Implementation of Some Non-Classical Mathematical Models of the Mechanics of a Deformable Body in the MathCad and MatLab System

On the basis of a non-classical approach to the solution of boundary value problems of statics, a mathematical model of deformation of elastic structures and their elements has been developed. This model is implemented in the MatLab system. It is shown that deformations can be determined by linear tensors of displacement gradients at any values of the latter.A mathematical model based on an equation expressing a quantitative relationship between the limiting values of the smallest and largest principal stresses is implemented in the MathCad system. The calculations performed showed that this equation determines all the stress states that lead to the destruction of the material. The envelope lines of the limiting stress circles of brittle and semi-brittle materials are constructed.In the MathCad system, the consistency of the generalized Hooke's law was tested based on a new criterion (equation of deformation diagram) derived for axial tension and compression of solid cylinders without the influence of the hypothesis of uniaxial stress state. Calculations in MathCad showed that this equation well describes the results of experiments throughout its entire length with the same values of constants of structural materials (steel 45, aluminum, duralumin).