Doctor of Philosophy (PhD)
Civil and Environmental Engineering
The thermodynamically consistent formulation and the subsequent numerical implementation of a gradient enhanced continuum coupled damage-plasticity model as a constitutive framework to model ill-posed localization problems is presented. By the introduction of "nonlocal," gradient-enhanced measures in the plasticity potential function and yield criterion and in the damage potential function and damage criterion, the proposed model introduces microstructural characteristic material length scales which allows the size of localized zones to be predicted based on material constants, as opposed to local models where the loss of ellipticity causes the localized zones to be mesh dependent.
The gradient model proposed introduces non-linear functions for the hardening terms and can account for a wide range of material models. Gradients of hardening terms are found directly by operating on the respective hardening terms, and numerical methods are used to compute these gradients. The gradient enhanced measure used in this work consists of a combination of the local measure and the local measure's Laplacian as justified by an approximation to nonlocal theory; however, through the expansion of various gradient terms in this nonlinear hardening plasticity model, gradients of both odd and even orders are introduced into the constitutive model.
The numerical implementation uses a small deformation finite element formulation and includes the displacements, the plastic multiplier, and the damage multiplier as nodal degrees of freedom, thus allowing the three fields to have different interpolation functions. The displacement field is interpolated using standard continuous elements; higher order elements (cubic Hermitian) are used for the plastic multiplier and for the damage multiplier to enforce continuity of the second order gradients. The effectiveness of the model is evaluated by studying the mesh-dependence issue in localization problems through numerical examples. Numerical results from this work are qualitatively compared with numerical simulations by other authors for different formulations.
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Dorgan, Robert J., "A nonlocal model for coupled damage-plasticity incorporating gradients of internal state variables at multiscales" (2006). LSU Doctoral Dissertations. 2991.
George Z. Voyiadjis