ABSTRACT
Infinitesimal strain at a point is defined by considering the undeformed and deformed geometrical configurations of the solid. Strain-displacement relations are derived in Cartesian and cylindrical polar coordinates. Conditions for strain compatibility are established. It is shown that strain, similar to stress, is a symmetric tensor composed of six components that transform from one set of orthogonal axes to another following the same transformation law of stress. Application to strain gauge rosettes is demonstrated. Expressions for the principal strains, maximum shear strain, octahedral dilatation, and deviatoric strains are obtained. Strain rate-velocity relations, which find application in the analysis of plastic flow, are also derived and a note on large strain definition is included. The strain-displacement relations involve three independent displacement functions u(x, y, z), v(x, y, z), and w(x, y, z). Strain fields for which a single-valued displacement solution exists are called compatible strain fields.
