assumptions linear - straight line relationship between load and deformation (or stress and strain) elastic - deformation is fully recoverable when load is removed homogeneous - material composition is the same throughout isotropic - material properties are the same in all directions
lateral strain ε' - strain perpendicular to the applied load (dimensionless) ε' = Δd / d

 

elastic constants

the factors of proportionality (K, E, ν, and G) that relate elastic displacement of a material to applied forces

modulus of elasticity, E The measure of rigidity or stiffness of a metal; the ratio of normal stress, below the proportional limit, to the corresponding normal strain. Also known as Young's modulus. elemental Young's modulus
Poisson's ratio, ν The absolute value of the ratio of transverse (lateral) strain to the corresponding axial (normal) strain resulting from uniformly distributed axial stress below the proportional limit of the material. elemental Poisson's ratio negative Poisson's ratio 1, 2, 3, 4 getting more stiffness with less
shear modulus, G The ratio of shear stress to the corresponding shear strain for shear stresses below the proportional limit of the material. Also known as the modulus of rigidity. elemental shear modulus others
bulk modulus, K The measure of resistance to change in volume. Also known as compression modulus, hydrostatic modulus, and volumetric modulus of elasticity.

 

unit volume change (or dilation)

e - the change in volume divided by the original volume (units: in³, m³)

 e = ΔV / V_o = ε (1 - 2ν)