Mechanics of Deformable Porous Media
This course provides a systematic introduction to the mechanics of deformable porous media from a variational perspective. Beginning with continuum mechanics fundamentals, participants will learn how variational principles – rooted in calculus of variations and energy methods –provide a unified framework for deriving governing equations in elasticity, plasticity, and fracture. The course progresses from small-strain linear elasticity through dissipative systems and phase-field fracture modeling to finite strain hyperelasticity. The course ends by showing how theory applies to pore-scale modeling, and what challenges and insights arise from probing deformation and failure on pore-scale geometries derived from imaging data. These insights simplify computations significantly in some cases but complicate them in others.
What Will You Learn?
• How variational and energy methods (e.g., virtual work, dissipation potentials) provide a unified framework for deriving governing equations of solid mechanics.
• Computational approaches to plasticity, fracture, and large deformations, including phase-field modeling of crack propagation.
• How pore-scale modeling on geometries derived from imaging data reveals insights and challenges related to deformation and failure in porous materials.
