А.А. Трещев NONLINEAR REFINEMENT OF THE DEFORMATION MODEL OF ORTHOTROPIC MATERIALS, THE RIGIDITY OF WHICH DEPENDS ON THE TYPE OF STRESS STATE

Abstract

As a result of numerous experimental and theoretical studies, it has been established that when deforming both traditional and new structural materials, which are polymers, composites and synthetic structures used in construction, mechanical engineering, and power engineering devices, complicated mechanical properties manifest themselves.Most of these materials have an orthotropic structure complicated by the dependence of deformation and strength characteristics on the type of stress state, which can be interpreted as deformation anisotropy. These properties contradict the generally accepted theories of deformation. Therefore, a number of models have been specially developed for such materials over the past 56 years, taking into account the complicated properties of materials. However, all of them have disadvantages and certain contradictions with the fundamental rules for constructing equations of state. The previous works of the authors of the presented studies establish general approaches to the construction of energetically nonlinear deformation models of composite materials with recommendations for calculating their constants based on a wide range of experiments.It turned out that the set of necessary experiments should include experiments on complex stress states, most of which are technically unrealizable. In another work of the authors in 2021, using the tensor space of normalized stresses, the deformation potential was formulated in a quasi-linear form, constructed in the main axes of orthotropy of materials, for determining constants, which is sufficient for the data of the simplest experiments. Along with the obvious advantages of the introduced potential, it has one drawback, which is to replace real nonlinear diagrams with direct rays with minimal error. Despite the unconditional adequacy of the quasi-linear potential, the use of this level of approximations leads to quantitative errors.Therefore, simplified nonlinear equations of state for composite materials are proposed here, the simplest experiments are sufficient to determine the material functions of which. These equations are based on the general laws of mechanics, on the basis of which the constants of material polynomials for a carbon-graphite composite are calculated, taking into account the Drucker constraints.

Keywords

• material functions, nonlinear deformation anisotropy, dimensional orthotropy, defining equations, strain and stress tensors, least squares method, main axes of orthotropy