Boundary Element Models

Problems in continuum mechanics can be solved using the principles of calculus, but these are often limited by the equations we can use to describe the geometries of three-dimensional bodies. Alternatively, we can define complex geometric surfaces and discretize them into geometric elements. Then solve analytically solve for the response of each element, and superpose (vector or tensor addition) the response of each element. I use a program called Poly3D that allows complex shapes to be represented by triangular dislocations (www.IGEOSS.com).

Principals of Fracture Mechanics

Continuum mechanics describes the deformation of bodies in response to stress or displacements. In Fracture Mechanics we examine how heterogeneity in these bodies, represented by surfaces or materials of different properties and geometric interfaces, locally cause variation in stressand displacement.

Stress and displacement are related through constitutive laws (rheology) that mathematically define the response of the displacements in a body due to stress or the stress due to displacements.

Mechanics and Mechanisms of Deformation

The response of a rock to distortion resulting from displacements or stress result from the physical properties of the material, and to boundary conditions such as deformation rate, temperature, chemistry, etc. Deformation often changes the physical properties of a material by promoting chemical dissolution or precipitation, by introduce new surfaces by breaking chemical bonds, or by distorting chemical latices. Studying these responses and how they evolve is the study of deformation mechanisms.

Stress around a borehole

One application of these principals is to the deformation around a borehole in response to stress in the Earth. When a well is drilled, stress is concentrated at the borehole walls. Deformation results from this concentration of stress: (1) elastic deformations are recoverable, and (2) in some cases the concentration of stress exceeds the strength of the rock and it breaks, producing a permanent deformation. We use these deformations to infer the stresses that caused them and thus “measure” the stress that drives faulting and deformation at depth in the Earth.

Poly3D: www.IGEOSS.com

© Nicholas C. Davatzes

Last Updated: 2008/12