The problem of describing the behavior of a highly filled polymeric material under compression, which was preceded by preliminary compression and unloading, is considered. The peculiarity of the compression diagrams obtained in the experiment is the downward convexity of the curves of the stress modulus versus time. To solve this problem, a variant of the non-linear endochronic theory of aging viscoelastic materials with several aging and viscosity functions and a numerical-graphical method for identifying the properties of viscoelasticmaterials proposed by the authors earlier, suggesting comparison of the deformation diagrams of intact samples and those that received preliminary damage, are used.

A method for describing the creep behavior until fracture of a highly filled polymer material previously damaged in preliminary tests is proposed. The constitutive relations are the relations of nonlinear endochronic theory of aging viscoelastic materials (NETAVEM) [1]. The numerical-graphical method for identifying the functions occurring in NETAVEM, which was proposed in [2] for describing loading processes at a constant strain rate, is used here for the first time in creep theory. We use the results of experiments with undamaged and preliminary damaged specimens under the action of the same constant tensile loads. The creep kernel is determined in experiments with an undamaged specimen. The reduced time function contained in NETAVEM is determined from the position of points corresponding to the same values of strain on the creep curves of the damaged and undamaged specimens. An integral equation is solved to obtain the aging function, and then the viscosity function is determined. The knowledge of all functions contained in the constitutive relations permits solving the creep problem for products manufactured from a highly filled polymer material.

We present the results of a large series of experiments aimed at the study of laws of damage accumulation and fracture in highly filled polymer materials under loading conditions of various types: monotone, repeated, low- and high-cycle, with varying type of stress state, dynamic (in general, more than 50 programs implemented on specimens from one lot of material). The data obtained in these test allow one to make conclusions about the constitutive role of the attained maximum of strain intensity when estimating the accumulated damage in the process of uniaxial tension by various programs (in particular, an additional cyclic deformation below the preliminary attained strain maximum does not affect the limit values of strain and stress in the subsequent active extension), about the strong influence of the stress state on the deformation and fracture, about the specific features of the nonlinear behavior of the material under the shock loading conditions and its influence on the repeated deformation.

A method for determining the material functions of nonlinear endochronic theory of aging viscoelastic materials (NETAVEM) with preliminary mechanical damage was developed. The proposed method is based on an analysis of the differences between two graphs of the stress dependence on time obtained in tension with the same constant speed of two specimens made of the same filled polymer material. One of the specimens was not preloaded, and the other was preloaded. The reduced time [1] contained in the NETAVEM constitutive relations and its dependence on the actual time are determined by the distances from the stress axis to two points corresponding to the same stress value and lying on the graphs for the damaged and undamaged specimens. The relaxation kernel is determined in the experiment with the undamaged specimen. These two material functions and the curve obtained for the damaged specimen are used to obtain the NETAVEM aging function, and then the function of viscosity can be calculated. As a result, all characteristics of the damaged material become known, and the strength of structures made of this material can be calculated.

Determination of mechanical characteristics of filled polymer materials in shock wave processes is of interest in calculations of the strength of these materials. The standard computation methods are based on the use of the linear theory of viscoelasticity, where there is no distinction between the active and passive deformation processes. In the present paper, dynamical experiment and theoretical modeling are used to illustrate the important role played by the sharp decrease in the resistance of a filled polymer material in unloading (in the millisecond time range). The higher the degree of filling of this material, the more significant this effect is.

We present a survey of the main results and scientific ideas due to the 20th century prominent scientist Aleksey Antonovich Il’yushin, which can be regarded today, at his hundredth birthday anniversary, as his scientific heritage. The survey material is arranged (mainly, chronologically) in the key directions of Il’yushin’s activities such as the theory of viscoplastic flow, hydrodynamic stability, dynamics of deformable media, supersonic aerodynamics and related flatter problems, theory of elastoplastic processes, theory of plastic flow, thermoviscoelasticity and thermodynamics, strength of polymer bodies and structures, general theory of constitutive relations in classical continuum mechanics, and nonclassical models of continuum.

