Mechanics of Solids最新文献

{"title":"Investigating the Flexural Behavior of Ultra-High-Molecular-Weight Polyethylene at a Low Bending Rate: Experimental and Numerical Study","authors":"Kazim Ercan,&nbsp;Mehmet Akif Dundar,&nbsp;Hamza Kemal Akyildiz","doi":"10.1134/S0025654424605032","DOIUrl":"10.1134/S0025654424605032","url":null,"abstract":"<p>This study examines the mechanical behavior of ultra-high-molecular-weight polyethylene (UHMWPE) under three-point bending at a low strain rate, with a particular focus on evaluating the influence of its distinct tensile and compressive properties on its bending response through finite element analysis. The tensile and compressive stress-strain characteristics of UHMWPE were experimentally determined at a strain rate of 5 × 10⁻³ s^–1, complemented by three-point bending tests conducted at a constant loading speed of 0.05 mm/s. To predict the flexural behavior of UHMWPE, two finite element models were constructed using the SAMP-1 material model in LS-DYNA: one incorporating the Von-Mises yield surface, which assumes similar material behavior in tension and compression, and the other employing the Drucker-Prager yield surface, which accounts for dissimilar material behaviors between tension and compression. Results of the numerical analyses revealed substantial discrepancies between the predictions of the Von-Mises and Drucker-Prager models, with the latter offering a more precise prediction of the flexural response of UHMWPE, thereby underscoring the critical importance of accounting for dissimilar material behaviors to achieve enhanced predictive accuracy.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 8","pages":"3968 - 3984"},"PeriodicalIF":0.6,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of Harmonic Wave Propagation in Fractional Derivative Viscoelastic Media Based on Time-Dependent Modulus of the P-Wave","authors":"M. V. Shitikova,&nbsp;K. A. Modestov","doi":"10.1134/S0025654424607079","DOIUrl":"10.1134/S0025654424607079","url":null,"abstract":"<p>In the present paper, harmonic waves propagating in 3D isotropic viscoelastic media are analyzed using the fractional derivative Scott-Blair model, Kelvin-Voigt model, Maxwell model and standard linear solid model. It is known that only the first and second Lamé constants, or the bulk and shear moduli, appear in Hooke’s law for three-dimensional media, but not Young’s modulus or Poisson’s ratio. This indicates that the bulk and Lamé operators are the most intrinsic operators to express stress in terms of strain when studying wave propagation in 3D viscoelastic media. That is why in the present paper, the emphasis is made on the comprehensive analysis of time-dependent operators for Lamé parameters. In so doing, the fractional derivative models are utilized for defining the time-dependent modulus of the P-wave, which governs the velocity of the longitudinal wave. Asymptotic values of the wave velocities, their coefficients of attenuation and logarithmic decrements have been found for the case of absence of bulk relaxation.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 8","pages":"3949 - 3967"},"PeriodicalIF":0.6,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Strain Localization Prediction of Anisotropic Sand under Plane Strain Conditions Based on a Non-Coaxial Constitutive Model","authors":"X. Wang,&nbsp;Y. Sun,&nbsp;Z. C. Zhang,&nbsp;B. L. Zhang,&nbsp;X. Wang","doi":"10.1134/S0025654424605585","DOIUrl":"10.1134/S0025654424605585","url":null,"abstract":"<p>Predicting the formation of shear bands is important for understanding the damage mechanisms of sands. Whereas the accuracy of strain localization predictions strongly relies on the selection of the constitutive model. In this paper, the generalized non-coaxial plastic flow theory proposed by Hashiguchi is firstly used to release the coaxiality limitation of the three-dimensional state-dependent dilatancy model of sand, and to establish the non-coaxial constitutive model of sand. In order to further accurately describe the characterization of the strength of the sand as a function of the angle of deposition (direction of principal stresses), the original anisotropic state variables were corrected using an interpolating function. After that, a series of plane strain simulations were carried out for Toyoura sands under different depositional angles and confining pressures. The results show that the established constitutive model can accurately capture the stress-strain relationship before bifurcation, reflect the variation pattern of the peak stress ratio of the sand with the deposition angle, and substantially improve the prediction of the bifurcation axial strain and the shear band inclination. On the other hand, it is proved by mathematical derivation that the non-coaxial stress rate tangent to the yield surface in the deviatoric plane is essentially composed of four orthogonal stress rate components.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 8","pages":"4066 - 4084"},"PeriodicalIF":0.6,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Design of Equi-Strength Nonhomogeneous Rotating Shafts","authors":"A. N. Prokudin,&nbsp;A. A. Burenin","doi":"10.1134/S0025654424606232","DOIUrl":"10.1134/S0025654424606232","url":null,"abstract":"<p>The article is devoted to the design of an equi-strength rotating cylinder under conditions of plane or generalized plane strain. Both solid and hollow cylinders are investigated. The problem statement is based on the equations of the linear theory of elasticity. The lateral surfaces of the cylinder are assumed to be traction-free. It is supposed that Young’s modulus is an unknown function of the radial coordinate, and the other physical and mechanical parameters of the material are constant. The dependencies of Young’s modulus are established, at which the desired stress state is achieved in the cylinder. As such a state, a constant hoop stress, a constant difference between the hoop and radial stress, and a constant linear combination of the hoop and radial stresses are considered.