### Monday, 11 October 2004 - 10:05 AM

### This presentation is part of : Graduate Student Competition

### A C1 Finite Element Multi-Field Solution of a Gradient Plasticity Model

**Robert J. Dorgan** and George Z. Voyiadjis. Louisiana State University, Department of Civil & Environmental Engineering, Baton Rouge, LA 70803
An overview of the formulation and numerical implementation of a gradient enhanced continuum plasticity model as a constitutive framework to model the nonlocal response of materials will be presented. The formulation uses a thermodynamically consistent framework to introduce material length scales through the second order gradients of the nonlinear isotropic and kinematic hardening variables. The gradient enhancements are investigated as powerful tools for modeling observations at the microscale that are not possible to interpret with classical deformation models. By the introduction of higher order gradients, our model will be able to predict the width of a shear band based on material constants, as opposed to local models where the loss of ellipticity causes the width of shear bands to be mesh dependent. Justification for the gradient theory is given by approximating nonlocal theory through a truncated Taylor expansion. The numerical implementation uses a small deformation finite element formulation and includes both the displacements and the plastic multiplier as nodal degrees of freedom, thus allowing the two fields to have different interpolation functions. Higher order elements (C1 elements) are used for the plastic multiplier to enforce continuity of the second gradients. The effectiveness of the model is evaluated by studying the mesh-dependence issue in localization problems through a 1D numerical example.

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