Linear stress to linear strain is modulus of elasticity
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✍️The relationship between the stress and strain that a particular material displays is known as that particular material's stress–strain curve. It is unique for each material and is found by recording the amount of deformation (strain) at distinct intervals of a variety of loadings (stress). These curves reveal many of the properties of a material (including data to establish the Modulus of Elasticity, E).
✍️Generally speaking, curves representing the relationship between stress and strain in any form of deformation can be regarded as stress-strain curves. The stress and strain can be normal, shear, or mixture, also can be uniaxial, biaxial, or multiaxial, even change with time. The form of deformation can be compression, stretching, torsion, rotation, and so on. If not mentioned otherwise, stress–strain curve refers to the relationship between axial normal stress and axial normal strain of materials measured in a tension test.
✍️Consider a bar of original cross sectional area A being subjected to equal and opposite forces F pulling at the ends so the bar is under tension. The material is experiencing a stress defined to be the ratio of the force to the cross sectional area of the bar, as well as an axial elongation.
✍️Subscript 0 denotes the original dimensions of the sample. The SI unit for stress is newton per square metre, or parscal (1 pascal = 1 Pa = 1 N/m2), and for strain is "1". Stress-strain curve for this material is plotted by elongating the sample and recording the stress variation with strain till the sample fractures. By convention, the strain is set to the horizontal axis and stress is set to vertical axis.
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