Integral equation and sensitivity analyses of creep behavior for PVDF thin films

Abstract

This paper presents an analytic study of a linear viscoelasticity constitutive equation involving stress, strain and creep compliance while simultaneously correcting a previously reported investigation [Vinogradov, A.M., Schmidt, V.H., Tuthill, G.F., Bohannan, G.W., (2004). Damping and electromechanical energy losses in the piezoelectric polymer PVDF. Mechanics of Materials 36, 1007–1016]. The constitutive equation is presented as a linear, weakly-singular Volterra integral equation of the second kind in the stress variable. An analytic solution is developed, using the Laplace transform technique, for acquiring the stress history based on a specified creep compliance function and input strain. The time-dependent stress solution is expressed in terms of an infinite series involving the provided strain history. An example is studied involving constant strain input. This example permits an aposteriori error estimate for the stress based on the truncated series. Finally, a novel first-order sensitivity analysis is presented to assist in developing experiments for estimating the parameters associated with the compliance function. Using the proposed first-order sensitivity analysis, it is possible to investigate how the uncertainty associated with these parameters propagate into the stress history.