Propagation of a spherical wave in elastoplastic medium with complex equations of state

The propagation of a spherical wave in the soil is solved in an analytically inverse way for soils with more complex equations of state. The results are obtained to propagate a spherical shock wave in soil with a more complex equation of state for the shape change in the medium. The study shows that taking into account the nonlinear elastic shock waves of the annular stress leads to an increase compared to the elastic medium. Note that in using a complicated equation of state of the soil, a spherical shock wave propagates in the soil, behind the front of which, in the disturbance region, the medium is unloaded.

Large deformations of a cylindrical tube with prestressed coatings

General theoretical relations for calculating the redistribution of the preliminary irreversible strain field during unloading or elastic loading of a medium are obtained for the nonlinear multiplicative gradient model of large elastic-plastic deformations. It is shown that the dynamics of elastic shock waves does not depend directly on the previously accumulated plastic strains. A formula for the plastic-strain rotation tensor is obtained. It is shown that rigid rotation of plastic strains under elastic shock waves can be jump-like. All results are obtained for the general case of model relations of isotropic media and are valid for both compressible and incompressible materials.

Учет влияния полей остаточных деформаций в современных физико-механических технологиях обработки конструкционных материалов

A strict determination of the mechanisms of redistribution of previously accumulated irreversible strains as a result of additional elastic shock actions on the material is given for a nonlinear gradient model of large elastic–plastic strain. It is shown that this redistribution is limited by rigid transport and rotation of the plastic strain tensor. Formulas for a change in the initial components of the plastic strain tensor in elastic waves are derived. It is shown that the preliminary plastic field affects the dynamics of further reversible strain as one of the factors of formation of the initial quasi-static elastic field, which cannot be obtained in a purely elastic process.