Development of porous implants with non-uniform mechanical properties distribution based on CT images

In this study, the mechanical properties (elastic modulus, yield stress, and Poisson's ratio) of rhombic dodecahedron (RD) unit cell has been studied analytically and numerically. For the analytical study, two well-known beam theories, namely Euler Bernoulli and Timoshenko, have been implemented. For validating the analytical relationships, finite element model of unit cell with repetitive boundary condition has been created. Moreover, the experimental results of recent studies have been used for validation. The results showed that the presented analytical relationships for RD lattice structure have good agreement with numerical and experimental results in all the relative densities particularly in lower relative densities. Besides, the analytical relationships based on Timoshenko theory showed closer results with numerical/experimental data. The derived analytical relationships for RD as well as the data extracted from CT scan images of a femur bone, were combined and used to create a porous femur implant model. The stress and strain distributions of the porous femur model under typical static compressive load due to human weight as well as axial rigidity of the model in the same loading conditions have been obtained and compared with the experimental results from other studies. The stress and strain distributions of the porous femur implant model based on RD unit cells, as well as its axial rigidity, showed good agreement with the results obtained for human femur.     

Recrystallization behavior of a Nb-microalloyed steel during hot compression

Using a Thermecmastor-Z hot simulator, dynamic recrystallization (DRX) and static recrystallization (SRX) behavior of a Nb-microalloyed steel was investigated by single-hit compression tests and double-hit compression tests, respectively. The experimental results show that DRX will more easily occur at higher deformation temperature and lower strain rate. The deformation activation energy and stress exponent for the Nb-microalloyed steel are calculated to be 379.29 ± 23.56 kJ/mol and 5.76 in temperature range of 950 °C to 1100 °C by regression analysis, respectively. Furthermore, a semi-empirical model is developed to identify the peak stress and strain for DRX. It is found that SRX kinetics follows Avrami’s law, and the softening fraction predicted by the model agrees well with experimental results.     

Simple loading of a polymer material with nonlinear creep

Nonlinear tensor relations between strain, stress, and time are examined for a memory-type medium using degenerate kernels. The material parameters are determined from creep tests in a simple state of stress. Expressions for the strain associated with a complex state of stress and simple loading, found on the basis of the local strains theory, are in satisfactory agreement with the experimental data obtained for specimens of high-density polyethylene.Mekhanika Polimerov, Vol. 3, No. 2, pp. 236–242, 1967     

On the constitutive relations for isotropic and transversely isotropic materials

In this work the strain and stress spaces constitutive relations for isotropic and transversely isotropic softening materials are developed. The loading surface is considered in the strain space and the normality rule; the stress relaxation is proportional to the gradient of the loading surface, is adopted. It is found that the strain space plasticity theory allows us to describe the hardening, perfectly plastic and softening materials more accurately. The validity of the strain space constitutive relation for transversely isotropic materials are confirmed by comparing with the experimental data for fiber reinforced composite materials. Some numerical examples in two and three dimensional elasto-plastic problems for various loading–unloading conditions are presented, and give a very good agreement with the existing results.     

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.     

Modeling and Simulation of the Portevin-Le Chatelier Effect

During deformation of an Al-Mg alloy (AA5754) dynamic strain aging occurs in a certain range of temperatures and strainrates. An extreme manifestation of this phenomenon, usually referred to as the Portevin-Le Chatelier (PLC) effect, consists in the occurrence of strain localisation bands accompanied with discontinuous yielding. The PLC effect stems from dynamic dislocation-solute interactions and results in negative strain-rate sensitivity of the flow stress. The PLC effect is detrimental to the surface quality of sheet metals and also affects the ductility of the material. Since the appearance of the effect strongly depends on the triaxiality of the stress state, three-dimensional finite element simulations are necessary in order to optimize metal forming operations. We present a geometrically nonlinear material model which reproduces the main features of the PLC effect. The material parameters were identified based on experimental data from tensile tests. Special emphasis was put on the critical strain for the onset of PLC effect, ε _c , and the statistical characteristics of the stress drop distribution. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite-element formulations of shear localization in granular materials

