Title page for ETD etd-11132008-111446

Type of Document Master's Thesis
Author Pekmezi, Gerald
URN etd-11132008-111446
Title Nonlocal Gradient-Dependent Modeling of Plasticity with Anisotropic Hardening
Degree Master of Science in Civil Engineering (M.S.C.E.)
Department Civil & Environmental Engineering
Advisory Committee
Advisor Name Title
George Voyiadjis Committee Chair
Suresh Moorthy Committee Member
Wenjin Meng Committee Member
  • thin films
  • strain gradient plasticity
  • nonlocal plasticity
Date of Defense 2008-11-07
Availability unrestricted
This work is concerned with the formulation of the thermodynamics of nonlocal plasticity

using the gradient theory. The formulation is based on the nonlocality energy residual

introduced by Eringen and Edelen (1972). Gradients are introduced for those variables

associated with isotropic and kinematic hardening. The formulation applies to small

strain gradient plasticity and makes use of the evanescent memory model for kinematic

hardening. This is accomplished using the kinematic flux evolution as developed by Zbib

and Aifantis (1987). Therefore, the present theory is a four nonlocal parameter-based

theory that accounts for the influence of large variations in the plastic strain, accumulated

plastic strain, accumulated plastic strain gradients, and the micromechanical evolution of

the kinematic flux. Using the principle of virtual power and the laws of thermodynamics,

thermodynamically-consistent equations are derived for the nonlocal plastic yield

criterion and associated flow rule. The presence of higher-order gradients in the plastic

strain is shown to enhance a corresponding history variable which arises from the

accumulation of the plastic strain gradients. Furthermore, anisotropy is introduced by

plastic strain gradients in the form of kinematic hardening. Plastic strain gradients can be

attributed to the net Burgers vector, while gradients in the accumulation of plastic strain

are responsible for the introduction of isotropic hardening. The equilibrium between

internal Cauchy stress and the microstresses conjugate to the higher-order gradients

frames the yield criterion, which is obtained from the principle of virtual power.

Microscopic boundary conditions, associated with plastic flow, are introduced to

supplement the macroscopic boundary conditions of classical plasticity. The nonlocal

formulation developed here preserves the classical assumption of local plasticity, wherein

plastic flow direction is governed by the deviatoric Cauchy stress. The theory is applied

to the problems of thin films on both soft and hard substrates. Numerical solutions are

presented for bi-axial tension and simple shear loading of thin films on substrates.

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