Non-linear theory of elastic microshear in periodic structures. Instability of homogeneous deformation

✍ Scribed by E.L Aero

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 617 KB
• Volume: 64
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(00)00092-7

✦ Synopsis

A theory of a crystal lar.tice with substantially non-linear interaction between the atoms during arbitrary mutual displacements under conditions of elastic shear of a layer is proposed. The energy of two-dimensional deformations contains periodic and gradient terms. The equilibrium equation in the form of the sine-Helmholtz equation (with two characteristic coherence lengths) is solved accurately. It is shown that a shear virain homogeneous along the layer unstable and is stabilized by modulations. As a result, a superstructure with long periods arises, i.e. there is a change in the long-range translational order. Relations are obtained, linking the size and the amplitude of the displacement field, which provide the conditions for the superstructure to exist. A bifurcation transition from purely elastic deformation of the lattice to elastoplastic deformation is found.