation of the method and solution procedures are discussed and numerical examples are presented showing the well established size effect for materials at small scales and mesh independence for a boundary value problem exhibiting localization due to softening.