Factors Influencing Quasistatic Modeling of Deformation and Failure in Rock-Like Solids by the Smoothed Particle Hydrodynamics Method

X W Tang,Y D Zhou,Y L Liu

doi:10.1155/2013/852875

Abstract

As a Lagrangian mesh-free numerical method, the Smoothed Particle Hydrodynamics (SPH) method has been traditionally applied for modeling astrophysics, fluid flows and thermal problems, and there has been a growing interest in applying SPH to solid deformation problems. However, the potential of this method for quasistatic analysis of rock-like brittle materials has not been clearly explored. The major aim of this paper is to investigate the effects of key factors in SPH on the load-deformation response of rock-like solids, including variations in the particle approximation theory, the magnitude of the smoothing length and its variable method. Simple uniaxial compression (UC) loading conditions were chosen, and a series of numerical studies were carried out sequentially on an idealized elastic case and an actual test of marble material. Typical results of the axial stress-strain response from infinitesimal to finite deformation as well as the progressive failure process for the marble tests are given and the influences of various factors are discussed. It is found that only provided proper choices of particle momentum equation and the smoothing length parameter, the SPH method is capable for favorably reproducing the deformation and progressive failure evolution in rock-like materials under quasistatic compression loads.

Highlights

Smoothed Particle Hydrodynamics (SPH) is a mesh-free, adaptive, Lagrangian particle method that can be used to obtain solutions to systems of partial differential equations
The paper is organized as follows: firstly, a brief introduction to the fundamentals of SPH is provided, forming the basis of following parametric numerical studies and discussions; secondly, the main part of this paper presents a series of numerical investigation into the effects of varied options in SPH on the uniaxial compression response, in which two typical cases are chosen, an idealized elastic case of a cubic specimen and an inelastic case considering possible damage and failure of marble materials; in the final part, a summary of the parametric studies and some conclusive discussions are provided
It can be observed that generally all the predictions using SPH method with varied options in Table 1 compare favorably with the one-element finite elements (FEs) solution at an early stage with relatively small top compression, lower than 1 mm for the studied model, whilst more noticeable discrepancy is shown at a later stage with greater compressions applied

Summary

Introduction

SPH is a mesh-free, adaptive, Lagrangian particle method that can be used to obtain solutions to systems of partial differential equations. There has been a growing interest in applying SPH for modeling solid deformation problems in a broad range of applications. Most of these studies were focused on the high velocity impact, blasting, and granular flow types of problems, such as the study of the deformation of a metal cylinder resulting from the normal impact against a rigid surface [8, 9], modeling of impact induced fractures in brittle solids [10, 11], and the simulation of broken-ice fields floating on the water surface and moving under the effect of wind forces [12].

Objectives

Results

Conclusion