Summary
Stress is the restoring force per unit area which causes strain (fractional change in dimension).
Types of Stress
— tensile stress
— compressive stress (caused by compression)
— longitudinal stress (caused by streching)
— shearing stress (caused by shear forces)
— hydraulic stress (caused by hydraulic forces)
Hooke's law
— for small deformations, stress is directly proportional to the strain for many materials (linear part of stressstrain curve).
— this modulus of elasticity is the constant of propotionallity.
— Young's modulus is used for stress / stain caused by tensile and compressive forces.
— shear modulus is used for stress / stain caused by shear forces.
— bulk modulus are used is used for stress / stain caused by hydraulic stress.
— describe the elastic behaviour of objects as they respond to deforming forces.
A class of solids called elastomers does not obey Hooke's law. Some polymers which are elastomers include polyisoprene or natural rubber, polybutadiene, polyisobutylene, and polyurethanes. Elastomers can be stretched to many times their original length without permanent deformation.
When an object is under tension or compression Hooke's law takes the form: Y = [^{(F/A)} /_{(ΔL/L)}] where Y is the Young's modulus for the object, F is the magnitude of the applied force causing the strain, A is the crosssectional area over which F is applied (perpendicular to A), ΔL is the extension or compression and L is the original length of the material. ΔL/L is the tensile or compressive strain of the object and the stress is F/A.
Shear Stress
— a pair of forces (F) when applied parallel to the upper and lower faces of a solid deforms the solid so that the upper face moves sideways with respect to the lower.
— the horizontal displacement ΔX of the upper face is perpendicular to the vertical height L.
— the corresponding stress [^{(F)}/_{(A)}] is the shearing stress and causes a strain [^{(ΔX)}/_{(L)}].
— this type of stress is possible only in solids.
— Hooke's law takes the form [^{(F)}/_{(A)}] = G [^{(ΔX)}/_{(L)}] where G is the Shear Modulus of the material.
Hydraulic Stress
— hydraulic compression due to a stress (P) exerted by a surrounding fluid where p is the pressure(hydraulic stress) on the object due to the fluid.
— Hooke's law takes the form P = B [^{(ΔV)}/_{(V)}] where B is the Bulk Modulus of the material.
— the volume strain [^{(ΔV)}/_{(V)}] is the absolute fractional change in the object's volume due to that pressure .
Young's Modulus
— Metals have larger values of than alloys and elastomers.
— large value of Young's modulus requires a large force to produce small changes in its length (strength)
— only holds for solids
Bulk modulus
— for solids, liquid and gases and is
— the change in volume when the entire body is under the uniform stress and the shape of the body remains unchanged.
Shear Modulus
— only holds for solids
Poisson ratio
— a deforming force in one direction can produce strains in other directions.
— the proportionality between stress and strain in such situations cannot be described by just one elastic constant.
— wire under longitudinal strain, the lateral dimensions (radius of cross section) will undergo a small change, which is described by another elastic constant of the material.
— Poisson ratio μ =  εt / εl . where. μ = Poisson's ratio. εt = transverse strain. εl = longitudinal or axial strain
Physicist vs Layman
Layman — thinks that a material which stretches more is more elastic
Physicist — material which stretches to a lesser extent for a given load is considered to be more elastic.
