Currently developing elements for a renewable hydrogen storage and transportation is needed and its demand is rapidly increasing. Metal hydrides are among optimum solutions for hydrogen storage in terms of effectiveness and safety. The promising material which is good for such approach is magnesium and its alloys that can reversibly absorb hydrogen in quantities up to 7.6 % by weight which meets the DOE requirement. At first, determining a fast hydrogen saturation of Mg-based alloys has consisted in mechanical grinding of materials up to delivering the micrometric grain size. Increasing markedly the specific surface of the treated powders by plastic deformation processing leads to delivering very reactive samples contrary to bulk materials which are markedly un-reactive. More recently, great improvements of the H-sorption characteristics were demonstrated efficiently when applying the Equal Channel Angular Pressing (ECAP) treatments to bulk Mg-alloys. The implementation of ECAP process entails workpieces to pass the dedicated matrix formed by two channels crossing at a certain angle, i.e. from 90, 105 up to 120 degrees according to the degree of plasticity of the material. Effectively, the stress level delivered to the material depends on the angle between the channels, the applied pressure on the sample, the friction and (or) counter-pressure effects and obviously the physical and mechanical characteristics of the sample versus temperature. As the dimensions of the workpiece in terms of cross section are not changed, the deformation process can be applied several times successively, with the aim to achieve extremely high degrees of stresses and deformation. So, during such a severe deformation process the achievement of a fine-grained microstructure in the magnesium bulk samples is accompanied by the formation of a high density of defects and overall texture. When considering the ECAP process applied to the magnesium alloys, the numerical simulations were developed to anticipate the mechanical behaviour of the workpieces parallel to experimental characterizations using different methods such as structural and texture analyses. The present article reports on the deformation process Mg-based materials by using the numerical simulation method. By using the numerical LS-Dyna package for spatial deformed states we have successively applied ECAP operations in order to determine the optimum conditions of deformation delivering fine-grained Mg-materials with a high level of internal stresses. The results of the calculations are found in good agreement with the experimental data; and make it possible to use the proposed optimised process and adapted tool to up-scale the effective mass production.

This paper is devoted to the solution of non-classical variational problems of mechanics consisting in the minimization of the integral-type functional under various constraints. As constraints we consider various conditions for unknown function, which minimizes the optimized functional. The considered constraints include various dependences of the unknown function on space variables. It is supposed that the minimized functional is integral and includes the dependence both on the unknown function and its partial derivatives. We suppose that the inclusion of the inequality constraints on the unknown function corresponds to the contact conditions arising when deformable bodies interact and when these bodies (medium) contact rigid obstacles. The type of the relevant arising conditions characterizes the considered minimization problem of the functional with local constraints imposed at separate points of the definition domain as the non-classical problem of calculus of variations. In order to solve the considered non-classical problem of calculus of variations we applied a new approach based on finite element approximations (Galerkin type approximation) and procedures of local variations. The original domain aiming to determine the minimizing functional and unknown varied function are decomposed into separate small sub domains (cells of domain). The unknown function is given in the nodes, and the approximation of the function is given with the help of the shape function. It is supposed that the shape functions belong to the space of Sobolev functions differentiable with the quadratic integrable, and the system of basic functions is polynomial and has a small definition domain. The problem constraints are transformed within the framework of introduced finite element approximations. The additive functional of the problem is approximated by the integrals for the cells from the entire domain. Then we consider the problem, formulated as the problem of finding the nodes values satisfying the arising non-classical double constraints on the unknown function and minimizing the optimized functional. The presented variational algorithm is affected by the successive approximations. After choosing the initial approximation satisfying the constraints, each iteration acts as a local variation of the unknown solution consistently for all the nodes and performs the minimization of the optimized functional. In this context we do not violate geometric (contact) constraints and reduce the integral sum over the domain of the varied point. When the local variation process in all the cells is completed and the updated version of the solution is constructed, the process is repeated until a complete convergence is achieved, with a gradual decrease in the variation step and the necessary refinement of the finite element mesh. Thus we provide the solution of the considered variational problem. As an example we present the problem solution related to the torsion of the elastic-plastic bar. The solution of this problem has been obtained for different cross-sectional areas for various angles of torsion using proposed method. The computed results, which are in agreement with the experimental results, are shown for the plastic distributions domains.

