Vabishchevych M. Numerical modeling of nonlinear deformation processes for inhomogeneous 3D bodies with appearance and propagation of cracks under dynamic loading

Based on the semi-analytical finite element method, a new effective approach to numerical modeling of dynamic elasto-plastic deformation and destruction of inhomogeneous bodies of revolution and prismatic bodies of complex configuration and structure taking into account contact interaction, plastic deformations, existing nonpropagating and propagating cracks is created. The equations system of SAFEM for elastic-plastic inhomogeneous prismatic bodies and bodies of revolution of complex shape with arbitrary boundary conditions under dynamic loading are obtained. Unification of object-oriented elastic-plastic, contact and special with cracks finite elements for approximation of massive, thin-walled and combined bodies with arbitrary boundary conditions within the dynamics problem is carried out. The effective algorithms to solve physically and structurally nonlinear problems of fracture mechanics under dynamic loading conditions, taking into account the existing nonpropagating and propagating cracks are proposed and implemented. Effective methods for determining the energy parameters of fracture dynamics for elasto-plastic bodies with stationary cracks have been developed. Algorithms for dynamic crack development under static and dynamic force or kinematic loading are constructed. New solutions of real practical problems of determining the residual strength of aircraft keels, elements of military equipment, expert assessment and study of crack resistance of building structures and their elements under the influence of dynamic influences taking into account plastic deformations, contact zones and cracks.