Application of the averaging method in the problem of long loading of a layered elastic-creeping composite
Abstract
Application of the averaging method in the problem of long loading of a layered elastic-creeping composite
Incoming article date: 05.10.2021The paper presents analytical estimates of the proximity of solutions to boundary value problems for elastic-creeping layered composite materials widely used in technology under long-term loading, and also gives the corresponding averaged model for such materials. The estimates show the possibility of using the averaged model over a long time interval for the problem of loading by a constantly acting force. Previously, this statement was confirmed by numerical experiments comparing solutions of boundary value problems for an effective (averaged) model and direct numerical calculation using the original model for a highly inhomogeneous layered material. Analytical estimates are based on previously obtained estimates of the proximity of solutions to stationary problems of elasticity theory. For the one-dimensional model considered in this work, the following property is established: if the constitutive relations for various phases of the composite material are written as dependences of deformations on stresses, then the coefficients for the same form of writing the constitutive relations of the averaged model are obtained as simple weighted average values of similar coefficients for individual phases.
Keywords: layered composite materials, creep theory, averaging method, evaluating the efficiency of the averaging method, asymptotically long time interval