# Adaptive Multiscale Homogenization of the Lattice Discrete Particle Model for the Analysis of Damage and Fracture in Concrete

## TL;DR

This paper introduces an adaptive multiscale homogenization approach coupling meso-scale discrete particle models with macro-scale finite element models to efficiently simulate damage and fracture in concrete, reducing computational costs.

## Contribution

It develops a novel adaptive framework that dynamically integrates homogenized RVE into finite element analysis based on a failure criterion, improving efficiency in damage localization simulations.

## Key findings

- Significant reduction in computational cost during damage localization
- Effective coupling of meso-scale models with macro-scale analysis
- Successful numerical validation of the adaptive homogenization scheme

## Abstract

This paper presents a new adaptive multiscale homogenization scheme for the simulation of damage and fracture in concrete structures. A two-scale homogenization method, coupling meso-scale discrete particle models to macro- scale finite element models, is formulated into an adaptive framework. A continuum multiaxial failure criterion for concrete is calibrated on the basis of fine-scale simulations, and it serves as the adaptive criterion in the multiscale framework. Thus, in this approach, simulations start without assigning any material Representative Volume Element (RVE) to the macro-scale finite elements. The finite elements that meet the adaptive criterion and must be entered into the multiscale homogenization framework are detected on the fly. This leads to a substantial reduction of the computational cost especially for loading conditions leading to damage localization in which only a small portion of the FE mesh is enriched with the homogenized RVE. Several numerical simulations are carried out to investigate the capability of the developed adaptive homogenization method. In addition, a detailed study on the computational cost is performed.