Models for solid response:

Any material has a particular shape in its state of rest called the rest shape. When stress is applied on it, it departs from its rest shape. The amount of departure from its rest shape is known as deformation. Strain is the ratio between the deformation and the original size. When the stress applied is sufficiently low, all solid materials exhibit such a behavior that the stress is directly proportional to the strain. The coefficient of this proportion is named as Young’s modulus or the modulus of elasticity. The area of deformation is called the linearly elastic area.

It is a common practice among analysts in the field of solid mechanics to make use of linear material models because of the ease of computation. But real materials mostly exhibit non- linear behavior. As new materials are coming to use and the old ones are dying out, non-linear material models are being used more commonly.

Three models are used to describe the response of a solid material to an applied stress:

• Elastically: When the stress applied is removed or released, the solid material reverts to its undeformed state. Linearly elastic models are those that deform proportionally to the applied load. They are described using linear elasticity equations such as Hooke’s law.
• Viscoelastically: The materials behave elastically and also have the property of damping. Damping is when the stress is removed and applied; work is required to be done against the effects f damping and is converted into heat within the material, resulting in a hysteresis loop for a graph of stress versus strain. This means that the response of the material id independent of time.
• Plastically: A material behaves elastically when the applied stress is lower than a yield value. When the applied stress exceeds the yield stress, materials behave plastically and do not return to their rest shape or the deformation is permanent.

Questions:

• Why are linear material models used?
• What is strain?