Parametric Optimization of Metal Rod Structures Using the Modified Gradient Projection Method

International Applied Mechanics - Problems of parametric optimization of rod structure stated in terms of the nonlinear programming problem are considered. Use is made of the method of projection...     

Identification of the model of nonlinear viscoelasticity of filled polymer materials in millisecond time range

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.     

Law of damage accumulation and fracture criteria in highly filled polymer materials

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. All tests are described (with an accuracy acceptable in practical calculations, both with respect to stresses and strains in the process of loading and at the moment of fracture) in the framework of the same model of nonlinear viscoelasticity with the same set of constants. The constants of the proposed model are calculated according to a relatively simple algorithm by using the results of standard uniaxial tension tests with constant values of the strain rate and hydrostatic pressure (each test for 2–3 levels of these parameters chosen from the ranges proposed in applications, each loading lasts until the fracture occurs, and one of the tests contains an intermediate interval of total loading and repeated loading) and one axial shock compression test if there are dynamic problems in the applications. The model is based on the use of the criterion fracture parameter which, in the class of proportional loading processes, is the sum of partial increments of the strain intensity on active segments of the process (where the strain intensity is at its historical maximum) with the form of the stress state and the intensity of strain rates taken into account.     

Constitutive relations for calculating the processes of quasistatic deformation,damage, and fracture of bodies (Including those with concentrators) made of filled polymer materials

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.     

Applied and engineering versions of the theory of elastoplastic processes of active complex loading part 2: Identification and verification

The deviator constitutive relation of the proposed theory of plasticity has a three-term form (the stress, stress rate, and strain rate vectors formed from the deviators are collinear) and, in the specialized (applied) version, in addition to the simple loading function, contains four dimensionless constants of the material determined from experiments along a two-link strain trajectory with an orthogonal break. The proposed simple mechanism is used to calculate the constants of themodel for four metallic materials that significantly differ in the composition and in the mechanical properties; the obtained constants do not deviate much from their average values (over the four materials). The latter are taken as universal constants in the engineering version of the model, which thus requires only one basic experiment, i. e., a simple loading test. If the material exhibits the strengthening property in cyclic circular deformation, then the model contains an additional constant determined from the experiment along a strain trajectory of this type. (In the engineering version of the model, the cyclic strengthening effect is not taken into account, which imposes a certain upper bound on the difference between the length of the strain trajectory arc and the module of the strain vector.)     

Applied and engineering versions of the theory of elastoplastic processes of active complex loading. Part 1: Conditions of mathematical well-posedness and methods for solving boundary value problems

In the proposed theory of plasticity, the deviator constitutive relation has a trinomial form (the vectors of stresses, stress rates, and strain rates, which are formed form the deviators, are coplanar) and contains two material functions; one of these functions depends on the modulus of the stress vector, and the other, on the angle between the stress vector and the strain rate, the length of the deformation trajectory arc, and the moduli of the stress and strain vectors. The spherical parts of the stress and strain tensors satisfy the relations of elastic variation in the volume.We obtain conditions on the material functions of the model which ensure the mathematical wellposedness of the statement of the initial–boundary value problem (i.e., the existence and uniqueness of the generalized solution, and its continuous dependence on the external loads). We also describe the scheme for solving the initial–boundary value problem step by step using the model and present the expression for the Jacobian of the boundary value problem at the time step. These results are formalized as a subprogram for prescribing the mechanical properties of the user material in the finite-element complex ABAQUS, which allows one to calculate the structure deformations on the basis of the proposed theory.     

Applied creep theory for bodies with anisotropy due to plastic prestrain

Plastic strains in structures at the stages of manufacturing, testing, and approaching the operation regime cause anisotropic variations in the mechanical properties of materials, including creep strength. We consider the following special but practically important class of loading processes for originally isotropic materials: a simple active plastic strain is followed by a long-term steady-state loading within the elastic limits. To describe the second stage, we present the creep strain deviator in the form of an additive orthogonal decomposition in the directions of the repeated loading and the vector anisotropy. The coefficients in the decomposition are material functions of time, of the intensities of the preliminary and repeated loadings, and of the angle between the directions of these loadings. We obtain conditions on the material functions under which, at any given time instant, there is a one-to-one continuous correspondence between the stress and strain tensors for the model proposed and the boundary-value problem in the generalized statement has a unique solution; we also prove the convergence of the iteration method of elastic solutions used to find this unique solution. The model is identified according to the creep diagrams (under steady-state stresses of different values) determined for the material in the original state and after the plastic prestrain at an angle (zero, extended, and intermediate) to the direction of the repeated loading. We show that our results are in good agreement with the results available in the literature concerning experiments in this class of processes for stainless steel at high temperature. We propose an engineering version of the theory in which only the experimental data for uniaxial tension are used. We discuss the versions of the model for the cases in which the plastic preloading is cyclic (one-dimensional or circular) and the repeated loading is unsteady.     

Constitutive relations of strain, anisotropic degradation, and fracture of filled polymer materials in prevailing-tension processes with varying axis direction and relaxations

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.