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Stress concentration due to an elliptic hole in a porous elastic plate

We study the state of stress and strain in a square plate containing an elliptic hole in the case of a porous elastic solid undergoing small strain, using a constitutive relation that has been put into place recently to describe the response of such solids undergoing small strains. We carry out the study by solving the problem numerically. We verify that our numerical solutions agree with those for the classical linearized elastic solid when certain appropriate material parameters are set to zero. We show that the stress concentration factor in the case of the porous elastic solid can be much higher, as much as 300% of the stress concentration in the case of the classical linearized elastic solid, when the aspect ratio is sufficiently small, depending on the values of certain material parameters. The difference between the stress concentration for the porous solid increases as the aspect ratio (the ratio of the major axis to the minor axis) decreases. By allowing the aspect ratio of the ellipse to go to zero, we can obtain the state of stress and strain adjacent to a crack in the square plate; however, in this limit, the strains would greatly exceed the assumption under which the constitutive theory is derived.