Variational Principles for Hydraulic Fracturing

A new application of an energy rate variational principle for hydraulic fracturing processes is introduced. The formation structural, fracture mechanics, and fracture fluid flow responses are integrally coupled in this treatment. This unified principle, with various specialized forms, provides a formal framework for the study of continuum as well as discrete models. The applicability of the developed formulations is demonstrated by deriving time-explicit solutions for a penny-shaped model and comparing numerical results with corresponding responses from Lagrangian and finite element methods.