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Explore a conference talk from the MFEM Workshop 2023 focusing on the Homogenized Energy Theory for solving elasticity problems. Delve into Zhang Chunyu's presentation from Sun Yat-Sen University, which addresses the limitations of classical continuum mechanics in handling highly inhomogeneous deformations. Discover how the proposed theory incorporates high-order microscopic deformation and refines strain gradient interpretation through averaged strain energy density. Learn about the theory's single scale parameter requirement and its application of variational approach and augmented Lagrangian method for deriving governing equations and numerical solutions. Examine the theory's ability to explain and predict phenomena unresolved by classical theory, such as size effects in deformation and stress singularity at crack tips. Gain insights into the advantages of using averaged strain energy for describing complex material behaviors and the effectiveness of the augmented Lagrangian method in solving high-order partial differential equations.
