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Thermodynamic Based Higher-Order Gradient Plasticity Captures Size and
Interfacial Effects at the Micron and Submicron Length Scales
Masoud K. Darabia and Rashid K. Abu Al-Rubb
Zachry Department of Civil Engineering, Texas A&M University
College Station, TX 77843, USA
amasouddrb@neo.tamu.edu, brabualrub@civil.tamu.edu
Abstract
A thermodynamic based higher-order gradient plasticity theory that enforces microscopic boundary
conditions at interfaces and free surfaces is presented. The elastic strain tensor, the effective plastic
strain, and its gradient are assumed as the state variables. It is shown that interfacial effects have a
profound impact on the scale-dependent yield strength and strain hardening of micro/nanosystems even
under uniform stressing. All of the thermodynamic conjugate forces are decomposed into energetic
components related to the Helmholtz free energy and dissipative components related to the rate of
energy dissipation. Moreover, a procedure based on maximum energy dissipation principle is proposed
for deriving the dissipative components directly from the rate of energy dissipation. A systematic way
for derivation of different local/nonlocal plasticity/viscoplasticity yield surfaces is also proposed.
Finally, the model capabilities in capturing size and interfacial hardening effects in metal matrix
composites, interfacial effects on the yield strength of thin metal films on substrates, and nonuniform
size-dependent deformation of micropillars under uniform stressing are illustrated through several
examples.
Introduction
It is well-known by now that the classical (local) plasticity theories cannot be used successfully in
either eliminating the meshdependency when simulating the strain localization problems or predicting
the experimentally observed size-effect (i.e. smaller is stronger) at the micron and submicron length
scales. Therefore, in the last decade there has been a significant interest by the mechanics community in
formulating higher-order gradient plasticity theories based on principle of virtual work/power and/or
the laws of thermodynamics. Most of these theories have been shown to completely or partially solve
the problem of strain localization and/or size-dependent problems at the micron and submicron length
scales. However, very few of these theories correctly estimate the rate of energy dissipation. The
correct estimation of rate of energy dissipation requires the decomposition of thermodynamic conjugate
forces into energetic and dissipative components as it is shown in the pioneering works of Shizawa and
Zbib [1] and Gurtin [2]. Also, a lower-order gradient plasticity theory could not predict any boundary
layer effect, which makes them unsuitable for modeling interfacial effects in thin films, particle-matrix
interfacial effects in nanocomposites, and nonuniform and scale-dependent response of micropillars
under uniform stressing. Hence, this work is an attempt to enhance the gradient-dependent plasticity
theories by including the interfacial effects and make them more thermodynamically consistent by
decomposing all thermodynamic conjugate forces into energetic and dissipative components and
subsequently deriving the dissipative components directly from the definition of the rate of energy
dissipation.
33 ABSTRACTS