Dynamics of plastic deformation: Waves of localized plastic deformation in solids

Physical mesomechanical criteria of plastic deformation and fracture

“…The fact that the rotation tensor component is constant indicates that the material rotates as a rigid body. In physical mesomechanics, the plasticity is characterized as the situation where the distortion tensor components are coordinate dependent [4,6]. Intuitively, this can be understood as follows.…”

“…Since the distortion tensor components contain spatial derivatives, this requires the replacement of the usual derivatives with covariant derivatives, or the introduction of a gauge term. With the application of the Lagrangian formalism to the gauge field, this leads to the following Maxwell type field equations [6]. The general solution to this field equation is a decaying transverse wave [7] of the translational and rotational displacement: ,…”

“…where v and ù are the rate of the translational displacement and the rotational displacement (angle from the rotational equilibrium), respectively, ε is the density of the material, and µ 1 is the shear modulus [8], 0 j and j are the currents of symmetry (the time and space components, respectively) [6]. Putting ε ρ = 0 j in Eq.…”

“…Further analysis leads to a criterion that describes that the material is about to fracture [6,9]. This criterion, called the critical fracture criterion, is given as below:…”

Molecular dynamics study of cluster structure and properties of rotational waves in solid nanostructures

“…The analytical theory of nonlinear waves of structural transformations has been developed in several works [4][5][6]. According to one of them, the control parameter of nonlinear waves in local structural transformations is a local curvature in a highly non-equilibrium structure.…”