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Localization and nonlocalization are characterized as a measure of degrees of separation between two material points in material’s discrete framework and as a measure of unshared and shared information, respectively, manifested as physical quantities between them, in the material’s continuous domain. A novel equation of motion to model the deformation dynamics of material is proposed. The shared information between two localizations is quantified as nonlocalization via a novel multiscale notion of Local and Nonlocal Deformation-Gamuts or DG Localization and Nonlocalization. Its applicability in continuum mechanics to model elastoplastic deformation is demonstrated. It is shown that the stress–strain curves obtained using local and nonlocal deformation-gamuts are found to be in good agreement with the Ramberg–Osgood equation for the material considered. It is also demonstrated that the cyclic strain hardening exponent and cyclic stress–strain coefficient computed using local and nonlocal deformation-gamuts are comparable with the experimental results as well as the theoretical estimations published in the open literature.

A Novel Notion of Local and Nonlocal Deformation-Gamuts to Model Elastoplastic Deformation