How does an increase in Poisson's ratio affect the calculated shear modulus of an isotropic, linearly elastic material, assuming Young's modulus remains constant?

For an isotropic, linearly elastic material, a specific relationship exists between its fundamental elastic properties: Young's modulus, shear modulus, and Poisson's ratio. An isotropic material possesses uniform properties in all directions, meaning its mechanical response is independent of the direction of applied stress. A linearly elastic material deforms proportionally to the applied load and fully recovers its original shape upon load removal. Young's....