While it is not the intend of this manual to give you a primer on the Math and Physics behind the Material Point Method, it is; however, essential to understand the basic concepts and working principles behind this new approach in simulating continuum body dynamics in thinkingParticles.
This section of the manual is intended to describe the MPM method as artist friendly and as easy as possible. Simplified terms and broad assumptions are used to clarify the main issues/culprits you might be facing as an artists. If needed, all the esoteric scientific mambo jumbo can be found in the reference section, found at the very end.
In short - the Material Point Method (MPM) is a method to calculate and track and simulate large object deformations. Another method that uses similar approaches is Particle-In-Cell (PIC), for example. However, when it comes to highly deformable body simulations, MPM is preferred as it offers great advantages over a pure Lagrangian or Eulerian method, .
This new simulation method in thinkingParticles uses Particles and a Grid at the same time to solve for the deformation or flow of particles in a simulation.
Generally Speaking these things happen in our MPM solver:
A volume of an object (3D space), is filled with Particles.
The space those particles take, is subdivided into voxels (cubes) which is referred to as "the Grid"
Particles 'carry' along, various material information. Things like Mass, Position, Speed and Stress factors
Particles continuously transfer their information to the Grid
After each simulation step, the Grid is deleted and the Particles start over to transfer their information into a fresh Grid
In-between those steps the actual 'Magic' of solving the data, is taking place.
While the above explanation of steps is a simplified one, it is in general what happens and all you really need to know to start working and creating amazing artwork!
The key culprits to take away here are: we have 2 discrete entities, interacting and transferring information. Both of these entities, Particles and Grid undergo their very own limitations. The Grid is created in a fixed equidistant pattern, the resolution or distance between grid cells influences the accuracy, stability and processing time of the simulation.
The particles on the other hand, are unbound and can be created, in theory, in an unlimited amount and with infinite small space between each other. Creating large amounts of particles also needs more memory and processing power. Like everything in life, it is about finding your balance to generate a successful outcome.
A pure Smoothed Particle Hydro Dynamics (SPH) solver, as it is used in thinkingParticles, offers many advantages and it can even 'forced' into creating non classical 'fluid' like simulations. Viscoelastic simulations are one example that can be easily done within thinkingParticles.
However, SPH has specific limitations and is not really meant to solve things like crack propagation, clumping or physically accurate tearing effects. Material properties like Sand,Snow,Rubber or cloth like materials are hard to achieve with SPH solvers. SPH solvers shine on their 'unbound' or unlimited space paradigm, SPH solvers have the advantage to work with an unlimited amount of particles and space. However, increasing particle amounts results usually in astronomical processing times for solving the simulation accurately.
MPM uses real world material properties modeled after real physical parameters seen in materials like bending metals, bursting ceramic or flowing sand. Highly elastic and extremely deformable objects can also be simulated with MPM solvers. In general, simulations are based on real world material properties that simulate the appearance of pressure points and stress propagation within a volume until it is deemed to be no longer stable and it breaks or bursts into pieces.
This stress tensor calculations along with enhanced pressure point calculations allow MPM to accurately simulate a wide variety of material properties. Multi-Physics simulations are also a prime candidate for MPM solvers.
With the release of thinkingParticles 7.0, you can witness the first breed of MPM Solvers with a fully procedural thinkingParticles integration.
To get an in depth explanation of the Math and Theory behind MPM check out this Wiki Entry
Real world physics parameters; learn about: Young's Modulus
Real world material properties: Poissson's Ratio