A model of the dynamic mechanical behavior of brittle materials based on the ideas of the kinetic theory of strength is developed. The proposed model is a generalization of the classical "quasi-static" Nikolaevsky plasticity model (non-associated flow law with the plasticity criterion in the form of Mises-Schleicher) to the strain rate interval corresponding to the dynamic loading. In contrast to the traditional approach to constructing dynamic models, in which the dependence of the model parameters on the strain rate is specified, the proposed model suggests to use the relaxation time and time of fracture as the key parameters. The presented model allows taking into account the change in the strength and rheological properties of brittle materials with an increase in the loading rate. This ensures a correct transition from the quasi-static regime of loading to the dynamic one in the range of strain rates within 10-3 < <103 s-1. Within the framework of the proposed model it is assumed that there exist the experimental data about the dependences of the strength and rheological characteristics of the material on the times of different scales discontinuities nucleation. However, in view of the complexity of obtaining this information, we propose a way of obtaining the estimates of these dependencies by transforming the dependences of the mechanical properties on the strain rate that can be gained with standard tests. The developed dynamic model can be implemented within various Lagrangian numerical methods using an explicit integration scheme (including the finite element and discrete element methods) and is relevant for solving a new class of applied problems related to natural and technogenic dynamic impacts to structures of artificial building materials, including concretes, ceramic elements of structures and natural rock materials.

The paper presents the solutions of the coupled boundary value problems for a thick-walled cylinder and a sphere made of shape memory alloy (SMA). Their material undergoes a direct thermoelastic martensitic phase transformation upon cooling under a constant internal pressure. We have considered slow cooling processes in which the temperature distribution over the material at each instant of time can be considered as uniform. The results are compared with the analytical solutions of the same problems previously obtained within the assumption of a uniform distribution over the material of the martensitic volume part parameter. A quasistatic motion is simulated in the material of the fronts of the onset and completion of the phase transition, as well as the redistribution of stresses and strains along the cross section associated with these motions. It is established that a direct phase transformation begins on the inner surface of the shells. The phase transition zone is quite fast (compared to the growth of the phase composition parameter at the points of the inner surface) propagating along the radial coordinate to the outer surface. After this, the phase transition develops over the entire thickness, the magnitude of the martensitic volume part parameter q being a weakly decreasing function of the radial coordinate (the difference in the values q on the inner and outer surfaces is a small fraction of the maximum q value equal to 1). The completion of the phase transition is observed for the first time on the inner surface, after which the boundary of the phase transition end rapidly moves through the thickness from the inner surface to the outer surface. The intensity of stresses and the annular stress in the process of the phase transition vary non-monotonically and in different ways for the inner and outer surfaces. On the inner surface, these stresses have the maximum values at the points of the beginning and the end of the phase transition; and the minimum values take place at an intermediate point. On the contrary, in case of the external surface, the minimum values of stresses are observed at the beginning and the end of the phase transition, while the maximum value take place at the intermediate point of the process.

