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Functional forms of hardening internal state variables in modeling elasto-plastic behavior

Dorgan R. J., Voyiadjis G. Z.

Archives of Mechanics

2007

Vol. 59, nr 1

35-58

In this work use is made of functional forms of hardening state variables within a consistent thermodynamic formulation to model the elasto-plastic behavior of materials. The formulation is then numerically implemented using the developed plasticity model. In deriving the constitutive model, a local yield surface is used to determine the occurrence of plasticity. Isotropic hardening and kinematic hardening are incorporated as state variables to describe the change of the yield surface. The hardening conjugate forces (stress-like terms) are general nonlinear functions of their corresponding hardening state variables (strain-like terms) and can be defined basing on the desired material behavior. Various exponential and power law functional forms are studied in this formulation. The paper discusses the general concept of using such functional forms; however, it does not address the relevant appropriateness of certain forms to solve different problems. It is shown that, depending on the functions used, standard models known from the literature can be recovered. The use of this formulation in solving boundary value problems will be presented in future.

Gradient formulation in coupled damage-plasticity

Voyiadjis G. Z., Dorgan R. J.

Archives of Mechanics

2001

Vol. 53, nr 4-5

565-597

This work provides a consistent and systematic framework for the gradient approach in coupled damage-plasticity that enables one to better understand the effects of material inhomogeneity on the macroscopic behavior and the material instabilities. The idea of multiple scale effects is made more general and complete by introducing damage and plasticity internal state variables and the corresponding gradients at both the macro and mesoscale levels. The mesoscale gradient approach allows one to obtain more precise characterization of the nonlinearity in the damage distribution; to address issues such as lack of statistical homogeneous state variables at the macroscale level such as debonding of fibers in composite materials, crack, voids, etc., and to address nonlocal influences associated with crack interaction. The macroscale gradients allow one to address non-local behavior of materials and interpret the collective behavior of defects such as dislocations and cracks. 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 latter. Computational issues of the gradient approach are introduced in a form that can be applied using the finite element approach.