Solfec-1.0 Theory Manual

Solfec-1.0 implements instances of the Non–Smooth Contact Dynamics Method 1, 2 and the Discrete Element Method. The software originated from the PhD research 3 and its further development 4. Thesis 3 can be used as an auxiliary “theory manual”. The intention behind this document is to provide a minimalist exposition of core computational methods and algorithms implemented in Solfec-1.0 and facilitate cross–referencing with the source code and the functionalities described in the User Manual. The theory manual comprises the following sections:

• Basics
• Kinematics
  • Rigid body
  • Pseudo–rigid body
  • Finite–element body
    • Shape functions
  • Implementation
• Dynamics
  • Rigid dynamics
  • Pseudo–rigid dynamics
  • Finite–element dynamics
  • Implementation
• Time integration
  • Rigid integration
  • Deformable integration
  • Implementation
• Constraints
  • From global to local velocity
    • Rigid kinematics
    • Pseudo–rigid kinematics
    • Finite–element kinematics
  • Time stepping with constraints
  • Implementation
• Local dynamics
  • Detailed multi–body notation
  • The \(\mathbf{W}\) matrix
  • Implementation
• Joints
  • Fixed point
  • Fixed direction
  • Prescribed displacement
  • Prescribed velocity
  • Prescribed acceleration
  • Rigid link constraint
  • Spring constraint
  • Implementation
• Contact points
  • Calculating volumetric intersection
  • Deriving contact points and normals
  • Contact sparsification
  • Broad phase contact detection
  • Geometric epsilon
  • Other implementation aspects
• Contact formulations
  • The frictional contact law
  • Projected gradient formulation
  • De Saxcé and Feng formulation
  • Non–smooth force equation formulation
  • Non–smooth velocity equation formulation
  • Semi–explicit penalty formulation
• Constraint solvers
  • Merit function
  • Gauss–Seidel solver
  • Projected Newton solver
  • Penalty Solver
  • Implementation
• Bulk materials
  • Kirchhoff – Saint Venant

1

CMAME, 177(3–4):329–349, 1999.

2

CMAME, 177(3–4):235–257, 1999.

3(1,2)

Koziara, PhD thesis, 2008.

4

IJNME, 87(1–5):437–456, 2011.