Peridynamic model of poroelasticity based on Hamilton's Principle
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Porous media theories play an important role in many branches of engineering. Despite significant advances, the existing theories suffer from many limitations and drawbacks when dealing with problems with discontinuities like fractures. The difficulties inherent in these problems arise from the basic incompatibility of spatial discontinuities with the partial differential equations that are used in the classical porous media theories. Peridynamics, a relatively new nonlocal formulation of continuum mechanics based on integral equations, provides a path forward in modeling spatial discontinuities in the field of solid mechanics. In this thesis, the nonlocal formulation of peridynamics is successfully combined with finite deformation poroelasticity. First, a thorough derivation of finite deformation poroelasticity based on extended Hamilton's principle is conducted. Then we include the integral formulation of peridynamic theory when deriving the nonlocal momentum balance equations for poroelasticity once again using extended Hamilton's principle. To complete our nonlocal poroelasticity theory, we also develop a new class of peridynamic constitutive models. Finally, the correspondence of our peridynamic poroelasticity theory to the classical finite deformation poroelasticity theory is shown by demonstrating that our peridynamic equations can be reduced to the classical momentum balance equations for poroelasticity if smooth and homogeneous deformation is assumed.