Beyond the proportional limit if the stress exceeds the proportional limit, the strain is no longer proportional to the stress.
View Hooke's Law Stress Strain Relation Gif. Figure 16.4 shows a graph of the absolute value of the restoring force versus the displacement for a system that can be described by hooke's law—a simple spring in this case. The solid will return to its original shape when the stress is removed.
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(isotropic means that it has equal stiffness in every direction.) it is the ratio of the sensitivity of strain to two stresses, one in line with the strain, and the other perpendicular to it. Beyond the proportional limit if the stress exceeds the proportional limit, the strain is no longer proportional to the stress. Hooke's law states that for small deformities, the stress and strain are proportional to each other.
Figure 16.4 shows a graph of the absolute value of the restoring force versus the displacement for a system that can be described by hooke's law—a simple spring in this case.
The reciprocal term of the equation is 1/e where e is the modulus of elasticity (young's modulus). We will see that poisson's ratio is 1/2 for incompressible materials such as rubber. When force is applied to a material, we know that it either stretches or compresses in response to the hooke's law states that the strain of the material is proportional to the applied stress within the elastic limit of that material. • since both stress and strain are 3×3 tensor quantities, the most general possible elastic medium has a constitutive equation of the form:
