Soft Body Dynamics

A foundational method where a deformable object is modeled as a network of point masses (nodes) connected by idealized springs. This creates a computationally efficient model for real-time applications.

• Spring Forces: Governed by Hooke's Law, where force is proportional to displacement from a rest length.
• Damping: Added to prevent perpetual oscillation and simulate energy loss.
• Applications: Widely used for real-time cloth simulation in games and basic soft tissue modeling due to its simplicity and speed.

A high-accuracy, computationally intensive technique that discretizes a continuous object into a mesh of small, simple elements (e.g., tetrahedra, hexahedra). It solves the equations of elasticity to compute stress and strain.

• High Fidelity: Provides physically accurate results for large deformations and complex material properties.
• Computational Cost: Requires solving large systems of equations, making it suitable for offline engineering analysis (e.g., crash testing, surgical simulation) rather than real-time.
• Elements: Common types include linear and quadratic elements, which trade off accuracy for computational expense.

A modern, stable approach that directly manipulates particle positions to satisfy constraints, bypassing the explicit computation of velocities and forces. It's known for its robustness and controllability.

• Constraint Projection: The solver iteratively moves particles to satisfy constraints like distance, bending, or volume preservation.
• Unconditional Stability: Lacks explicit forces, making it very stable with large time steps.
• Use Cases: Dominant in real-time visual effects for cloth, fluids, and character soft bodies in film and games.

A hybrid, mesh-free technique that combines Lagrangian particles (material points) with a background Eulerian grid. It excels at simulating materials undergoing extreme deformation and phase changes.

• Lagrangian Particles: Carry material properties like mass, velocity, and deformation gradient.
• Eulerian Grid: Used to calculate gradients and apply forces, avoiding mesh tangling issues.
• Complex Materials: The standard for simulating snow, sand, mud, and fracturing solids in high-end visual effects.

The physical behavior of a soft body is defined by its constitutive model, which relates stress to strain (deformation).

• Linear Elasticity (Hookean): Assumes a linear relationship; valid for small deformations. The basis for simple springs.
• Neo-Hookean & Mooney-Rivlin: Non-linear models for rubber-like materials (elastomers) that can undergo large, reversible stretches.
• Plasticity: Models permanent deformation, where material yields under stress and does not return to its original shape.
• Viscoelasticity: Combines elastic (solid) and viscous (fluid) properties, causing time-dependent, rate-sensitive deformation like in gels or flesh.

A major challenge in soft body simulation is detecting and resolving collisions, both with the environment and the body folding onto itself.

• Continuous Detection: Essential for thin, fast-moving soft bodies (like cloth) to prevent tunneling.
• Constraint-Based Response: Often handled by generating collision constraints (e.g., non-penetration) fed into the main solver (PBD, FEM).
• Spatial Hashing: Used to accelerate self-collision tests by only checking particles that are spatially close.
• Friction: Modeling static and kinetic friction is critical for realistic interaction with surfaces.

The Finite Element Method (FEM) is a high-accuracy numerical technique for simulating deformable bodies by discretizing a continuous object into a mesh of small, interconnected elements. It solves complex partial differential equations to compute stress, strain, and deformation under load.

• Primary Use: High-fidelity engineering analysis (e.g., crash tests, structural integrity).
• Trade-off: Computationally expensive, often not real-time.
• Example: Simulating the precise deformation of a car bumper in a virtual crash test.

Position-Based Dynamics (PBD) is a simulation method that directly manipulates the positions of particles or vertices to enforce constraints like stretching, bending, and volume preservation. It prioritizes stability and speed over physical accuracy.

• Primary Use: Real-time simulations for games and interactive applications (e.g., cloth, simple soft bodies).
• Key Feature: Highly stable and controllable, but not strictly momentum-conserving.
• Example: The realistic draping of a character's cape in a video game.

A Mass-Spring System models a deformable object as a network of point masses (nodes) connected by ideal springs. The dynamics are governed by Hooke's law, which applies forces based on spring deformation.

• Primary Use: Simple, efficient simulations of cloth, ropes, and basic soft tissues.
• Limitation: Can be overly "bouncy" and may require damping for stability.
• Example: Simulating a trampoline surface or a simple flag waving in the wind.

The Material Point Method (MPM) is a hybrid, mesh-free technique that combines Lagrangian particles (material points) with an Eulerian background grid. It excels at simulating materials undergoing extreme deformation and phase changes.

• Primary Use: Complex materials like snow, sand, mud, and melting solids.
• Key Feature: Naturally handles history-dependent materials and topological changes.
• Example: The realistic behavior of snow piling up and compacting under a robot's treads in a simulation.

Smoothed-Particle Hydrodynamics (SPH) is a Lagrangian, mesh-free method where a fluid (or other continuum) is represented by a set of discrete particles. Properties like density and pressure are smoothed over a local kernel function.

• Primary Use: Simulating fluids, gases, and sometimes granular materials.
• Characteristic: Naturally handles splashing and free surfaces but can be computationally heavy for large volumes.
• Example: Simulating hydraulic fluid leakage or the pouring of granular material like rice.

A Constraint Solver is the algorithmic core of a physics engine that resolves forces and impulses to satisfy defined rules or limits. For soft bodies, it enforces constraints like maximum stretch, bend stiffness, or volume conservation.

• Function: Iteratively calculates corrections to keep a simulated system within physical limits.
• Common Algorithms: Projected Gauss-Seidel (PGS) or Sequential Impulse solvers.
• Role in Soft Bodies: Critical for maintaining the shape and structural integrity of deformable objects during simulation.