Stress distribution around a circular hole in transversely isotropic elastic bodies whose material moduli depend on density

In this paper, we study the stress distribution around a circular hole in transversely isotropic elastic bodies, whose material moduli depend on density under small deformations. Two special constitutive relations are considered within the framework of implicit elasticity to describe the nonlinear stress–strain response of such bodies. We studied the stress concentration problem in a thin plate under uniaxial tension. The constitutive relations presented herein exhibit stiffening or softening mechanical response under tension and compression depending on the values of the material parameters. While the stress distribution at the circumference of the hole resembles that of a classical linearized elastic body, the peak value of the normalized hoop stress at the hole is not constant and varies as a function of the applied stress. Furthermore, we perform a parametric study to understand the influence of different material parameters on the stress distribution around the hole.