The paper presents phenomenological constitutive relations for a crystallizing polymer medium, obtained in the framework of nonlinear solid mechanics. The relationships are based on the representation of the medium in the form of a composition of a molten and fully crystallized material, taking into account the history of a continuous nucleation and deformation of a new phase in the temperature range of phase transformations. A general formulation is carried out regarding the evolutionary boundary-value problem of the nonlinear mechanics of polymer materials under phase transitions with the use of the proposed constitutive relations. Algorithms are considered that are aimed at a numerical realization of the thermokinetic problem and determining the stress-strain state of the solidifying system for the case of a plane deformed state. A linearization procedure is developed - which is convenient for constructing numerical algorithms to solve the set evolutionary boundary value problems - using the assumption of the proximity of each intermediate configuration to the current one, which corresponds to the procedure for superimposing small deformations of crystallized particles on finite deformations of a crystallizing medium. The linearization procedure for the initial formulation of mechanics problem is realized taking into account temperature and structural deformations. A numerical algorithm aimed at solving a flat boundary value problem is developed and implemented with the aim of investigating the evolution of the stress-strain state in a polymer structure. A method is proposed and implemented to construct a discrete analogue of boundary value problems, based on the use of the Galerkin method with a selection basis functions with a compact support by the finite element method. In this case, the increments of the displacement functions at the current time step are taken as nodal unknowns. The regularities of a shell type defect’s formation in the crystallizing polymer cylinder are established.

The structure of the oriented martensite, which determines the macroscopic deformation of shape memory alloys (SMA), can be formed in two ways: directly from the austenitic phase as a result of direct phase transformation under load, and also from the chaotic martensite under its isothermal structural transformation. The deformation produced by the first method is called the phase deformation, the deformation produced by the second method is called the structural deformation, but the difference in the terms used reflects only the difference in the mechanisms of their initiation, whereas the final product - the oriented martensite - is the same for both types of deformation. Therefore, some SMA phenomenological models take into account the uniformity of these two deformation components by determining their interrelation through the direct transformation diagrams F1 (for phase deformation) and the diagrams of martensitic inelasticity F2 (for structural deformation). The theoretical framework of these models is based on the hypothesis that the process of further deformation of the oriented martensite does not depend on the mechanism of its formation and involves three material functions: F1, F2, and also the function of their interrelation f . The experimental study of wire samples of TiNi, described in this paper, was performed with the aim to substantiate the developed hypothesis and establish three material functions used in the suggested theoretical description. A new method for determining the function f , which can be used as a verifying experiment, is proposed. The range of validity of the hypothesis has been determined both for the succeeding isothermal deformation of the samples with initial phase and structural deformations, and for the processes associated with their subsequent heating. The experiments demonstrated that the further-orientation diagrams for such samples coincide, which is indicative of the cross- hardening effect.

The mathematical model is developed aimed at locating pressure non-uniformity along a fiber optic-piezo-electro-luminescent sensor using the location scanning electrical video pulse with a step by step change of its value. The algorithm of finding the function of pressure distribution along a local section and the whole length of the sensor is developed based on the results of the intensity of light proceeding from a fiber optic phase measured on the edge section of the sensor for a case of nonlinear “luminescence function”, which is a dependence between the intensity of light and voltage acting on the luminescent element. The problem is reduced to the solution of the Fredholm integral equation of the 1st kind with the differential kernel depending on the operating and informative transfer coefficients of the sensor and on the set luminescence function of the element. Analytical solutions for the pressure distribution functions along the sensor are obtained for special cases, when the kernel or the function of distribution density is expressed via delta function, and the Fredholm integral equation becomes algebraic. Domains of admissible values of the operating voltage for various modes of diagnostics of pressure distribution are defined. Results of numerical solutions of direct and reverse problems for non-uniform distribution of pressure by means of “pointed” scanning of this pressure are presented by an extremely narrow impulse of the operating voltage. Luminescence functions at the exit from the optical fiber at various time points and values of the impulse of the operating voltage taking into account the set luminescence function of an electroluminescent element are found in the direct problem. The distribution of pressure depending on the values of the luminescence intensity function at various time points is found in the reverse problem.

An experimental-calculation method aimed at evaluating the stiffness properties of a cylindrical shell structure made of a composite material with a polymer matrix at the initial stage of its curing is considered. Evaluation of the stiffness composition parameters at this stage of polymerization due to the different physical state of the reinforcing elements and the binder by the methods of composite materials mechanics leads to poorly determined stiffness matrices that are not suitable for a reliable description of the mechanical behavior of the structure. The research relevance is related to the study of the manufacturing large-sized pneumatic structures technology based on compositions subjected to curing in space conditions. In the proposed method, the cylinder deployment pressure (the pressure at which the cylinder diameter assumes a nominal value) corresponding to the current binder polymerization degree is determined experimentally. The degree of polymerization is characterized by viscosity and the dynamic polymer module, measured with the viscosimeter. The structure specification as well as devices used in the experiments, instruments that fix the measured state parameters and the test procedure description are provided. The effective modulus of the cylinder’s elasticity of the material has to be corresponding to its stiffness characteristics during the loading by internal pressure to the deployment pressure. It is determined by the method of successive approximations based on a geometrically nonlinear elastic model. The deployment time is much shorter, than the total binder curing time. By comparing the experimental and calculated data, the dependence of the effective elasticity modulus on the binder curing parameters is established. The almost linear dependence of the cylinder deployment pressure on the effective modulus of elasticity is revealed. It allows to extrapolate the results of the study to the values of binder parameters that are not backed up by the experience. These results allow us to evaluate the internal pressure necessary for the deployment of composite cylindrical shells with a partially cured binder, by solving the problems of solid mechanics.

The complexity of phenomena caused by grinding and fracturing of solid particles makes it difficult to provide the theoretical description of this process. In this case, it is important to establish relationships between the parameters that determine the characteristics of the grinding process, determine the degree of their influence on each other, create and analyze the grinding process model taking into account crusher’s parameters, physical and mechanical properties of the material. Consequently, the improvement of formal calculation methods and justification of rational parameters of crushers ensure the effectiveness of their use during operation. By analyzing real materials’ state, a large group of scientists have created a number of theories explaining fracture conditions and mechanisms in solid materials. However, it is quite difficult to apply the existing theories for calculation of grinding processes. Therefore, there is a need to develop a new simple and convenient theory for practical application. Authors offer a new method aimed at theoretical description of a material’s fracture. Based on the simplified energy hypothesis and applied technical theory of wave spreading in elastic continuous medium, we have obtained a new refined solution of the fundamental dynamic mechanical problem of an elastically deformable rigid body about a longitudinal collision of a beam having a constant arbitrary cross section (simulating the material’s particle) with an absolutely rigid surface (simulating the working body of the crusher), taking into account the time parameter and linear dimension of the moving rod element (particle). The developed refined mechanical and mathematical model, which has been reduced to applicable calculated analytical dependencies and illustrated by typical numerical examples, allows to quantify the strength of the solid particle under destruction and grinding, makes it possible to implement a comprehensive descriptive approach regarding the dynamic process of material particles’ grinding by regulating and selecting the optimal physical and geometric characteristics, which provide the required grinding quality and predict the particles’ grinding process depending on the process parameters.