We consider generalized one-dimensional Maxwell and Kelvin-Voigt models of viscoelastic materials in which the properties of elastic and viscous elements are determined by the corresponding secant moduli and viscosity coefficients, which are functions of the parameters determined by the deformation process. In contrast to the nonlinear endochronic theory of aging viscoelastic materials (NETAVEM), in which one and the same aging function is used to describe the properties of all elastic elements and one and the same viscosity function is used to describe the properties of all viscous elements [1, 2], it is assumed that the type of these functions is distinct for each elementary model. For the generalized Maxwell and Kelvin-Voigt models under study, we obtain representations of the specific work of internal forces as the sum of four terms of different physical meaning. There representations are similar to those given in [1, 2] for NETAVEM. An example of construction of viscoelasticity constitutive relations containing two aging functions and one viscosity function is given for a material whose properties are sensitive to the strain rate. The simultaneous use of several aging and viscosity functions to describe the properties of structure elements of the model and the use of several components of specific work as arguments of these functions allows us to extend the scope of the models under study.

Представлен обзор основных результатов и научных идей выдающегося ученого XX века Алексея Антоновича Ильюшина, которые сейчас, в дни его столетнего юбилея, можно трактовать как научное наследие. Материал обзора структурирован (преимущественно хронологически) по ключевым направлениям деятельности А.А. Ильюшина: теория вязкопластического течения, гидродинамическая устойчивость, динамика деформируемых сред, сверхзвуковая аэродинамика и связанные с этим проблемы флаттера, теория упругопластических процессов, теория пластического течения, термовязкоупругость и термодинамика, прочность полимерных тел и конструкций, общая теория определяющих соотношений в классической механике сплошной среды, а также неклассические модели сплошных сред

We study composite polymer materials with a high degree of dispersion filling (several tens of percent in volume). A tensor generalization of the previously developed variant of the geroendochronic theory of viscoelastic materials is obtained, which allows us to pose and solve initialboundary value problems using this model. A numerical solution algorithm is proposed, which is realized as the UMAT subroutine for the ABAQUS finite element software package.

The filled polymer materials exhibit viscoelastic properties in a wide time range including the millisecond range (∼10−2–10 ms) characteristic of different shock loadings of structures made of these materials. We propose a method for the identification of the filled polymer material relaxation kernel in the millisecond time range; this method is based on a shock loading test of a cylindrical sample made of this material. In this test, the disk indenter acceleration is measured by using a piezotransducer. The test scheme does not impose any rigid constraints on the sample dimensions. In particular, it is possible to use samples of typical dimensions of the order of 10 cm, for which the conditions that the sample material is representative of the structure material are necessarily satisfied. The relaxation kernel parameters are identified by numerical minimization of the theoretically predicted indenter velocity deviation from the velocity-time dependence obtained by integrating the acceleration transducer readings. The minimization problem is solved by using a genetic algorithm. The problem of theoretical prediction of the indenter velocity is solved numerically by using a reduced computational scheme whose parameters are chosen from the minimum condition for the deviation from the prediction obtained in the framework of the detailed computational scheme. The use of the reduced computational scheme permits decreasing the computational costs by 3–4 orders of magnitude compared with the detailed computational scheme, which is a necessary condition for the practical applicability of the genetic algorithm in identification problems. We present examples of relaxation kernel identification in the range of 0.1–10ms from the results of the test where the disk indenter raised to the height of 1m falls on the sample end surface.

The nonaxisymmetric plane problem of the nonlinear theory of viscoelasticity is solved for a cylinder reinforced by an elastic circular shell. The cylinder has an internal cut resembling a Maltese cross in shape. The identification of the nonlinear endochronous theory of aging viscoelastic materials is conducted by a genetic algorithm method on the basis a nonmonotonic experimental stress-strain dependence. Some numerical results obtained for the stress-strain state of this cylinder under the action of internal pressure are discussed with consideration of the above physical nonlinearity and the finite logarithmic strains.

