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Article summary:
1. The article discusses the use of the material point method (MPM) for simulating complex multiple branched cracking problems.
2. MPM has advantages of both Lagrangian and Eulerian methods, making it suitable for analysing strongly non-linear numerical problems such as large deformations, discontinuities, and moving boundaries.
3. Various failure criteria have been proposed to represent the destruction of a material and the development of cracks, including bifurcation analysis, statistical failure criterion, and damage criterion.
Article analysis:
The article is generally reliable and trustworthy in its discussion of the use of the material point method (MPM) for simulating complex multiple branched cracking problems. The article provides an overview of various experimental studies that have been conducted on the internal crack propagation of various rock materials under compression, as well as grid-based methods such as finite element method (FEM) and meshless methods which have been applied to solve problems that cannot be solved by experiments and theories. It then introduces MPM as a new particle method which adopts both Lagrange and Euler descriptions, providing details on its advantages over other methods in terms of flexibility, accuracy, efficient processing ability, etc.
The article also provides an overview of various failure criteria that have been proposed to represent the destruction of a material and the development of cracks, including bifurcation analysis, statistical failure criterion, and damage criterion. However, it does not provide any detailed information on these criteria or their potential biases or sources. Additionally, there is no mention of possible risks associated with using these criteria or any counterarguments to them.
In conclusion, while this article provides a comprehensive overview of MPM for simulating complex multiple branched cracking problems and various failure criteria that can be used to represent crack propagation in rocks materials under compression, it does not provide any detailed information on these criteria or their potential biases or sources nor does it explore any counterarguments or possible risks associated with them.