Contact Mechanics Solver

Governing Equations

GEOS contact solvers solve the the balance of linear momentum within a fractured solid, accounting for the continuity of stress across surfaces (i.e., fractures), i.e.

\nabla \cdot \sigma = 0 \\\\
[[\sigma]] \cdot \mathbf{n} = 0


  • \sigma is the stress tensor in the solid,

  • \mathbf{n} is the outward unit normal to the surface,

  • [[\sigma]] is the stress jump across the surface.

On each fracture surface, a no-interpenetration constraint is enforced. Additionally, tangential tractions can also be generated, which are modeled using a regularized Coulomb model to describe frictional sliding.


There exist two broad classes of discretization methods that model fractures as lower dimensional entities (eg, 2D surfaces in a 3D domain): conforming grid methods and nonconforming (or embedded) methods. Both approaches have been implemented in GEOS in the following solvers: