The concept of multifractal elasticity

TL;DR

This paper introduces a new concept of multifractal elasticity for random structures, providing constitutive equations and potential applications in predicting material behavior and estimating fractal dimensions from experimental data.

Contribution

It proposes a novel elasticity theory for multifractal structures based on phenomenological laws, expanding understanding of complex microstructured materials.

Findings

Derived constitutive equations for multifractal elasticity

Potential to predict mechanical behavior of complex materials

Method to estimate fractal dimensions from elastic data

Abstract

A new type of elasticity of random (multifractal) structures is suggested. A closed system of constitutive equations is obtained on the basis of two proposed phenomenological laws of reversible deformations of multifractal structures. The results may be used for predictions of the mechanical behavior of materials with multifractal microstructure, as well as for the estimation of the metric, information, and correlation dimensions using experimental data on the elastic behavior of materials with random microstructure.