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 7","pages":"3704 - 3711"},"PeriodicalIF":0.6,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Study of the Effect of Viscous Filler on the Penetrating of Auxetic and Non-Auxetic Metamaterials","authors":"S. Yu. Ivanova,&nbsp;K. Yu. Osipenko,&nbsp;N. V. Banichuk,&nbsp;D. S. Lisovenko","doi":"10.1134/S0025654424606633","DOIUrl":"10.1134/S0025654424606633","url":null,"abstract":"<p>The properties of metamaterials with negative and positive Poisson’s ratio (with an auxetic structure based on a cell in the form of a concave hexagon or a conventional honeycomb structure of convex hexagons) to resist penetration by a rigid spherical striker along the normal have been experimentally studied. Samples of metamaterials, including those with a chiral structure, are made of e‑PLA plastic using a 3D printer. Auxetic and non-auxetic samples, approximately equal in mass, have been compared by their ability to reduce the kinetic energy of penetrating strikers in conditions of cells filled with air and gelatin. We have established a fact of a significant increase in penetration resistance when auxetic chiral samples are filled with gelatin compared to those filled with chiral non-auxetics. In experiments with chiral metamaterials filled with gelatin, a deviation of the striker motion direction after leaving the sample being penetrated from the approach direction (normal to the side surface) has been recorded.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 7","pages":"3727 - 3734"},"PeriodicalIF":0.6,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of Thermoelastic Geometric Irregular Plate S.P. Timoshenko, Symmetrically Strengthened by Ribs","authors":"V. V. Myltsin,&nbsp;O. A. Myltsina,&nbsp;D. K. Andreychenko,&nbsp;I. V. Papkova","doi":"10.1134/S002565442460661X","DOIUrl":"10.1134/S002565442460661X","url":null,"abstract":"<p>The paper presents a mathematical model of oscillations of a preheated orthotropic plate reinforced with stiffeners. The paper is based on a continuum model of a geometrically irregular plate. Equations, boundary and initial conditions are derived from the Ostrogradsky-Hamilton variational principle. The kinematic hypothesis of S.P. Timoshenko is used. The analysis of the natural frequencies of plate oscillations is performed for various geometric and thermomechanical parameters.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 7","pages":"3859 - 3869"},"PeriodicalIF":0.6,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Question of the Effect of the Loading Method on the Cancellous Bone Effective Elasticity Modulus","authors":"I. F. Parshina,&nbsp;A. V. Dol’,&nbsp;L. V. Bessonov,&nbsp;A. S. Falkovich,&nbsp;D. V. Ivanov","doi":"10.1134/S0025654424606645","DOIUrl":"10.1134/S0025654424606645","url":null,"abstract":"<p>Many research groups are studying the strength properties of cancellous bone in uniaxial compression experiments. The effective modulus of elasticity is determined by the linear section of the diagram under the assumption that the specimen is in a uniaxial stress state. Obviously, this is correct only in the case of compression of long specimens, whose length in the direction of load application is significantly greater than the transverse dimensions. Most researchers compress short cubic or cylindrical specimens with an aspect ratio of 2 to 1. It is also noted that under uniaxial compression, tissue in the grip area is damaged, which leads to an underestimation of the calculated effective modulus of elasticity by 20–40%. It is believed that errors in measuring the effective modulus of elasticity can be avoided if the deformation is not measured directly, evaluating only the displacement of the movable crosshead, but a contact or contactless extensometer is used or the ends of the specimens are protected from destruction using end caps. At the first stage of the work, the influence of the relative height of the specimen on the effective modulus of elasticity of the spongy bone of cattle calculated according to the rod theory was studied (a total of 90 bone specimens were tested). At the second stage, the modulus was assessed with direct application of load to the specimen, as well as with gluing plastic and aluminum plugs to its end (a total of 75 bone samples were tested). Regression dependencies were constructed linking the mineral density of the bone and its modulus of elasticity.</p><p>It was revealed that when the relative height of the specimen is not less than 5 units, it ceases to affect the modulus of elasticity. It was shown that during uniaxial compression of such long specimen, the method of their loading does not affect the modulus of elasticity. It was found that the relationship between the effective modulus of elasticity and mineral density does not depend on the method of loading the specimen, provided that its relative height is not less than 5 units.</p><p>In this article, a step was made to develop a standard for conducting uniaxial experiments on bone tissue compression aimed at calculating the effective modulus of elasticity. It is shown that when planning such experiments, it is necessary to prepare specimen with a relative height of at least 5 units. This allows for the correct calculation of the effective modulus of elasticity of cancellous bone according to the rod theory, using data on the displacement of the upper grip of the testing machine.