Scale independent approach to strength physics and optical interferometry

Abstract

Dynamics of deformation and fracture is considered based on a field theoretical approach. The basic postulate of this approach is that deformation is always locally linear elastic, and that the nonlinear behavior in the plastic regime can be formulated by considering the interaction of these local dynamics. By requesting that the transformation matrix representing the local elastic deformation is coordinate dependent so that it describes nonlinearity, and that the law of elasticity be invariant under the coordinate dependent transformation, this formalism introduces a compensating field known as the gauge field. By applying the Lagrangian formalism to the gauge field, the theory derives field equations that describe interaction between the translational and rotational modes of displacement. The plasticity is viewed as energy dissipating dynamics of the deformation charge, a quantity derived from the symmetry charge associated with the invariance of the elastic law. Recent analysis indicates that transition from plastic deformation to fracture is governed by the behavior of the deformation charge, and that an optical interfermetric technique known as the electronic speckle-pattern interferometry can be used to visualize the deformation charge.