ABSTRACT
To determine the displacements, strains and stresses in a deformable body, one needs to solve the set of the following three governing equations: (i) strain-displacement or kinematic relation; (ii) stress-strain or constitutive relation and (iii) equation of motion. The equation of motion is related to the balance of forces and moments acting on the body and constitutes one of the postulates of mechanics. It must be satisfied by every rigid or deformable body. It has been described in Section 3.6. The strain-displacement relation describes the geometric changes (or the deformation) that a deformable body undergoes due to external forces acting on it. Depending on whether the deformation is infinitesimal (i.e. small) or finite (i.e. large), this relation has different forms. Further, the case of finite deformation can also be analyzed either incrementally or using the rate form of the measure of deformation. Chapter 4 describes all these cases: linear strain tensor for infinitesimal deformation; Green, Almansi and logarithmic strain tensors for finite deformation; incremental strain tensor for infinitesimal incremental deformation; and the rate of deformation tensor for the rate form.
