Endochronic model of plasticity generalizing Sanders theory

The Sanders’s theory of plasticity and quasi-statistical variant of incremental plastic theory with isotropic and kinematic hardening in Novozhilov’s version are generalized in the frameworks of the endochronic approach. The constitutive equations of endochronic theory of inelasticity including the ideas of Sanders, Novozhilov and Valanis are formulated. The relations for the calculation of stresses and strains in uniaxial active and reversible material loadings are proposed. The formulas  are obtained by using the elementary average principle of local values and by the simplest set of material constants and functions. Two types of initial conditions  are considered in the calculations. The results of numerical modeling of inelastic  material behavior under uniaxial active and cyclic loadings are presented. The results are compared with each other and with original Sanders’s theory. The similarity and differences between the generalized endochronic theory and the Sanders’s  version are demonstrated. Several unusual manifestations of inelastic material behavior that require further theoretical analysis, calculations on the complex loading  paths and the experimental verification are noted.

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