1. C. Wu, Universal meshes for branched crack propagation.

 

Illustration of the final conforming mesh for a crack with a quadruple junction. The original mesh is shown in grey. It can be observed, like the previous cases, that only a small fraction of the nodes are needed to perturb in order to obtain a conforming mesh.

2. Y. Li，Energy-based Mesh Adaption Method for the Phase Field Approach to Fracture

 

 

Mesh refinement results: by decreasing the energy tolerance μ_bc (b > c), finer mesh is obtained; the mesh successfully captured the crack without being influenced by the inner holes. The characteristic of the adaptive mesh is similar to what has been observed in Figure 4.5.

3. W. Yang, The successive node snapping scheme to obtain conforming meshes for evolving domains

4. Y. Liu, Phase Field Approach to Fracture: Homogenization-based Model Development and Manifold Learning Acceleration

Figure 4.11: Crack microstructures mapped into the manifold described by the first two coordinates of LLE. Representative microstructures are shown next to the square points. The solid line shows a continuous mode change of microstructures.

 

 

5. W. Lai, Phase field modeling of brittle fracture in an Euler–Bernoulli beam accounting for transverse part-through cracks

Fig14: Comparison between 1d-model and 2d bulk form model for a cantilevered beam with two initial cracks test

 

 

6. F. Jiang, Peridynamics: Mathematical Analysis and Coupling with Continuum Mechanics Model

A schematic diagram of the domain decomposition of a linear elastic body subjected to body force and traction

 

7. W. Ma, Numerical Simulation of Solid State Sintering Process with Proper Generalized Decomposition

c field of θ = 1000K (a)the traditional method, (b)the PGD method, and θ = 1400K (c)Traditional method, (d)PGD method after t = 0.03s sintering.

 

 

8. X. Suo,  A Hybrid Approach to Simulate Multiple Fracture Mechanisms in Fiber-reinforced Composites

different failure mechanisms of metal fiber-reinforced composites

 

interface debonding and matrix cracking of metal fiber-reinforced composites