Variable formation plasticity matrices of a three-dimensional body when implementing a step loading procedure

Abstract

Nowadays, the task of creating and improving computational algorithms for determining the stress-strain state (SSS) of technosphere objects and systems, taking into account the physically non-linear stage of operation of the material of structures and their elements, is quite relevant. A variational approach to the formation of a plasticity matrix at the loading step for a three-dimensional body is presented on the deformation theory of plasticity. A variant of obtaining the plasticity matrix using the operations of differentiating the covariant components of the stress tensor with respect to the covariant components of the strain tensor is considered. As an alternative to it, an option has been developed for the formation of a plasticity matrix at the loading step, based on the hypothesis of proportionality of the components of the deviator of stress increments to the components of the deviator of strain increments for three-dimensional bodies. The use of such option of forming a plasticity matrix at the loading step in software systems can significantly simplify the programming process and make it more understandable to potential users of computing systems in the design and reconstruction of technosphere objects and systems.