Deformability of surfaces of positive curvature

For surfaces of positive Gaussian curvature bounded away from zero the following statement is proved: A piece of a given surface containing a preassigned finite set of points and having a Lyapunov boundary can be deformed with an arbitrary given (as large as we like) bending at these points under the condition that the area of the piece is sufficiently small.Translated from Matematicheskie Zametki, Vol. 19, No. 5, pp. 815–823, May, 1976.I thank V. T. Fomenko for guidance.     

Deformability of expanded polystyrene under short-term compression

The results obtained in an experimental investigation of deformability of expanded polystyrene (EPS) under short-term compression are presented. The density of EPS varied from 13 to 28 kg/m³. The method of design of experiments was used to determine the elastic modulus and the ultimate strain (corresponding to the end of quasi-linear deformability) under compression stresses operating perpendicularly and parallel to the faces of EPS products. A graphical interpretation of the models is also presented. Based on the experimental data obtained, it was concluded that the expanded polystyrene was homogeneous in mutually perpendicular planes with respect to its deformability in compression. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 639–656, September–October, 2007.     

Deformability of thermoplastics in physiological salt solution

Conclusions 1. The creep of thermoplastics in physiological salt solution is characterized by change in the rate of creep deformation relative to the creep in air. The bending creep deformations of HMWPE and phenylone and the compressive creep deformation of HMWPE are described by a binomial equation [Eq. (5)] and the compressive creep deformation of phenylone is described by Eq. (6).2. The lifetime of the thermoplastics studied under static compression and bending determined relative to limiting deformations is described by Eq. (7). Under the same stresses and limiting deformations, the lifetime of phenylone in physiological salt solution is greater than the lifetime of HMWPE.3. After the simultaneous action of physiological salt solution and static stress over one month, most of the characteristics of short-term strength in phenylone are significantly reduced due to swelling in the model medium.Paper presented at the Third All-Union Conference on Polymer Mechanics, Riga, 1976.N. N. Priorov Central Scientific-Research Institute of Traumatology and Orthopedics, Moscow. Kazan Construction Engineering Institute. Translated from Mekhanika Polimerov, No. 2, pp. 325–331, March–April, 1978.     

Rigidity and Infinitesimal Deformability of Ricci Solitons

In this paper, an obstruction against the integrability of certain infinitesimal solitonic deformations is given. Using this obstruction, we show that the complex projective spaces of even complex dimension are rigid as Ricci solitons although they have infinitesimal solitonic deformations.     

Deformability and strength of compact bone tissue during tensioning

The deformability and strength characteristics of compact bone tissue of human tibia during tensioning along all three main anisotropy axes was determined experimentally. The character of change in the secant moduli of elasticity and specific energies of deformation during the loading process were studied. A correlation was established between the mechanical characteristics and the biochemical composition of the bone tissue.     

Predicting the Deformability of Expanded Polystyrene in Short-Term Compression

A regressive model is presented for the relationship between the compressive stress and strain of expanded polystyrene (EPS) on a 0–35% strain range. On the whole, the model agrees well with experimental data. A practical way is suggested for determining the coefficients of the model from the known density of EPS plates and their compressive stress at a 10% strain. The model allows one to predict the critical compressive stress and the elastic modulus of EPS.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 157–162, March–April, 2005.     

Predicting the Deformability of Expanded Polystyrene in Long-Term Compression

The interval prediction of creep strain on the basis of 15 years is carried out for slabs of expanded polystyrene (EPS) subjected to a compressive load. The expansion of the confidence interval caused by the discounted prediction information is allowed for by an additional factor. The creep compliance _c (t = 15) of the EPS is determined based on empirically estimating the long-term creep of this material subjected to a compressive stress σ _c = 0.3σ_10% for 15 years. A relationship between _c (t = 15) and EPS density in the slabs is established. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 5, pp. 607–618, September–October, 2005.     

