Effect of the Interface Roughness on the Elastic Moduli

Abstract

In this paper, we study the effect of the interface roughness on the elastic parameters of layered media. We consider the three-dimensional models of a layered medium with two different elastic materials inside and outside the layer. We generate the first class of models, where the interfaces between the layers are rough, and the elastic parameters of the inner layers are fixed. Then, the numerical upscaling technique is applied to estimate the effective stiffness tensor. Next, we downscale the stiffness tensor to reconstruct the new elastic parameters of the inner layer for the model of second class with flat interfaces; that is the uncertainty of the model geometry is mapped to the uncertainty of the stiffness tensor component for a fixed geometry of the model. After that, we propose an algorithm for extending the results of restoring the elastic tensors for arbitrary parameters of uncertainty applying the bilinear regression with respect to interface rough parameters and bilinear interpolation using two nearest points with respect to the physical parameters of the inner layers. Verification of the algorithm shows that the errors in the recovering covariance matrix do not exceed 7%; that is, it can be used to statistically simulate models of the second class with a flat interface by arbitrary values of the interface roughness and the physical parameters of the layers in the first class of models.

V. Lisitsa performed numerical simulation using the Supercomputer of the Saint-Petersburg Polytechnical University under the support of Russian Science Foundation grant no. 21-71-20003. D. Kolyukhin generated the models with rough interfaces under the support of Russian Science Foundation grant no. 19-77-20004. T. Khachkova did the statistical analysis of the results.