Phase field model of brittle fracture based on polynomial degradation function

Abstract

In order to make the phase field model better describe the brittle fracture process of materials, a polynomial degradation function is given in this paper, and the elastic limit stress and strain corresponding to the phase field model, the critical phase field value, and the critical stress and strain formulas are deduced so as to quantitatively describe the fracture change process of materials. From the formula of the critical phase field value, it can be found that the value decreases with the increasing of number of functions continuously, which indicates that the damage degree of the model decreases gradually when it is damaged. The influence of the degradation function on the fracture process of the material is analyzed by a numerical example. When the function order is small, the phase field model can keep the linear elastic response process well. With the increasing of number of functions, the decreasing trend of the function increases at the beginning, which will aggravate the damage trend inside the material and cause the material to damage earlierly, indicating that the change trend of the degradation function will affect the failure process of the material to a certain extent.

Keywords

• phase field model
• brittle fracture
• polynomial
• degradation function
• failure