Biomedical Engineering (BME) 3 Practice Test

Incompressible deformation means volume stays constant as the material deforms. The volume element after deformation is the same as before, so there’s no change in volume even when the shape changes. Because mass is conserved, this also means density doesn’t change during deformation. For isotropic, linear-elastic materials, incompressibility corresponds to Poisson’s ratio approaching 0.5, not zero. So the idea that Poisson’s ratio equals zero isn’t correct for incompressible behavior. The relation between Young’s modulus and shear modulus is E = 2G(1 + ν); with ν near 0.5, this gives E ≈ 3G, so the two moduli are not equal. Finally, density would not increase with compression in an incompressible material, since volume doesn’t contract and mass stays the same. So the statement that volume remains constant during deformation is the correct description.