A method is proposed for determining the stiffness and rheological characteristics of composite materials, which is based on minimizing the disagreement between experimental data and results of numerical simulations of deformation of hemispherical shells under explosive loading. The damping characteristics of randomly reinforced polymer materials are analyzed with the use of this method.Design of advanced structures frequently involves new composite materials possessing, in contract to metals, much better dissipative properties. As the composite material and the structure are normally created within a single technological process, it is necessary to determine the elastic and damping characteristics of the composite material during its operation within the structure. This problem has to be solved to construct adequate models of material and structure deformation for subsequent prediction of their behavior under prescribed loads. Conventional methods of solving this problems, which are based on testing the samples by the method of free decaying oscillations, are often inapplicable because the measured results are substantially affected by fixation conditions, method of excitation of oscillations, inhomogeneity of the stress-strain state, and technological difficulties in manufacturing the samples.One method of determining the parameters of deformation models is the direct use of experimental information obtained by loading structural elements. Such methods of identification of materials and models have been used to determine the effective elastic characteristics of composite materials on the basis of static experiments [1-4]. Among papers dealing with determining physical and mechanical characteristics in dynamic tests, we can note only the studies [5,6] where experimental results were analyzed and the damping characteristics of composite materials with explosive loading of rings and hemispherical shells were determined. The present paper continues these studies and describes a hybrid experimental and computational approach to determining the stiffness and rheological characteristics of a composite material by an example of deformation of dynamically loaded hemispherical shells. In essence, this method involves solving an inverse problem, which allows obtaining the characteristics of the material and model used in calculating a particular structure. The method of identification of the stiffness and rheological characteristics of composite materials is based on comparing information obtained in an experiment and the numerical solution of the direct problem of viscoelastic dynamic deformation of a hemispherical shell.1. We consider a hemispherical shell in the Gaussian curvilinear coordinate system α i (i = 1, 3) whose Lamé coefficients and principal curvatures areHere A 1 = R, A 2 = R sin α 1 , z 1 = z 2 = z = 1 + kα 3 , α 1 is the central angle determining the position of the point on the shell meridian, α 3 is the distance between the point and the mid-surface of the shell, and R is the radius of the hemispherical...
