Explain Deformation of Solids

It has been noted that external force applied to a body in equilibrium is reacted by internal forces set up within the material. If, therefore, a bar is subjected to a uniform tension or compression, i e, a direct force, which is uniformly or equally applied across the cross section, then the internal forces set up are also distributed uniformly as well as the bar is said to be subjected to a uniform direct or normal stress, the stress being defined asStress, $sigma$ = $frac{Load}{Area}$. = $frac{P}{A}$. . Stress $sigma$ may thus be tensile or compressive depending on the nature of the load, which is measured in newtons per square meter (N/m2) or multiples of this. In some cases the loading situation is such that the stress will vary across any given section as well as in such cases the stress at any point is given by the limiting value of $frac{delta P}{delta A}$. as $delta A$ tends to zero. . . . . . . . . . . . Deformation refers to a change in the shape of a material. Since homogeneous displacement of material points doesn’t cause deformation, deformation must be related to spatial variation or gradient of displacement. Therefore, deformation is characterized by a displacement gradient tensor. However, this displacement gradient includes the rigid body rotation that has nothing to do with deformation. . . . . . . . . .

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