Post-buckling analysis of a hyperelastic layer-substrate structure under compression

Abstract eng:
The compression of a hyperelastic layer-substrate structure is considered in our paper. We consider the whole structure is relatively thin so that it will buckle when the external loads reach certain critical value. Considering the effect of Young’s modulus between layer and substrate, the asymptotic model equations are obtained by use of the combined series-asymptotic expansion method. Both the linear and weak non-linear analysis are carried out in this paper. The good agreements of critical stretch from our model and the exact one shows the validity of our model. Then, we unitizing the solvability condition technique to obtain the analytic solutions of two cases, i.e., the ratio of Young’s modulus between layer and substrate is of O(1) or large. Corresponding numerical solutions verified that our approach can obtain quite good results and from the analytic formulas of strains, deflections, one can easily see how the parameters affect the quantities.

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