Stress concentration due to the bi-axial deformation of a plate of a porous elastic body with a hole

Summary: The study focuses on the mathematical properties of a novel implicit constitutive relation where stress and linearized strain appear linearly, recently introduced to describe the elastic response of porous metals and materials like rocks and concrete. The mixed variational formulation involves displacement, deviatoric stress, and spherical stress as three independent fields, with the well-posedness of the quasi-linear elliptic problem being ensured through one-parameter dependence, regularization, and the application of the Browder-Minty existence theorem. An analytical solution to the nonlinear problem under constant compression/extension is also presented.