The phase-field model with an auto-calibrated degradation function based on general softening laws for cohesive fracture

Abstract

Phase-field models have become popular to simulate cohesive failure problems because of their capability of predicting crack initiation and propagation without additional criteria. In this paper, new phase-field damage model coupled with general softening law for cohesive fracture is proposed based on the unified phase-field theory. The commonly used quadratic geometric function in the classical phase-field model is implemented in the proposed model. The modified degradation function related to the failure strength and length scale is used to obtain the length scale insensitive model. Based on the analytical solution of a 1-D case, general softening laws in cohesive zone models can be considered. Parameters in the degradation function can be calibrated according to different softening curves and material properties. Numerical examples show that the results obtained by the proposed model have a good agreement with experimental results and the length scale has a negligible influence on the load-displacement curves in most cases, which cannot be observed in classical phase-field model.

The fast multipole method–accelerated line integration boundary element method for 3D heat conduction analysis with heat source

“…Further, as a common phenomenon in the engineering field, the heat conduction analysis with heat source also deserves attention. For example, the concrete structures can generate heat by themselves during the process of pouring and curing, and this heating process may lead to fractures (Liu et al ., 2020; Wang et al ., 2020a, b) and damage the concrete structures (De Belie et al ., 2018; Shi et al ., 2020). So far, some research is done on heat conduction analysis considering heat source on the fundamental of the BEM.…”

A high-performance boundary element method and its applications in engineering

“…On the other hand, the fracture theory is much more mature for continuously based methods, including FEM [268][269][270] , extended finite element method (XFEM) [271,272] , phase-field method [114,171] , and BEM [273,274] , and therefore can be applied to obtain the internal stress distribution within a particle. Several continuous-discontinuous methods have been proposed to fulfil the breakage requirements.…”

“…Gravity is a basic load for every engineering structure on earth and it can bring inner stress and strain changes to engineering structures, and the gravity load is a key factor for the design of engineering structures, like buildings and dams. The thermal load [166][167][168] , which has drawn much attention of many researchers for a long time, is a vital factor that leads to fractures [169,170] or damage in structures [114,171] , especially those mass concrete structures, like concrete dams, concrete foundation, column structure in buildings and so on. Hence, it is rather important to obtain thermal stress under different conditions in numerical simulation accurately.…”

“…As a common phenomenon in engineering, heat conduction analysis with heat sources also deserves attention. For example, concrete structures can generate heat by themselves during the process of pouring and curing, and this heating process may lead to fractures [4,114,115] and break engineering structures [116,117] . So far, some research are done on heat conduction analysis considering heat source on the fundamental of the BEM.…”