Criterion for Imminent Failure During Loading—Discrete Element Method Analysis

Wojciech Dȩbski,Alex Hansen,Srutarshi Pradhan

doi:10.3389/fphy.2021.675309

Abstract

It has recently been reported that the equal load sharing fiber bundle model predicts the rate of change of the elastic energy stored in the bundle reaches its maximum before catastrophic failure occurs, making it a possible predictor for imminent collapse. The equal load sharing fiber bundle model does not contain central mechanisms that often play an important role in failure processes, such as localization. Thus, there is an obvious question whether a similar phenomenon is observed in more realistic systems. We address this question using the discrete element method to simulate breaking of a thin tissue subjected to a stretching load. Our simulations confirm that for a class of virtual materials which respond to stretching with a well-pronounced peak in force, its derivative and elastic energy we always observe an existence of the maximum of the elastic energy change rate prior to maximum loading force. Moreover, we find that the amount of energy released at failure is related to the maximum of the elastic energy absorption rate.

Highlights

Fracturing, breaking, or more generally fragmentation of solid materials is a common physical processes that we meet in our daily lives
The simulations provide us with macroscopic quantities, like total elastic energy absorbed by the sample and stored in inter-particle bonds, deformation of the sample, number of broken bonds, and total force acting on the upper, moving up plate
Considering the posed question whether the signature of imminent failure predicted by the Fiber Bundle Model (FBM) method is visible in the Discrete Element Method (DEM) simulations, we can positively answer yes

Summary

INTRODUCTION

Fracturing, breaking, or more generally fragmentation of solid materials is a common physical processes that we meet in our daily lives. In the current application we have further enhanced this similarity by choosing in DEM simulations a classical, elasticbrittle interaction model It assumes that bonds joining nearneighborhood particles are represented by perfectly elastic “springs” which break if extended over some critical value, just like the fibers in the FBM model. If particles are randomly packed, the inter-particle bonds are randomly orientated in space, in contradiction to the FBM fibers which are always parallel to the external load Comparing both approaches we would point out that DEM inherently includes geometry of the analyzed body, while FBM does not. In this work we explore the possibility of verifying the appearance of the maximum of an elastic energy absorption rate prior to the catastrophic failure predicted by the FBM [5] is visible in DEM simulations To answer this question, we have designed a series of numerical simulations of stretching a thin tissue.

FIBER BUNDLE MODEL

Strength and Stability of the Fiber Bundle Model

Energy Variation and Warning Sign of Collapse

DISCRETE ELEMENT METHOD

NUMERICAL EXPERIMENT—SETUP AND DATA PROCESSING

RESULTS

Uncertainty Analysis

Breaking Mechanisms

Signature of Imminent Failure

DISCUSSION AND CONCLUSIONS

DATA AVAILABILITY STATEMENT