The paper is concerned with the developed numerical 3D model of the piezoelectro luminescent fibre-optical sensor aiming to diagnose the volume deformed state in a composite structure using ANSYS finite element analysis. In general, the model is a parallelepiped with the sensor fragment located on the central axis. The sensor is the sector-compound layered cylinder made from the central optical fiber with electroluminescent, piezoelectric layers and an external uniform elastic buffer layer. The electroluminescent and piezoelectric layers of the sensor are divided by the radial-longitudinal borders, which are shared by both layers, into the geometrically equal six "measuring elements" in the form of the cylindrical two-layer sectors. The directions of the volume polarization for piezoelectric phases and frequencies of lights for electroluminescent phases are different in various sectors. The piezoelectric phases of all the six sectors are represented by one and the same transversal-isotropic polymeric piezoelectric PVDF material but with different acoplanar directions of volume polarization. The translucent "internal" thin cylindrical operating electrode is located between the optical fiber and electroluminescent layer, and the "external" operating electrode is located between the piezoelectric and buffer layers of the sensor. The properties of the parallelepiped are equated to the transversal-isotropic properties of the unidirectional fibrous fibreglass; various simple monoaxial or shear deformations of the parallelepiped are set through the corresponding displacements of points of his sides. The numerical modeling of non-uniform coupled electroelastic fields in the sensor fragment elements is made. The sensor is implemented in the deformed composite volume of fibrous fibreglass and the operating voltage acts on his electrodes. The numerical values of the informative and operating coefficients of the sensor are calculated; these coefficients are necessary to diagnose the components of deformation tensors on macro- and microlevels of the composite.

The paper considers the numerical analysis method of mechanical fields in deformable bodies based on the graph model of an elastic medium in the form of the directed graph. According to the applied method the elastic medium along the coordinate planes is divided into separate elements. In line with this notion we have established an elementary cell configuration, a subgraph of the element by installing hypothetical meters on the solid’s element. The derivation of the cell equations which is based on the element conversion into the cell relies on an invariant. The deformation energy is the invariant. The whole body’s graph is built following the same rule as in the elementary cell. Apart from the opportunity to present the system configuration and mutual connections of its variables, the graphs allow to conduct complex mathematical transformations deliberately in the frameworks of the definite algorithm. The matrices which present several structural elements of the graph and the equations which describe the elementary cells both contribute to deriving the constitutive equations of the intact body. There are matrices that set such structural elements of the graph as cycles, paths and chords. The graph of a whole body is built by following the same rule as in the elementary cell. The method is based on transforming the generalized coordinates of a solid body separated into pieces to a system of generalized coordinates of the initial solid body. The nonsingular and mutually inverse matrices do this transform. The specific nature of the graph model lies in the possibility to construct these matrices with no need for their numerical inversion. The derivation of the defining system of equations is based on the use of vertex and contour of Kirchhoff’s laws for graphs, and the properties of the constructed square transformation matrices. The potentials of the graph method are illustrated by solving a test example.

The paper presents the finite element (FE) model validation. The definition of the term is given as a sequence of operations on a construction and its FE model to get the model reflecting the stress-strain behavior, and/or the dynamic properties of the construction as accurate as only possible. In this study, the validation was illustrated by a FE model of an antenna which has a complex divergent structure. Eigenmodes were selected as responses for FE model validation. Special matrices which are calculated using the FE method program are analyzed to define whether a sensor placement is optimal. Sensors are utilized to get the structural responses during structure tests. This analysis shows dominant eigenmodes that correspond with the deformation of the considerable amount of construction mass, location of the sensors which are placed in the nodes having the maximum values of kinetic energy fractions and the excitation points of all the required structure eigenmodes. According to the previous analysis, the location of the sensors (e.g. accelerometers) and excitation points are chosen. Mathematically, the selection of the sensor positions is accompanied with a reduction of the global FE model matrices to the nodes (degrees of freedom) where the sensors will potentially be placed. The next step is to confirm that the location of the sensors is optimal by means of special correlation matrices. They are employed to compare eigenvectors in the selected nodes of the base and reduced FE models. The certain values of the elements of the correlation matrices are the confirmation that the sensors are located in the optimal way. Further, structural tests are conducted by utilizing the results of the previous analysis. Afterwards, the correlation matrices are calculated again to compare the base finite element model of eigenvectors in the previously chosen nodes (points) with the reduced ones. If the correlation degree of the eigenvectors is high, the base FE model is considered as validated. If the correlation degree of the eigenvectors is low, the base FE model must be updated.