An overview of the formulation of a gradient enhanced continuum coupled damage-plasticity model as a constitutive framework to model the nonlocal response of materials is presented. The formulation uses a thermodynamically consistent framework to introduce material length scales through the gradients of the hardening variables. The development of evolution equations for plasticity and damage is treated in a similar mathematical approach and formulation since both address defects such as dislocations for the former and cracks/voids for the later. 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, this model is able to predict the size of localized zones based on material constants, as opposed to local models where the loss of ellipticity causes the localized zones to be mesh dependent. Justification for the gradient theory is given by approximating nonlocal theory through a truncated Taylor expansion.
Formulation of a Gradient Enhanced Coupled Damage-Plasticity Model
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Voyiadjis, GZ, & Dorgan, RJ. "Formulation of a Gradient Enhanced Coupled Damage-Plasticity Model." Proceedings of the ASME 2004 International Mechanical Engineering Congress and Exposition. Applied Mechanics. Anaheim, California, USA. November 13–19, 2004. pp. 15-22. ASME. https://doi.org/10.1115/IMECE2004-59890
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