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Stress-strain curve: Plot the calculated stress versus the applied strain to create a stress-strain curve. The slope of the initial, linear portion of this curve gives Young's modulus. Mathematically, Young's modulus E is calculated using the formula E=σ/ϵ, where σ is the stress and ϵ is the strain. Shear modulus (G)
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. It is the modulus of elasticity for tension or axial ...
The stress and strain can be normal, shear, or a mixture, and can also be uniaxial, biaxial, or multiaxial, and can even change with time. The form of deformation can be compression, stretching, torsion, rotation, and so on. If not mentioned otherwise, stress–strain curve typically refers to the relationship between axial normal stress and ...
The elasticity tensor is a fourth-rank tensor describing the stress-strain relation in a linear elastic material. [ 1 ] [ 2 ] Other names are elastic modulus tensor and stiffness tensor . Common symbols include C {\displaystyle \mathbf {C} } and Y {\displaystyle \mathbf {Y} } .
The fundamental "linearizing" assumptions of linear elasticity are: infinitesimal strains or "small" deformations (or strains) and linear relationships between the components of stress and strain. In addition linear elasticity is valid only for stress states that do not produce yielding. These assumptions are reasonable for many engineering ...
In solid mechanics, the tangent modulus is the slope of the stress–strain curve at any specified stress or strain. Below the proportional limit (the limit of the linear elastic regime) the tangent modulus is equivalent to Young's modulus. Above the proportional limit the tangent modulus varies with strain and is most accurately found from ...
In engineering, the elasticity of a material is quantified by the elastic modulus such as the Young's modulus, bulk modulus or shear modulus which measure the amount of stress needed to achieve a unit of strain; a higher modulus indicates that the material is harder to deform.
The stress relaxation modulus () is the ratio of the stress remaining at time after a step strain was applied at time =: = (), which is the time-dependent generalization of Hooke's law . For visco-elastic solids, G ( t ) {\displaystyle G\left(t\right)} converges to the equilibrium shear modulus [ 4 ] G {\displaystyle G} :