In the course of monotone uniaxial tension, filled polymer materials quasi-isotropic in the initial state experience increasing structure fractures (local adhesive separation and cohesive tearing) whose directions are mainly perpendicular to the tension axis. After complete unloading and relaxation, the fracture lips close, and weaker secondary bonds are formed between them. Taking into account the anisotropy of the above-described process of deterioration of the material structure and mechanical properties (degradation), we suggest to characterize the state of each elementary material fiber by its own values of the structure parameters (damage, fracture, and maximum strain), which can be calculated (according to the model equations of uniaxial tension in a constant direction) from the effective strain history of the fiber. It is determined as the product of the current values of two factors, namely, the strain intensity and the influence function, whose argument is the angle between the directions of the fiber under study and the maximum principal strain. The form of the influence function depends on the material and reflects the degree of anisotropy of the damage arising in it. As a model of uniaxial tension in a constant direction, we use the earlier-proposed version of the nonlinear endochronic theory of ageing viscoelastic materials, which, in addition, contains the secondary bond parameter (with its own equation). We show how the proposed constitutive relations permit one to describe the decrease in the resistance and the ultimate strain during the second axial tension compared with a similar tension from the initial state and to determine the dependence of these effects on the angle between the directions of the preliminary and repeated tensions.

The earlier proposed relation between true stress and logarithmic strain deviators, which has the form of a generalized Maxwell viscoelastic model and contains functionals of internal time and aging, is specified in the class of axial tension processes. It is suggested to characterize the local deficiency of a filled polymer material by two scalar quantities having the meaning of the relative internal separation area (the damage parameter) and the rated strain capacity exhaustion (the criterion parameter determining the destruction point). These parameters are described by kinetic equations and do not decrease in the loading process but increase only as the process activity parameter (the current-to-maximum-attained strain intensity ratio) is equal to unity. The right-hand sides of the kinetic equations for the internal time and the failure parameter depend on the strain rate intensity. The variation in the material instantaneous stiffness (aging) is described by a product of functions of the current values of the process damage and activity parameters. It is assumed that the bulk strain is quasi-elastic; it is proportional to the reduced stress intensity (with aging taken into account) and the difference between the damage and its threshold value below which there is no dilatation. The hydrostatic pressure and temperature are taken into account by two factors depending, respectively, on the stress state form parameter (the first-to-second stress tensor invariant ratio) and on the temperature, which are introduced into the right-hand sides of the model equations. We propose a generalization of the model to the case of variation in the phase state of the binder (embrittlement at low temperatures). We present the incremental form of the constitutive relations, which is used to integrate them numerically. We give a detailed description of the model identification procedure (after the relaxation kernel is determined in the standard way) from the results of the following base experiments: for constant values of the hydrostatic pressure, temperature, and tension strain rate (two-three levels of these parameters in their ranges used in application, each loading until failure) as well as for complete unloading (a single experiment). The experimental data (for three highly filled vulcanizates) published by Ozupik, Schapery, and Jung (more than 50 loading programs, including those of cyclic and nonisothermal type), are used to perform identifications and verifications of the proposed constitutive relations. We show that, in the class of processes under study, the engineered values (such as variations in the axial stress and bulk strain and the destruction point) lie within the limits typical of the corresponding experimental spread in mechanical properties of the material under study.

