The analytical and numerical solution of the problem of stretching a system of parallel elements with random strength characteristics taking into account the postcritical stage of deformation and rigidity of the loading system

The work studies the influence of the postcritical stage of deformation and rigidity of the loading system on the deformation of the material using the example of the system of parallel-connected elements that have the random strength characteristics and postcritical stage of deformation. In this case, by taking into account the rigidity of the loading system we predict the moment of destruction of the system of the deformable elements at the postcritical stage caused by the loss of stability of the deformation process. A new analytical solution makes it possible to calculate the systems with a large number of elements. Strength reserves are determined by taking into account the postcritical stage of deformation. A high rigidity of the loading system has a positive effect on the stable deformation process. An algorithm of the developed program that allows solving a similar problem for a finite number of elements is presented. We determine how a number of structural elements influences the form of the loading diagrams of the system of parallel elements and calculated strength values. The proposed approach makes it possible to carry out the refined calculations to predict the mechanical behavior of the systems of elements that are characterized by the manifestation of supercritical deformation with the known statistical spreads of characteristics. The solution can be applied to predict the mechanical behavior of the unidirectional composite materials, in particular, basalt plastics, and their structural elements, such as a fiber bundle or fabric. A comparison of the obtained results of the solutions with the experimental data of stretching the basalt filament samples and bundles of them is carried out. A good convergence between the developed model and experimental results is shown. We confirm the rationality of taking into account the postcritical stage of the material deformation in the considered problems of deformation and fracture.