Deformability of an expanded polystyrene EPS 200 under long-term compression

The results of a study on the creep of EPS 200 plates under compressive stresses σ_c in the interval 0.22 ≤ σ_c/σ_10% ≤ 0.80 are presented. From experimental data, the domain of linear creep of the material in the interval of compressive stresses is determined. Under variations of the stress on the interval 0.22 ≤ σ_c/σ_10% ≤ 0.36, the prognostic value of creep strain of the EPS 200 plates for a lead time of 25 years is found to be 2.4%, with a coefficient of variation equal to 18%.     

Effect of Interruptions in Loading on the Durability and Deformability of Structural Plastics

An alternative way of estimating the durability of structural plastics under stresses = const 0.4-0.8_f(_f is the failure stress) based on test data obtained in multiple rectangular loading-rest cycles is proposed. It is also suggested to employ the decrease in the instantaneous elastic modulus as a criterion for evaluating the residual service life of plastic parts and structures and elucidating the reasons for their early failure. For the first time, a possibility of considerably increasing the durability and endurance of structural plastics under short pulsed loadings with relatively long interruptions at the initial stage of stress concentration is considered. The cases of a significantly increased endurance of plastics caused by long interruptions after some fatigue loading by high-frequency tension cycles with a zero maximum stress are explained. First experimental confirmations of an increased durability and endurance of microcomposites subjected to short pulsed loadings alternating with long interruptions are obtained. The evolution of the effect of the loading-rest modes on the durability of massive specimens, microcomposites, and dry fibrous reinforcing fillers is demonstrated with examples of a glass-fabric laminate, a microcomposite, and a nonimpregnated glass strand.     

Deformability and load-carrying capacity of netted composite rod assemblies with metal fittings

A technology is proposed for making netted rod assemblies with metal joints 3–5 times lighter than existing comparable structures. A procedure was developed for winding assemblies out of carbon-fiber-reinforced plastic (UKN-5000 and binder EKhD-MK). Results are presented from a study of the strain characteristics and load-carrying capacity of assemblies with different reinforcement schemes for different conditions of static damage. It is shown that the design of netted rod assembly proposed here is significantly superior to all known analogs with respect to specific stiffness characteristics and provides great dimensional stability in the case of unilateral heating of the product. The method is most effective if used to develop framework-type structures for use in space — platforms, telescope and antenna supports, and masts.Paper to be presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 387–392, May–June, 1995.     

Deformability and strengh of expanded polystyrene (EPS) under short-term shear loading

Data obtained in investigating the ultimate strength and deformability of expanded polystyrene under short-term shear loading according to EN 12090 are discussed. Linear regression equations are used for describing the ultimate shear strength and modulus in relation to the density of EPS. A correlation is found to exist between the ultimate strength of EPS and its density and specimen thickness. An empirical dependence between the shear modulus and density of EPS is established. The strains corresponding to the conditional limit of proportionality and to the ultimate shear strength of EPS in short-term loading are determined. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 121–134, January–February, 2007.     

Uniform,uniaxial elongation of polyethylenes

The uniform, uniaxial elongation of polyethylenes of various crystallinity and the effect of strain rate on this process are analyzed. Quantitative relations between the stress, the degree of elongation, and the strain rate are established, and the factors controlling the uniform, uniaxial elongation of polyethylenes are defined.M. I. Kalinin Polytechnic Institute, Leningrad. Translated from Mekhanika Polimerov, No. 6, pp. 987–992, November–December, 1972.     

Linear theory of nonisothermal forced elongation

In this work the linearized equations of nonisothermal forced elongation are analyzed. It is shown that solutions for the associated boundary-initial value problem are governed by a strongly continuous semigroup of bounded linear operators on the physically correct state space and that the semigroup is eventually differentiable. The regularity of the semigroup is proven via two complementing methods. Whilst the first method is based on Pazy’s classical result on eventual differentiability, the second method provides a direct argument. The regularity properties of the semigroup correspond to the expected physical behavior of the elongational flow.     

Jeffreys fluids in forced elongation

In this paper we study existence, uniqueness and regularity of solutions for the equations governing the forced elongation of fluids with differential constitutive law of Jeffreys type. These equations consist of nonlinear first-order hyperbolic equations in one spatial dimension. Forced elongation is imposed through velocity boundary conditions at the domain entry and exit. The existence result is based on the Schauder fixed point theorem and energy methods in the space of boundary-regular functions.