Criticism of the law of deformation ugent for elastoplastic materials and an alternative to it | Mekhanika | kompozitsionnykh | materialov i konstruktsii

Criticism of the law of deformation ugent for elastoplastic materials and an alternative to it



An empirical UGent model for an elastoplastic material with hardening is analyzed. The deformation curve, according to this model, is composite. The definition area is divided into three segments. On the first and third, the Ramberg-Osgood law with different exponents is postulated, and on the second, a curve is postulated that smoothly connects the curves on the first and third segments so that, on the whole, the curve is differentiable. It is shown here that this brilliant idea of the authors of the UGent law was implemented by them with several logical flaws. To correct these shortcomings, the spline is modified so that the deformation law on the second segment contains a linear combination of two linear polynomials and two power functions with different exponents included in the structures of the deformation laws on the first and third segments. Also, new conditions have been formulated that must be satisfied by the law of deformation on the third segment at its initial and final points. It is shown that there are just enough new arbitrariness to satisfy all the identified requirements for a differentiable three-link spline of the deformation curve. From a sample of 582 experimental points for steel 35, ten significant physical parameters of the proposed model were determined. Two of them, the coordinates of the strength point on the true curve in the strain-stress coordinates, are selected as normalizing factors. The remaining eight are determined from the minimum requirement of the objective function by the gradient descent method. The total quadratic deviation is selected as the objective function. The corresponding theoretical deformation curve with the established parameters is constructed. It is shown that the accuracy of the proposed model is quite high. The standard deviation of the constructed curve from the sample of experimental points is 1.8%.