Displacement and mixed finite element formulations of shear localization in granular materials are presented. The formulations are based on hypoplastic constitutive laws for soils and the mixed-enhanced treatment involving displacement, strain and stress rates as independently varied fields. Included in these formulations are the standard displacement method, the three-field mixed formulation, the method of incompatible modes, the enhanced assumed strain method and the mixed enhanced strain method. Several numerical examples demonstrating the capability and performance of the different finite element formulations are presented. The numerical results are compared with available experimental data of Hostun RF sand and numerical results of Karlsruhe sand on biaxial tests. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the theory of orientation of linear amorphous polymers

The previously derived orientation equations are solved for uniaxial extension at constant true stress, unloading, stress relaxation, and biaxial orientation at constant strain rate. The dependence of the birefringence of biaxially oriented PMMA on the magnitude and conditions of preliminary orientation has been experimentally investigated. There is good qualitative agreement between the theoretical and experimental results.For communication 1 see [1].Lenin Moscow State Pedagogic Institute. Translated from Mekhanika Polimerov, No. 1, pp. 14–21, January–February, 1973.     

Equilibrium shear of rubber specimens in practical testing

The stress and strain distribution in rectangular rubber specimens in equilibrium shear has been analyzed with allowance for the effect of the inhomogeneity of large nonlinear deformations. The results obtained satisfy the basic equations of the nonlinear theory of elasticity as well as the experimental data on the displacements of the points of a rectangular grid inscribed on the surface of the specimens before deformation.Mekhanika Polimerov, Vol. 3, No. 6, pp. 1024–1029, 1967     

Estimation of temperature in rubber-like materials using non-linear finite element analysis based on strain history

A finite element procedure for hyper-elastic materials such as rubber has been developed to estimate the temperature rise during cyclic loading. The irreversible mechanical work developed in rubber has been used to determine the heat generation rate for carrying out thermal analysis. The evaluation of the heat energy is dependent on the strains. The finite element analysis assumes Green–Lagrangian strain displacement relations, Mooney–Rivlin strain energy density function for constitutive relationship, incremental equilibrium equations, and Total Lagrangian approach and the stress and strain of the rubber-like materials are evaluated using a degenerated shell element with assumed strain field technique, considering both material and geometric non-linearities. A transient heat conduction analysis has been carried out to estimate the temperature rise for different time steps in rubber-like materials using Galerkin's formulations. A numerical example is presented and the computed temperature values for various load steps agree closely with the experimental results reported in the literature.     

Theoretical and experimental study of the elastoplastic state of cylindrical shells with rigid inclusions

A study is made of the stress distribution around a rigid circular inclusion on the lateral surface of a cylindrical shell subjected to a uniformly distributed load. The stress distribution present during the elastoplastic stage of deformation of the shell material is studied. Calculated results are obtained on the basis of the numerical solution of inelastic problems in accordance with the theory of thin shells and the strain theory of plasticity for the case of active loading. Experimental data for shells loaded by internal pressure are obtained with the use of pneumatic gauges. The data are in the form of values of the strains and changes in curvature in characteristic sections of the shell. The theoretical and experimental results are compared and analyzed.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 72–76, 1987.     

Experimental and Numerical Study of Polypropylene/Polyethylene Thin Foil in Biaxial Tension

The material under consideration is a thermoplastic copolymer blend of polypropylene and polyethylene (PP/PE), constituting the core layer of a steel/polymer/steel composite material. A biaxial loading machine was developed for studying the behavior of the copolymer subjected to in-plane complex stress states. A study on the shape of the specimen by means of numerical finite element simulations and preliminary experimental tests are carried out, in order to obtain a maximization of the strain distribution in the middle region of the cruciform specimen. Afterwards, the sensitivity of the mechanical response under both equibiaxial and non-equibiaxial conditions is addressed. All the experiments are monitored by means of a digital image correlation (DIC) system, providing full-field measurements of the displacements, and, consequently, of the strain distribution. The presented experimental results will be used for validating the material model developed for the PP/PE layer material. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Semianalytical methods for analyzing stress concentrations in thick-walled multilayered composites

For analyzing the stress, strain, and displacement fields in thick-walled anisotropic multilayered composites, sophisticated semianalytical solution methods based on a first-order shear deformation theory have been developed at the Insitut für Leichtbau und Kunststofftechnik and validated in a great number of numerical finite-element simulations and extensive experimental tests. A comparison of results obtained by the different methods for general multilayered composites made from unidirectional, bidirectional, and textile-reinforced layers show a good agreement.     

