On the extended use of Backus average

TL;DR

This paper extends Backus averaging, originally for linear elastic layered media, to finitely deformed materials using two approaches: nonlinear elasticity and prestress, with the first approach showing promising results.

Contribution

It introduces a novel extension of Backus average to handle large deformations in layered structures through two different theoretical approaches.

Findings

The nonlinear elasticity approach can be successfully applied with some limitations.

The prestress-based approach provides an alternative method for deformed layered media.

The extended method broadens the applicability of Backus averaging to more realistic geophysical scenarios.

Abstract

Backus (1962) developed his technique for homogenization of a layered structure solely within the context of linear elastic theory. In this paper we propose an extended use of Backus average for finitely deformed materials of a layered structure. We attempt to use two different approaches to account for large deformations. The first approach utilizes the connections between linear and nonlinear transverse elasticity. For the second approach we use a formulation based on prestress in the material. We conclude that the first approach, although with some limitations, can be used successfully.