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 7","pages":"3870 - 3879"},"PeriodicalIF":0.6,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Limit State of a Multilayered Physically Nonlinear Concrete Rods","authors":"S. V. Tikhonov","doi":"10.1134/S0025654424606487","DOIUrl":"10.1134/S0025654424606487","url":null,"abstract":"<p>The paper considers the problem of longitudinal and transverse bending of the multilayered concrete rods of constant cross section under the quasi-static loads. It is assumed that concretes are deformed linearly at deformations below the elastic limit, and nonlinearly quasi-elastically above it. In the area of nonlinear deformation, the correlations between strain and deformation are taken in the form of the second-order polynomials with different coefficients for different grades of concrete. It is supposed that there is a uniaxial strain condition, and in the compression area all layers of the rod are elastically deformed, while in the tension area the layers can be in the areas of elastic, nonlinear quasi-elastic deformation and include the boundary of these two areas. The presented analytical correlations are obtained to determine the distribution of displacements, deformations, forces, and the position of the neutral line in the case of a statically determinable problem of transverse bending of a hinged rod. An algorithm to determine the possible external loads is given for each of the possible deformation configurations in the rod layers.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 7","pages":"3803 - 3810"},"PeriodicalIF":0.6,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asymptotic Model of Non-Stationary Processes in Shells of Revolution under the Action of End Impact Loads of Bending Type","authors":"I. V. Kirillova","doi":"10.1134/S0025654424606591","DOIUrl":"10.1134/S0025654424606591","url":null,"abstract":"<p>The present study deals with the construction of an asymptotic model of propagation of non-stationary waves in thin shells of revolution under the action of end impact loads of the bending type. The developed asymptotic methods for solving boundary value problems for the components of the stress-strain state that are the main ones for the considered type of waves, namely the bending component according to the Kirchhoff-Love theory and the hyperbolic boundary layer, are described. The asymptotic methods are based on various types of expansions in power series in a small parameter of thinness of the wall depending on the values of the indices of variability and dynamicity. In this case, integral Laplace transforms in time and Fourier transforms in the spatial coordinate, methods of frontal asymptotics, expansions in special functions are used. Calculations performed on the example of a spherical shell have shown the efficiency of the developed methods.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 7","pages":"3756 - 3768"},"PeriodicalIF":0.6,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Decomposition of Motion in the Description of Interdiffusion in a Viscoelastic Body","authors":"D. S. Dudin,&nbsp;I. E. Keller","doi":"10.1134/S0025654424606013","DOIUrl":"10.1134/S0025654424606013","url":null,"abstract":"<p>The influence of stresses on diffusion is recognized, along with diffusion’s role in the viscous deformation of solids. The interconnection between interdiffusion and deformations in metallic alloys and steels significantly affects the durability of machine components exposed to harsh conditions with substantial temperature and force. In such instances, diffusion facilitates the transportation of alloying elements from the surface layer, impacting the intensity of corrosion and corrosion cracking. Laws correlating diffusion flows to chemical potential gradients can be related to various diffusion reference frames, determined by the base experiment used or the convenience of establishing the boundary value problem. In the related equations of interdiffusion in a deformable solid, we must consider that diffusion happens in a local material volume transported by the convective velocity, and that diffusion is described in a local diffusion frame of reference moving relative to the material. A decision must be made regarding convective velocity and diffusion reference frame (decomposing the material motion into convective and diffusive parts). Within the linear thermodynamics of irreversible processes, a related system of equations is set for a multicomponent medium, where balance equations for composition variables are considered, and stress and strain tensors are introduced for the medium on the whole. Two diffusion descriptions are considered: one assumes a diffusion reference frame frozen into a local material volume, and the other involves a system of markers, small inert particles, moving relative to the material due to unbalanced diffusion flows. Both methods are employed in basic diffusion pair experiments to determine diffusion coefficients. For each of the diffusion descriptions – “material” and “marker” – within the process coupled with viscoelastic deformation, the thermodynamically resolved relations are derived for two-component and three-component metallic alloys. To compare the associated models, a one-dimensional problem is proposed. The perturbation method is applied, yielding the dependency of the relaxation time spectrum on the perturbation wavelength. The values of the effective interdiffusion coefficients align with the inclined asymptotes of these dependencies, and the effective viscosity coefficients match the horizontal ones. The dependency of these effective coefficients on the diffusion and viscoelastic properties for an austenitic alloy Fe65-Cr20-Ni15 at high temperature is examined. Overall, the marker description of interdiffusion provides more information and it is more convenient for setting boundary value problems with boundary diffusion of components.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 7","pages":"3781 - 3797"},"PeriodicalIF":0.6,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}