Journal
INTERNATIONAL JOURNAL OF PLASTICITY
Volume 19, Issue 1, Pages 47-90Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/S0749-6419(01)00018-3
Keywords
viscoplastic material
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This study develops a general theory for small-deformation viscoplasticity based on a system of microforces consistent with its own balance; a mechanical version of the second law that includes, via the microforces, work performed during viscoplastic flow; a constitutive theory that allows for dependences on plastic strain-gradients. The microforce balance and the constitutive equations-suitably restricted by the second law-are shown to be together equivalent to a flow rule that accounts for variations in free energy due to flow. When this energy is the sum of an elastic strain energy and a defect energy quadratic, isotropic, and positive definite in the plastic-strain gradients, the flow rule takes the form of a second-order parabolic PDE for the plastic strain coupled to the usual PDE arising from the standard macroscopic force balance and the elastic stress-strain relation. The classical macroscopic boundary conditions are supplemented by nonstandard boundary conditions associated with viscoplastic flow. As an aid to solution, a weak (virtual power) formulation of the nonlocal flow rule is derived. (C) 2002 Elsevier Science Ltd. All rights reserved.
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