Steven Amerson

Background

About Steven Amerson

small strains, or infinitesimal strains, εij are appropriate for situations with |∂uk/∂Xl|<< 1 for all k and l. Two infinitesimal material fibres, one initially in the 1 direction and the other in the 2 direction, are shown in Figure 6 as dashed lines in the reference configuration and as solid lines in the deformed configuration. To first-order accuracy in components of [∂u/∂X], the extensional strains of these fibres are ε11 = ∂u1/∂X1 and ε22 = ∂u2/∂X2, and the reduction of the angle between them is γ12 = ∂u2/∂X1 + ∂u1/∂X2. For the shear strain denoted ε12, however, half of γ12 is used. Thus, considering all extensional and shear strains associated with infinitesimal fibres in the 1, 2, and 3 directions at a point of the material, the set of strains is given by