Mathematical formulation of a constitutive Lambert-type differential equation for predicting the dynamic response of materials

M. D. Monsia

Abstract


This paper presents a mathematical formulation of a constitutive Lambert-type differential equation on the basis of the stress decomposition theory in order to predict the dynamic behavior of a variety of materials. The expansion of the nonlinear elastic spring force law required in terms of a generalized form of the Newton’s binomial function of deformation provided, under relaxation of stress conditions, the time versus deformation variation as a Chapman-Richards-type growth model. Numerical applications carried out demonstrated successfully the ability of the model to reproduce the S-shaped response of viscoelastic materials. It has been shown that an increase of viscoelastic characteristics, increases significantly the sensitivity of the model, which becomes flexible enough for experimental data fitting.


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Published: 2012-07-01

How to Cite this Article:

M. D. Monsia, Mathematical formulation of a constitutive Lambert-type differential equation for predicting the dynamic response of materials, Engineering Mathematics Letters, Vol 1 (2012), 18-31

Copyright © 2012 M. D. Monsia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Engineering Mathematics Letters

ISSN 2049-9337

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