Two Dimensional Minimax Theory on Shear Stress and a General Classification Model for Nonlinear Constitutive Relations
A theoretical framework that provides a general representation of two-dimensional nonlinear constitutive relations is proposed. The theory is based upon minimization of maximum shear stress that links functional forms of energy dissipation and constitutive relation. Its application to a polynomial energy dissipation function leads to a power-law relationship between strain rate and stress magnitudes. On the basis of this relationship, a general categorization model for constitutive relations is developed and used to analyze forms commonly encountered in ice studies.
KeywordsConstitutive Relation Maximum Shear Stress Dissipation Function Constitutive Form Principal Strain Rate
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