Approximation-evaluation tests for a stress-strain state of deformable solids

When analyzing some applied problems, it is of interest to obtain certain statistical criteria. These criteria could determine the moment when a monotonically increasing quantity, given in the form of a table and whose analytical form is unknown, changes the linear increasing to the nonlinear one. In this paper, we consider “approximation-evaluation tests”, which allows us to determine the point, when the type of increase in the monotone sequence of numerical parameters of deformable solid, characterizing its stress-strain state, is changed from linear to parabolic. This point could be considered as a harbinger of the strength loss. This criterion is based on the comparison of the quadratic errors of the linear and the incomplete parabolic approximations. Approximating functions are constructed locally, not overall values of the sequence, but only over several of them. These points are located in the left half-neighborhood of the investigated point. An inverse problem is solved in which the critical values of the sequence are calculated, for which the quadratic errors of the linear and incomplete parabolic approximations are equal. The example shows that a simple comparison of finite differences cannot be used to determine the point at which a linear increase becomes parabolic.