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Young's modulus represents the factor of proportionality in Hooke's law, which relates the stress and the strain. However, Hooke's law is only valid under the assumption of an elastic and linear response. Any real material will eventually fail and break when stretched over a very large distance or with a very large force; however, all solid ...
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
where is the Young's modulus along axis , is the shear modulus in direction on the plane whose normal is in direction , and is the Poisson's ratio that corresponds to a contraction in direction when an extension is applied in direction .
[1]: 58 For example, low-carbon steel generally exhibits a very linear stress–strain relationship up to a well-defined yield point. The linear portion of the curve is the elastic region, and the slope of this region is the modulus of elasticity or Young's modulus. Plastic flow initiates at the upper yield point and continues at the lower ...
where is the volume fraction of the fibers in the composite (and is the volume fraction of the matrix).. If it is assumed that the composite material behaves as a linear-elastic material, i.e., abiding Hooke's law = for some elastic modulus of the composite and some strain of the composite , then equations 1 and 2 can be combined to give
where E is the elastic modulus and η is the material coefficient of viscosity. This model describes the damper as a Newtonian fluid and models the spring with Hooke's law. In a Maxwell material, stress σ, strain ε and their rates of change with respect to time t are governed by equations of the form: [1]
Elastic properties describe the reversible deformation (elastic response) of a material to an applied stress. They are a subset of the material properties that provide a quantitative description of the characteristics of a material, like its strength .
Springs, which represent the elastic component of a viscoelastic material, obey Hooke's law: = where σ is the applied stress, E is the Young's modulus of the material, and ε is the strain. The spring represents the elastic component of the model's response. [2]