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Response of power-law-viscoelastic and time-dependent materials to rate jumps

Published online by Cambridge University Press:  31 January 2011

A.H.W. Ngan  and
B. Tang
A.H.W. Ngan*
Affiliation:
Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, People’s Republic of China
B. Tang
Affiliation:
Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, People’s Republic of China
*
a) Address all correspondence to this author. e-mail: hwngan@hku.hk
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Abstract

Nonlinear viscoelastic problems are in general not analytically solvable. However, it is shown here that, for any viscoelastic materials describable by a constitutive law with linear elastic and (in general) nonlinear viscous elements arranged in any network fashion, such as the Maxwell or standard linear solid arrangements, it is always possible to eliminate the viscous terms by replacing the displacement, strain, and stress fields of the problem by the jumps in rates of these fields. After the viscous terms are eliminated, the problem is reduced to a linear elastic problem defined on the same spatial domain and with the same elastic constant as in the original viscoelastic problem. Such a reduced elastic problem is analytically solvable in many practical cases, and the solution yields a relation between jumps in the load rate and the displacement rate, pertinent to the boundary conditions in the original problem. Such a relation can often be used as the basis for an experimental scheme to measure the elastic constants of materials. The material can be time- or strain-dependent, and the value of the elastic constant measured corresponds to the time instant or the strain value when the jump in load or displacement rate is implemented.

Keywords

Elastic propertiesNanoindentationViscoelasticity
Type
Articles
Information
Journal of Materials Research , Volume 24 , Issue 3 , March 2009 , pp. 853 - 862
Copyright
Copyright © Materials Research Society 2009

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