The bulk modulus relates hydrostatic compressive pressure to fractional volume compression. In isotropic three-dimensional linear elasticity, the spherical part of the stress tensor is , so uniform dilation has strain energy density . Positive bulk modulus and positive shear modulus make the isotropic elastic stiffness tensor positive on nonzero symmetric strains.
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The bulk modulus, often denoted by the symbol \( K \), is a measure of a material's resistance to uniform compression. It quantifies how incompressible a substance is; the higher the bulk modulus, the less compressible the material. Mathematically, the bulk modulus is defined as the ratio of the change in pressure to the relative change in volume of the material.