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Article summary:
1. The Material Point Method (MPM) has been used to solve complex engineering problems involving large deformations, multi-phase interactions and history-dependent material behaviour.
2. Different methods have been developed to mitigate the effect of grid-crossings, such as the Generalised Interpolation Material Point (GIMP) and Convected Particle Domain Interpolation (CPDI) methods.
3. This paper proposes an extension of BSMPM to unstructured triangulations using quadratic Powell–Sabin (PS) splines, which are C1-continuous and hence overcome the grid-crossing issue within MPM by design.
Article analysis:
The article is generally reliable and trustworthy in its reporting of the development of the B-spline Material Point Method (BSMPM). It provides a comprehensive overview of existing methods for mitigating grid-crossings, such as GIMP and CPDI, before introducing its own proposed extension to unstructured triangulations using PS splines. The article is well written and clearly explains the advantages of PS splines over piecewise linear Lagrange basis functions in terms of their C1 continuity and higher accuracy per degree of freedom.
The article does not appear to be biased or one-sided in its reporting, nor does it contain any promotional content or partiality towards any particular method or approach. All claims made are supported by evidence from previous research studies, although some counterarguments may have been unexplored or missing points of consideration may have been overlooked. Additionally, there is no mention of possible risks associated with using this method, so readers should be aware that these may exist but are not discussed in this article.