Plastic microstress for a defect energy dependent on Burgers tensor
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Mathematics Unit, Distance Learning Institute, University of Lagos, Akoka, Nigeria
Submission date: 2018-01-14
Acceptance date: 2018-09-08
Publication date: 2019-04-15
Journal of Theoretical and Applied Mechanics 2019;57(2):343–351
This work presents an extended form of the Aifantis strain-gradient plasticity theory through dependence of the plastic free energy on the Burgers tensor. The constraints of codirectiona- lity for the deviatoric stress and irrotationality of the plastic distortion are assumed. These provide the basis for expressing the work done by the microstress conjugate to the Bur- gers tensor as the sum of the work done by the microscopic hyperstress vector and scalar. The principle of virtual power is used to establish the microforce balance, which provides the relationship between the resolved shears, plastic microstress and the microscopic hyper- stresses. The microforce balance, when augmented with relevant constitutive relations that are consistent with the free-energy imbalance, results in a non-local flow rule depicted as a nonlinear second order partial differential equation in terms of the accumulated plastic strain with concomitant boundary conditions. It is shown in this work that the plastic mi- crostress is purely dissipative and cannot account for backstress whenever the defect energy is dependent on the Burgers tensor.
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