A machine learning based material homogenization technique for in-plane loaded masonry walls

TL;DR

This work tackles efficient in-plane modeling of masonry by learning a macro-scale damage constitutive law directly from micro-scale simulations. It introduces a two-field damage framework and a data-driven homogenization workflow that uses a virtual laboratory to generate coupled strain-dissipated-work histories, isotropizes data, and optimizes macro-parameters Θ for a post-ML constitutive law. Validation on a Flemish bond masonry wall shows the macro model closely reproduces micro-scale responses for compression and shear compression, while offering significant computational savings. The approach advances practical analysis of masonry structures by enabling accurate macro-scale predictions without full micro-model resolution, with potential extensions to real experiments and displacement-field data.

Abstract

In recent years, significant advancements have been made in computational methods for analyzing masonry structures. Within the Finite Element Method, two primary approaches have gained traction: Micro and Macro Scale modeling, and their subsequent integration via Multi-scale methods based on homogenization theory and the representative volume element concept. While Micro and Multi-scale approaches offer high fidelity, they often come with a substantial computational burden. On the other hand, calibrating homogenized material parameters in Macro-scale approaches presents challenges for practical engineering problems. Machine learning techniques have emerged as powerful tools for training models using vast datasets from various domains. In this context, we propose leveraging Machine Learning methods to develop a novel homogenization strategy for the in-plane analysis of masonry structures. This strategy involves automatically calibrating a continuum nonlinear damage constitutive law and an appropriate yield criteria using relevant data derived from Micro-scale analysis. The optimization process not only enhances material parameters but also refines yield criteria and damage evolution laws to better align with existing data. To achieve this, a virtual laboratory is created to conduct micro-model simulations that account for the individual behaviors of constituent materials. Subsequently, a data isotropization process is employed to reconcile the results with typical isotropic constitutive models. Next, an optimization algorithm that minimizes the difference of internal dissipated work between the micro and macro scales is executed. We apply this technique to the in-plane homogenization of a Flemish bond masonry wall. Evaluation examples, including simulations of shear and compression tests, demonstrate the method's accuracy compared to micro modeling of the entire structure.

Figures (20)

• Figure 1: Overview of available micro modeling techniques for masonry. Showing the modeling background for the brick units, the mortar and a unit mortar joint interaction. Source: Kalkbrenner PhilippThesis.
• Figure 2: Yield surfaces for the tension equivalent stress $\tau^+$ and the compression equivalent stress $\tau^-$ in the two dimensional principal stress state. Original source Kalkbrenner PhilippThesis.
• Figure 3: Different available hardening/softening stress-strain curves.
• Figure 4: Overview of the machine learning homogenization technique, showing all included procedures at multiple scales and the machine learning technique as connector.
• Figure 5: Parameter optimization procedure $\mathcal{P}$.