Nonlocal strength criteria for the calculation of critical loads in bended structural elements, taking into account the nonlinearity of the material deformation

Abstract

The destruction of artificial materials (plexiglas, ebonite) in non-uniform stress fields was experimentally investigated. Testing of one batch of samples is carried out using various methods: three-point and clean (four-point) bending of rectangular cross-section beams, Brazilian test (method of splitting a cylinder along a generator). The comparison of the strength characteristics obtained by the Brazilian test with the uniaxial tensile strength, as well as with the tensile strength during bending tests. Experiments on the fracture of beams on a three-point flexural test revealed higher values of ultimate tensile stress than those of a four-point flexural test. The processing of the experimental data obtained by the Brazilian test is carried out using various non-local strength criteria. A sequential analysis of the applicability of the criteria used in the determination of failure loads is carried out. Computer simulation was performed using the finite-element method for the destruction of a cylinder by splitting along a generator, three-point and four-point bending flexural test of a beam in a geometrically nonlinear formulation, taking into account the non-linearity of the material deformation diagram. The problem was solved in the updated Lagrangian formulation taking into account the physical and geometric nonlinearity based on the governing equations of the hypoelastic material. A comparative analysis of the numerical, analytical and experimental results is carried out. A qualitative correspondence was obtained between the experimental data and the results of numerical calculations.