Abstract
As a direct extension of the asymptotic spatial homogenization method we develop a temporal homogenization scheme for a class of homogeneous solids with an intrinsic time scale significantly longer than a period of prescribed loading. Two rate-dependent material models, the Maxwell viscoelastic model and the power-law viscoplastic model, are studied as an illustrative examples. Double scale asymptotic analysis in time domain is utilized to obtain a sequence of initial-boundary value problems with various orders of temporal scaling parameter. It is shown that various order initial-boundary value problems can be further decomposed into: (i) the global initial-boundary value problem with smooth loading for the entire loading history, and (ii) the local initial-boundary value problem with the remaining (oscillatory) portion of loading for a single load period. Large time increments can be used for integrating the global problem due to smooth loading, whereas the integration of the local initial-boundary value problem requires a significantly smaller time step, but only locally in a single load period. The present temporal homogenization approach has been found to be in good agreement with a closed-form analytical solution for one-dimensional case and with a numerical solution in multidimensional case obtained by using a sufficiently small time step required to resolve the load oscillations.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 22 November 2001 / Accepted: 21 May 2002
Rights and permissions
About this article
Cite this article
Yu, Q., Fish, J. Temporal homogenization of viscoelastic and viscoplastic solids subjected to locally periodic loading. Computational Mechanics 29, 199–211 (2002). https://doi.org/10.1007/s00466-002-0334-y
Issue Date:
DOI: https://doi.org/10.1007/s00466-002-0334-y