Вычисление коэффициентов определяющих соотношений нелинейно-упругих материалов с использованием эволюционных алгоритмов

Abstract

Abstract. The possibility of parameter identification for constitutive relations of materials based on uniaxial stretching of a nonlinear-elastic prismatic sample and on inflating a hollow cylinder has been studied. The experiments are modeled using the semi-inverse method of nonlinear theory of elasticity. To describe the mechanical properties of the studied objects, the potentials of compressible nonlinearly elastic media - Blatz and Ko material, and Murnaghan model are used. In the first stage, a series of direct problems are solved. Analytical expressions for the load-elongation dependence are used for the stretching problem. The three-dimensional problem of a cylinder inflation is reduced to a nonlinear boundary value problem for an ordinary second-order differential equation for the function of the radial displacement of cylinder points. In all cases, load diagrams are constructed based on the specified parameters of the nonlinearly elastic models, which are subsequently considered as initial data for the inverse problem of parameter identification. The problem is reduced to finding the minimum of the objective function which is defined as a least squares function. Two evolutionary algorithms were used for analysis: the Squirrel search algorithm (SSA), based on the model of the foraging behaviour of southern flying squirrel population, and the differential evolution algorithm (DE) from the SciPy library. Reliable identification of material parameters of models was shown using evolutionary algorithms based on load diagrams of samples, including condition of artificial noise of "experimental" data.