Body Forces ,Contact Forces, Stress Invariants and Octahedral Stresses

Hi,

• Body forces: These are the types of forces which act on the whole body at a time. Their magnitude depends upon the mass of the body, so they are generally measured as force per unit mass. These forces do not need any contact with the other body which is applying that force to it, but their magnitude depends on the distance between the two bodies.

The examples are gravitational forces, magnetic forces and electromagnetic forces. Gravitational force depends upon the product of the masses of the two bodies, and is inversely proportional to the square of the distance between two bodies. Force do not depend upon the surface area.

• Contact Forces: These are the forces which are applicable through the contact between two bodies. So they are measured as force per unit area.Contact forces are classified into two broad categories, normal forces and tangential/shear forces.Normal forces act normal to the plane of the action of the force, and shear forces act tangential to the plane of action of the forces.Normal and shear stress, both are measured as the stress per unit area (N/mm2).

• Stress In variants:When a stress tensor is transformed from one co-ordinate axis to some another co-ordinate axis, their are some values linked to the tensor matrix which do not change even when the elements of the stress matrix are changed.

These values are known as the stress invariant of a given stress tensor. They are generally expressed as I1, I2, and I3.

• Octahedral stresses: When we take an octahedral element of a stressed body, each of its eight faces will have some stress co-ordinates with respect to the principal stress axes.

All the normal stresses in the eights faces of the octahedral will make some specific/equal angle with the principal axis/reference axes. These stresses on the octahedral planes are known as the octahedral stresses.

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