Boundary variational methods for the solution of problems of deformation and diffusion

The mathematical simulation of coupled diffusion-deformation processes is suggested. The constitutive equations based on real mechanisms of the dislocation hardening and softening connected with the accumulation of microdefects during deformation are considered in the paper. The boundary variational principle is formulated for the deformation problems. The linear equations of mechanics and the boundary conditions of the boundary value problem are satisfied with the help of the boundary integral equations, while the nonlinear constitutive equations are satisfied, using the variational method. The surface stresses and the surface displacements are the unknown values. These values can be well predicted in the zero approximation. The boundary variational principle for the solution of diffusion problems is formulated similarly. The problem of the extrusion of the composite consisting of the copper matrix and filaments the titanium alloy is considered.