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 modulus, denoted as E, quantifies a material's stiffness or resistance to elastic deformation under axial (tensile or compressive) stress, indicating its resistance to stretching or shortening. The shear modulus, denoted as G, measures the material's resistance to elastic deformation under shear stress, reflecting its ability to resist twisting or changes in shape without a change in volume. Poisson's ratio, denoted as ν (nu), describes the ratio of transverse strain to axial strain, indicating how much a material contracts or expands laterally when stretched or compressed longitudinally. For an isotropic, linearly elastic material, these properties are mathematically related by the formula: G = E / (2 (1 + ν)). If Young's modulus (E) remains constant, and Poisson's ratio (ν) increases, the value of (1 + ν) in the denominator will increase. Consequently, the entire denominator, (2 (1 + ν)), will increase. Since the shear modulus (G) is obtained by dividing a constant Young's modulus by an increasing denominator, the calculated shear modulus (G) will decrease.