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Elastic constants are specific parameters that quantify the stiffness of a material in response to applied stresses and are fundamental in defining the elastic properties of materials. These constants form the elements of the stiffness matrix in tensor notation, which relates stress to strain through linear equations in anisotropic materials.
Temporary deformation is also called elastic deformation, ... E is a material constant called Young's ... the value of engineering stress can be expressed by ...
The constant is called the modulus of elasticity (or just modulus) while its reciprocal is called the modulus of compliance (or just compliance). There are three postulates that define the ideal elastic behaviour: (1) the strain response to each level of applied stress (or vice versa) has a unique equilibrium value;
Young's modulus is the slope of the linear part of the stress–strain curve for a material under tension or compression.. Young's modulus (or Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise.
The elastic components, as previously mentioned, can be modeled as springs of elastic constant E, given the formula: = where σ is the stress, E is the elastic modulus of the material, and ε is the strain that occurs under the given stress, similar to Hooke's law.
This is known as perfect elasticity, in which a given object will return to its original shape no matter how strongly it is deformed. This is an ideal concept only; most materials which possess elasticity in practice remain purely elastic only up to very small deformations, after which plastic (permanent) deformation occurs.
The stiffness, , of a body is a measure of the resistance offered by an elastic body to deformation. For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as k = F δ {\displaystyle k={\frac {F}{\delta }}} where,
The torsion constant or torsion coefficient is a geometrical property of a bar's cross-section. It is involved in the relationship between angle of twist and applied torque along the axis of the bar, for a homogeneous linear elastic bar. The torsion constant, together with material properties and length, describes a bar's torsional stiffness.