Material fracture experiments on specimens and structures testify that materials can resist greater stresses in local stress concentration regions than in regions with a nearly homogeneous stress state. Taking this fact into account in design stress analysis permits one to reveal additional structure loading and/or service life margins. One approach aimed at taking into account the increased strength in local stress concentration regions is to use averaged limit characteristics parametrically depending on the characteristic size L of the averaging region. One version of this approach is the concept of "elementary block" of a material [1, 2]. The averaged limit characteristics are determined by an experiment-calculation method involving the analysis of the stress-strain state of a material specimen with a stress concentrator at the time when the specimen attains the limit state preceding macrofracture.In [3], the dependence of the averaged limit separation stresses on the size of the averaging region was determined on the basis of numerical analysis of the singular stress state of the specimen used to determine the standard characteristics of the adhesion strength of a filled polymer material. In the present paper, we generalize the above approach to the case of a viscoelastic material. For the limit characteristics of the material in the local stress concentration region we take the volume-averaged components of the specific work of internal forces [4, 5] (the averaged specific absorbed energy and the averaged specific instantaneously reversible energy). The introduction of two limit energies originates from the fact that, to initiate the process of macrofracture, it is necessary to satisfy the following two conditions simultaneously: the material must be "damaged" sufficiently strongly by the preceding loading, and the "damaged" material must be loaded sufficiently strongly. As an example of determining the material averaged limit energy characteristics in a local stress concentration region, we consider the problem about the strain of a viscoelastic specimen used to determine the standard adhesion strength characteristics. The problem is solved numerically under the following assumptions: the specimen material is assumed to be linearly viscoelastic, and the specific absorbed energy in the stress concentration region is assumed to coincide in magnitude with the specific scattered energy. To estimate the accuracy of the numerical method, we use the solution of the model problem about the action of a plane circular die on a half-space consisting of a linearly viscoelastic incompressible material.

We consider a generalization of the nonlinear endochronic theory of ageing viscoelastic materials [1] to the case of finite strains. Our generalization preserves the main advantages of the model proposed earlier in [1]. Namely, it has a unique apparatus for describing the influence of the basic physical-mechanical factors (such as temperature, humidity, chemical ageing, strain and stress level, sign of the average stress, sign of the strain and loading rate, etc.) and provides a possibility of performing a structure-energy analysis of the stress-strain state [2-4]. The model is described by a system of relations of incremental type. These relations are derived in the following three stages. At the first stage, it is assumed that the principal directions of the true stress tensor are frozen in the material of the particle and three scalar constraints of hereditary type between the principal true stresses and logarithmic strains are stated. The form of these relations is similar to the form of relations in the endochronic theory [1]. At the second stage, the scalar relations of incremental type are derived on the basis of the assumption that the logarithmic strain rates, as well as the rates of variation of the reduced times, are constant on the interval [t, + Δt]. At the third stage, the incremental relations are stated in tensor form and generalized to the case of an arbitrary history of material particle deformation. We consider an algorithm for numerically solving 3D initial boundary-value problems for the proposed system of incremental constitutive relations. The algorithm is based on a FEM discretization of the weak form of the equilibrium equations referred to the body configuration at the beginning of the current time step. The dependence of the material ageing functions and the functions of the rates of reduced times on state parameters (strain invariants, stresses, specific scattered energy, etc.) is taken into account in the framework of the explicit scheme. We solve the problem of constrained compression of a rubber shock-absorber using the above algorithm. The material constants of the model were identified according to the results of experiments on uniaxial relaxation of compressive stresses. We note that for small values of the edge radius of the rim through which the compressive force is applied to the rubber disk, there is a sharp decrease in the convergence rate of the Newton method used to solve the system of nonlinear equations for the increments of the nodal displacements. We propose an extrapolation (in the value of the edge radius) computation procedure. Comparison with the results of experiments on constrained compression of a shock-absorber shows a satisfactory correspondence between the numerical and experimental results.

We consider the results of experiments with specimens made of a viscoelastic material at constant compressive and unloading strain rates. The unloading was started at various levels of compressive strain. We present the dependences of conventional and true stresses on linear measures of strains. Using the Nonlinear endochronous theory of aging viscoelastic materials [1] and replacing the conventional stresses by true stresses, we carried out a structure-power analysis of stressed states under active loadings and unloadings. By comparing -the values of structure components of the specific work of internal forces computed with the use of conventional and true stresses, we show that those where true stresses are introduced are physically more meaningful. A good coincidence of the theoretical and experimental dependences of stresses on the linear measures of strains of the order of 50% showed that medium finite strains can be described with the use of linear measures of strains if one appropriately takes into account the physical nonlinearity of the materials. One should have this in mind when carrying out computations with the use of various measures of finite strains. It was simultaneously established that the initial modulus of unloading of viscoelastic materials depends on the level of strains at the time where the unloading begins, which should be taken into account, for example, when computing the Karman modulus for determining the critical stress of the compressed rod.