Open Access

ARTICLE

A Novel Multiscale Approach for Modelling Fracture Response of Heterogeneous Materials

Ante Jurčević¹, Tomislav Lesičar², Zdenko Tonković², Jurica Sorić^2,*

1 Institute of Processes Engineering, Faculty of Forestry and Wood Technology, University of Zagreb, Zagreb, Croatia
2 Institute of Applied Mechanics, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia

* Corresponding Author: Jurica Sorić. Email:

Computer Modeling in Engineering & Sciences 2026, 148(3), 7 https://doi.org/10.32604/cmes.2026.087199

Received 11 June 2026; Accepted 27 August 2026; Issue published 28 September 2026

Abstract

Accurate and computationally efficient numerical modelling of damage and fracture in heterogeneous materials requires the incorporation of a multiscale approach. However, the information transfer between the lower and upper scale with the presence of a specific damage algorithm represents a significant challenge. This paper presents a robust two-scale concurrent multiscale approach for modelling damage and fracture in brittle and ductile heterogeneous materials. The developed multiscale procedure utilises the self-consistent clustering analysis (SCA) at the microlevel, and a phase-field (PF) fracture method at the macrolevel in order to meet the main criteria of an accurate and computationally efficient concurrent multiscale damage algorithm. A particularly important characteristic of this framework is the full separation of the damage analysis from the microstructural domain, defined through the representative volume element (RVE). This decoupling allows for a stable, robust and objective numerical calculation of damage and fracture in heterogeneous materials. The computational efficiency of the proposed algorithm is demonstrated on simple and complex microstructures for several different geometrical specimens. The results indicate that the presented procedure captures macroscopic crack paths accurately, while maintaining a high level of computational efficiency in contrast to the classical ${\text{finite element}}^2$$({\text{FE}}^2)$ approach.

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Keywords

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