A simple Discrete-Element-Model of Brazilian Test

TL;DR

This paper introduces a simple statistical discrete-element model to simulate the Brazilian test, capturing key features like stress-strain behavior, system strength, and damage profiles, with results matching experimental observations.

Contribution

The model incorporates breakable elements with weakening effects, providing new insights into the failure process and scaling behavior in Brazilian test simulations.

Findings

System strength approaches 1/6 for uniform thresholds

System strength approaches 5/18 for Weibull thresholds

Damage profiles at maximum stress match experimental data

Abstract

We present a statistical model which is able to capture some interesting features exhibited in the Brazilian test. The model is based on breakable elements which break when the force experienced by the elements exceed their own load capacity. In this model when an element breaks, the capacity of the neighboring elements are decreased by a certain amount assuming weakening effect around the defected zone. We numerically investigate the stress-strain behavior, the strength of the system, how it scales with the system size and also it's fluctuation for both uniformly and weibull distributed breaking threshold of the elements in the system. We find that the strength of the system approaches it's asymptotic value $\sigma_c=1/6$ and $\sigma_c=5/18$ for uniformly and Weibull distributed breaking threshold of the elements respectively. We have also shown the damage profile right at the point when the stress-strain curve reaches at it's maximum and then it is compared with our experimental observations.