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.

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

Where:

• \(\sigma\) 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.

Solvers

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:

• Solid mechanics conforming fractures solver
• Solid mechanics embedded fractures solver