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Resolution of a Conjecture in Nonlocal Strain-gradient Plasticity | | Jordan S. Cotler
; Felipe Hernandez
; | | Date: |
12 Oct 2013 | | Abstract: | Strain-gradient theories of elasticity have been successful in modeling
complex material behaviors including crystal plasticity and the superelasticity
of shape memory alloys. However, the traditional formulation of these theories
lacks a material length scale, and is thus incapable of capturing
experimentally observed size effects that play an important role in the
behavior of nano structures. As a result, a modified theory was proposed which
incorporates an intrinsic dissipative length scale. The theory predicts that
the solutions to the flow rule are global minimizers of the functional for
energy dissipation. We prove that there are no global minimizers of the
functional, thus resolving a previously unsolved conjecture. Our result shows
that the variational formulation of the theory is unviable. The non-existence
of a global minimizer appears to be related to the formation of infinitely fine
plastic boundary layers. | | Source: | arXiv, 1310.3426 | | Services: | Forum | Review | PDF | Favorites | |
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