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For someone with high-school level understanding of classical Newtonian mechanics, what would be the best way forward to learn Continuum Mechanics and things li

For someone with high-school level understanding of classical Newtonian mechanics, what would be the best way forward to learn Continuum Mechanics and things like MPM, etc.? Any book/course recommendations?

semi-extrinsic 2y ago
Continuum mechanics in itself is a very different subject from particle-based methods to approximate continuum mechanics, like MPM. To actually learn continuum mechanics you need first a good understanding of vector calculus. But this is not necessary at all for using and tweaking particle based methods.
- HexDecOctBin 2y ago
  I see. What are the pre-requisites for understanding and playing around with MPM then? It's very hard to figure this out as someone who hasn't studied physics for a decade.
  - semi-extrinsic 2y ago
    Disclaimer: I'm not an MPM expert at all, but I work in computational fluid dynamics. I would suggest to start with the paper I link to below. First skim read it to understand the structure. Then try to follow in detail the parts that interest you most, and play with the code they provide. If you encounter concepts you don't understand, which are necessary for progressing, go look those up on Wikipedia or Google Books (for textbooks). https://www.researchgate.net/publication/336796234_Material_point_method_after_25_years_theory_implementation_and_applications https://www.researchgate.net/publication/336796234_Material_... And don't be discouraged by the math notation. It's mostly just shorthand for things you probably understand very well in code. For example the capital sigma (sideways M) with a letter "p" or something underneath simply means "loop over the range of the index p, and sum up the following expression for the different values of the index". The capital delta (triangle pointing up) means "difference", for example delta-t is the increment from one time step to the next. The upside-down delta is the Nabla, which means gradient, which means derivative in each spatial dimension.
    - HexDecOctBin 2y ago
      Thanks!
obsoletehippo 2y ago
http://alexey.stomakhin.com/research/mpm.html http://alexey.stomakhin.com/research/mpm.html
cyber_kinetist 2y ago
For a nice overview: https://nialltl.neocities.org/articles/mpm_guide https://nialltl.neocities.org/articles/mpm_guide

semi-extrinsic 2y ago

Continuum mechanics in itself is a very different subject from particle-based methods to approximate continuum mechanics, like MPM. To actually learn continuum mechanics you need first a good understanding of vector calculus. But this is not necessary at all for using and tweaking particle based methods.

HexDecOctBin 2y ago
I see. What are the pre-requisites for understanding and playing around with MPM then? It's very hard to figure this out as someone who hasn't studied physics for a decade.
- semi-extrinsic 2y ago
  Disclaimer: I'm not an MPM expert at all, but I work in computational fluid dynamics. I would suggest to start with the paper I link to below. First skim read it to understand the structure. Then try to follow in detail the parts that interest you most, and play with the code they provide. If you encounter concepts you don't understand, which are necessary for progressing, go look those up on Wikipedia or Google Books (for textbooks). https://www.researchgate.net/publication/336796234_Material_point_method_after_25_years_theory_implementation_and_applications https://www.researchgate.net/publication/336796234_Material_... And don't be discouraged by the math notation. It's mostly just shorthand for things you probably understand very well in code. For example the capital sigma (sideways M) with a letter "p" or something underneath simply means "loop over the range of the index p, and sum up the following expression for the different values of the index". The capital delta (triangle pointing up) means "difference", for example delta-t is the increment from one time step to the next. The upside-down delta is the Nabla, which means gradient, which means derivative in each spatial dimension.
  - HexDecOctBin 2y ago
    Thanks!

obsoletehippo 2y ago

http://alexey.stomakhin.com/research/mpm.html http://alexey.stomakhin.com/research/mpm.html

cyber_kinetist 2y ago

For a nice overview: https://nialltl.neocities.org/articles/mpm_guide https://nialltl.neocities.org/articles/mpm_guide