A Discontinuous Galerkin Method for Strain Gradient Plasticity.

[摘要] This dissertation presents a formulation of incompatibility based strain gradientplasticity utilizing discontinuous Galerkin finite element methods. Foundations ofthe classical theory of plasticity are laid out including a discussion of computationalimplementation and a series of numerical examples. A gradient plasticity constitutivetheory is developed based on micromechanical arguments emanating from dislocationtheory generalized into a continuum, tensorial treatment. The variationalstatement of the gradient plasticity equations utilizes concepts from discontinuousGalerkin methods to account for the continuity requirements dictated by the theory.Implementation of the method and solution procedures are discussed and numericalexamples are presented showing the well established size effect for materials at smallscales and mesh independence for a boundary value problem exhibiting localizationdue to softening.

[发布机构] University of Michigan

[效力级别] Mechanical Engineering

[关键词] Gradient Plasticity;Mechanical Engineering;Engineering;Mechanical Engineering and Scientific Computing