A damage model for granite subjected to quasi-static contact loading

TL;DR

This paper develops an anisotropic damage model for Bohus granite to simulate fracture patterns under quasi-static spherical indentation, successfully matching experimental results and enabling calibration of tensile strength variability.

Contribution

It introduces a damage model integrated with Drucker-Prager plasticity for granite, incorporating Weibull statistics to account for tensile strength variability.

Findings

Good agreement between simulation and experimental fracture patterns

Indentation tests can calibrate tensile strength distribution

Model captures initial fragmentation and force-penetration behavior

Abstract

An anisotropic damage model is employed in order to simulate the fracture pattern of Bohus granite under quasi-static spherical indentation loading. The chosen damage description is added to the previously employed Drucker-Prager plasticity model with variable dilation angle. The resulting constitutive model is implemented to simulate the behavior of Bohus granite under indentation up to the load capacity of the material. The initial fragmentation, corresponding to the first small load-drop in the force-penetration curve, is likely due to the high radial tensile stress state at or close to the contact boundary. Both predicted fracture pattern and force-penetration results from the numerical simulation are compared to experimental data and a good agreement is found. The variability in tensile strength of the material is included in the chosen damage model by taking advantage of Weibull statistics. In this work, it is suggested that indentation test results by themselves may be used to calibrate the statistical distribution of tensile strength at small size scales such as in indentation applications.