An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically (i. e. , non-permanently) when a force is applied to it. In Physics, a force is whatever can cause an object with Mass to Accelerate. The elastic modulus of an object is defined as the slope of its stress-strain curve in the elastic deformation region:
where λ (lambda) is the elastic modulus; stress is the force causing the deformation divided by the area to which the force is applied; and strain is the ratio of the change caused by the stress to the original state of the object. Slope is used to describe the steepness incline gradient or grade of a straight line. During testing of a material sample the stress–strain curve is a graphical representation of the relationship between stress, derived from measuring the load applied on the Stress is a measure of the average amount of Force exerted per unit Area. If stress is measured in pascals, since strain is a unitless ratio, then the units of λ are pascals as well. An alternative definition is that the elastic modulus is the stress required to cause a sample of the material to double in length. This is not realistic for most materials because the value is far greater than the yield stress of the material or the point where elongation becomes nonlinear, but some may find this definition more intuitive.
Specifying how stress and strain are to be measured, including directions, allows for many types of elastic moduli to be defined. The three primary ones are
Three other elastic moduli are Poisson's ratio, Lamé's first parameter, and P-wave modulus. Poisson's ratio ( ν) named after Simeon Poisson, is the ratio of the relative contraction strain, or transverse strain (normal to In Linear elasticity, the Lamé parameters are the two parameters λ also called Lamé's first parameter. In Linear elasticity, the P-wave modulus M also known as the longitudinal modulus, is one of the elastic moduli available to describe isotropic homogeneous
Homogeneous and isotropic (similar in all directions) materials (solids) have their (linear) elastic properties fully described by two elastic moduli, and one may choose any pair. Isotropy is uniformity in all directions Precise definitions depend on the subject area Given a pair of elastic moduli, all other elastic moduli can be calculated according to formulas in the table below.
Inviscid fluids are special in that they cannot support shear stress, meaning that the shear modulus is always zero. Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress. This also implies that Young's modulus is always zero. In Solid mechanics, Young's modulus (E is a measure of the Stiffness of an isotropic elastic material
|Homogeneous isotropic linear elastic materials have their elastic properties uniquely determined by any two moduli among these, thus given any two, any other of the elastic moduli can be calculated according to these formulas.|