Analitical Description of the Creep of Expanded Polystyrene under Compressive Loading

Data obtained in testing the creep of expanded polystyrene plates in compression are discussed. Power-type and exponential regression equations are used for describing the compression creep curves. Within the limits of data spread, both these equations represent experimental results equally well. A correlation between the creep strain and density, the compressive stress at a 10% strain, and the elastic modulus in compression is revealed for the material investigated.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 525–534, July–August, 2005     

Complex loading of a polymer material with nonlinear creep

The nonlinear tensor stress, strain, and time relations for a memory-type medium under complex loading are examined using degenerate kernels. The basic expressions for simple loading and the material parameters were determined in [5]. The local strains theory is used to find expressions for the strain components in the presence of stepwise complex variation of the stress components, and these expressions are shown to be in satisfactory agreement with the experimental data for high-density polyethylene.Mekhanika Polimerov, Vol. 3, No. 3, pp. 421–426, 1967     

Experimental determination of the concentration of stresses and strains around a circular hole in a glass-reinforced plastic specimen

The results of experimental studies on the concentration of stresses and strains at a circular hole in a glass-reinforced plastic specimen, involving the use of the photoelastic coating method, are given. The effects of the anisotropy of the material, of ratio of the hole diameter to the width of the model, and of the load level on the magnitude of the stress and strain concentration factor are indicated.Translated from Mekhanika Polimerov, No. 1, pp. 159–163, January–February, 1972.     

Analytical and experimental analysis of stress concentration in notched multilayered composites with finite outer boundaries

A solution method for stress concentration problems of fibre- and textile-reinforced multilayered composites with account of the influence of a circular or elliptical cut-out and of the finite outer boundary of a composite plate is presented. The method is based on complex-valued displacement functions and conformal mappings in combination with the boundary collocation and least squares methods. This allows a layer-by-layer calculation of full stress, strain, and displacement fields in a generally multilayered anisotropic plate. To verify the calculation model, extensive experimental studies have been carried out. For all the combinations of multilayered GF/PP plates, laminate lay-ups, and notch and specimen dimensions investigated so far, a very good agreement between the analytical calculations and experimental results is found to exist.     

Structural diagram of furfural-acetone plastic concrete in compression

The attenuation of plastic concrete creep is analyzed on the basis of the structural diagram, and a formula relating total strain and compressive stress is derived. This formula is in good agreement with the experimental data, as demonstrated by fitting the experimental creep curves.Mekhanika Polimerov, Vol. 4, No. 3, pp. 454–461, 1968     

高温合金GH4169的失效特性及失效模型研究

对GH4169高温合金开展了不同应力三轴度（-0.33~0.33）、不同应变率（0.001~5 000 s-1）、不同温度（293~1 073 K）条件下的材料性能试验.基于Johnson-Cook失效模型的框架,研究了Johnson-Cook(JC)失效模型及已有文献提出的修改形式中应力三轴度项拟合结果的不确定性及应变率对失效应变的线性关系描述局限性问题,通过提出的特定参数确定方法与耦合应力三轴度的应变率效应指数函数,建立了一种唯象修正的失效模型.基于GH4169高温合金的试验结果,标定了修正的失效模型与JC模型中各个参数.结果表明:在不同应力三轴度下,GH4169的失效应变表现出不同的应变率效应;与传统的JC模型相比,修正的失效模型更能够较好地描述GH4169的失效行为;同时能够保证失效应变的非负性.     

Effect of supermolecular structure on the relaxation properties of polyformaldehyde in tension and compression

An experimental investigation of the stress relaxation at various strain values in polyformaldehyde blocks has revealed two regions with different stress relaxation mechanisms. The effect of the supermolecular structure on each of these regions is discussed.Scientific Research Institute of Plastics, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 787–792, September–October, 1969.