A complex computer model of thermomechanical phenomena in a solid deformable material as a result of the action of intense energy fluxes was constructed. An algorithm has been developed for the end-to-end calculation of heating, evaporation, dynamics of vaporized matter and elastic-plastic wave processes leading to destruction in a solid material. A method for dynamic control of changes in the aggregate state of a condensed medium was proposed. Calculations of the destruction of polymer and composite materials under the action of ionizing radiation were carried out.

A complex computer model of thermomechanical phenomena and a technique for end-to-end modeling of processes occurring in a solid material under the action of an intense energy flux are developed. Using the example of calculating the impact on a polymer material, the dynamics of nonlinear wave processes leading to internal damage in a sample of the material and spalling phenomena are discussed. The created software can be used in the analysis of the results of intense energy impacts in engineering practice, verification of models of volumetric fractures, and spallation in brittle materials, as well as validation of wide-range equations of state.

A physical and mathematical model is considered to support the investigation of the prospects of using the effect of metal’s “magnetic memory” for the nondestructive testing of items made from ferromagnetic materials located in the Earth’s magnetic field. Based on the finite-element method, an algorithm and a computer code for the 3D computations of the magnetic potential distribution in a medium with nonuniform magnetic permeability are worked out. The developed methods and software tools are used to model the leakage field near the clamped heating pipes of steam boilers. Relationships demonstrating the interdependence between the change in magnetic induction and the magnetic leakage field are obtained. Satisfactory agreement is observed between the calculated and experimental data on the distribution of the field strength of the magnetic leakage on the surface of the heating pipe.

A complex model for supercomputing the parameters of radiation-induced thermomechanical fields in heterogeneous media of a complex dispersed structure is developed. A technique for calculating the parameters of the photon-electron cascade generated in the object by the interaction of radiation with matter is constructed. A geometric model of the medium with a direct resolution of its microstructure is worked out. The model of the detecting system for the statistical evaluation of the energy deposit of radiation is part of the geometric description of the medium. The continuum mechanics equations taken in the Euler form of the conservation laws are the base for calculating thermomechanical processes. The results of trial simulations in the form of the calculated thermomechanical fields are presented.

Using the support operator technique for two-dimensional problems of the elasticity theory we constructed integrally consistent approximations of the components of the strain tensor and the elastic energy of the medium for the equations of the elasticity theory in terms of displacements. Approximations are constructed for the case of irregular difference grids in the R–Z plane of a cylindrical coordinate system. We use the limiting process assuming that the azimuthal angle tends to zero for passing from the full three-dimensional approximations to the two-dimensional approximations in the R–Z plane. The used technique preserves the divergent form, self-adjointness, and sign-definiteness of the two-dimensional approximations. These properties are inherent in their 3D predecessors corresponding to the operators in the governing differential equations.

We study the quality of simulations related to high-intensity impacts which may lead to critical stresses and destruction of solids. The simulations are done under conditions close to applicability limits of models built with the use of local thermodynamic equilibrium principle. We use Prandtl-Reuss approach to elastic-plastic flows. Numerical experiments are performed using explicit monotonized techniques. The following models are considered: (a) Mises model (check of the integral load at any point); (b) Tuler-Butcher model (check of the incubation time); (c) Hashin model (check of stresses with respect to their ultimate values). We discuss the results of solving model problems: fracture in fiberglass suffered to high-energy loads. This work was supported by the RSF (project No. 16-11-00100p).

Finite-difference approximations of elastic forces on the staggered moving grid were constructed. For the displacement vectors at the irregular grids in which topological and geometrical structures are subjected to minimal reasonable restrictions, with regard to the finite-difference schemes of the elasticity theory problems, approximations of the vector analysis operators in plane and cylindrical geometries were constructed. Taking into account the energy balance of the medium, the families of integral consistent approximations of the vector analysis operators, which are sufficient for the discrete modeling of these processes considering the space curvature caused by the cylindrical geometry of the system, were built. The schemes, both using a stress tensor in the full form and dividing it into volumetric and deviator components, were studied. This separation is used to construct homogeneous equations that are applicable for solid body and vaporized phase. The linear theory of elasticity was used. The resulting expressions for the elastic forces were presented in the explicit form for two-dimensional flat and axisymmetric geometries for a mesh consisting of triangular and quadrangular cells. Generalization of the method for other cases (non-linear strain tensor, non-Hookean relation between strain and stress, full 3D geometry, etc.) can be performed by analogy, but this was not a subject of the current paper. Using the model problem, comparison between different temporal discretizations for the obtained ordinary differential equations system was carried out. In particular, we considered fully implicit approximation, conservative implicit approximation (Crank-Nicolson method), and explicit approximation, which is similar to the "leap-frog" method. The analysis of full energy imbalance and calculation costs showed that the latter is more advantageous. The analysis of the effectiveness of various temporal approximations was performed via numerical experiments.