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This paper presents a data‐driven method to identify a bound for the structural response of interest when a data set of elastic material responses is available. The obtained bound is probable in the sense that, at least with a certain confidence level, the probability that the structural response is within the bound is no smaller than a certain target value of reliability. The confidence level is ensured by considering the order statistics of the given data points. In this manner, this paper introduces the concept of reliability to the framework of data‐driven computational elasticity to address uncertainty in the data set. The method does not require any statistical information of the data points. Two numerical examples demonstrate the use of the proposed method to analyze static responses of structures by using only given material data sets. [ABSTRACT FROM AUTHOR]

The catenary is a curve that has played a significant role in the history of mathematics, finding applications in various disciplines such as mechanics, technology, architecture, the arts, and biology. In this paper, we introduce some generalizations by applying the variational method to deformable strings. We explore two specific cases: (i) in the first case, we investigate the nonlinear behavior of an elastic string with variable length, dependent on the applied boundary conditions; specifically, this analysis serves to introduce the variational method and demonstrate the process of finding analytical solutions; (ii) in the second case, we examine a deformable string with a constant length; however, we introduce mass redistribution within the string through nonlinear elastic interactions. In the first scenario, the deformation state of the string always describes elongation, as compression states prove to be unstable for fully flexible strings. In contrast, in the second scenario, the finite length constraint induces compressive states in specific configurations and regions of the string. However, it is worth noting that the solution to this problem exists only for values of the elastic constant that are not too low, a phenomenon that is studied in detail. We conduct here both analytical and graphical analyses of various geometries, comparing the elastic behavior of the two aforementioned types of strings. Understanding the elastic behavior of deformable strings, especially the second type involving mass redistribution, is crucial for enhancing comprehension in the study of biological filaments or fibers and soft matter. For instance, these investigations can contribute to understanding the mechanisms employed by cells to sense gravity or other mechanical conditions. [ABSTRACT FROM AUTHOR]

In this paper, the problem of a heterogeneous elastic micropolar nanostructure with a periodic structure subject to imperfect contact conditions is analyzed through the two‐scale asymptotic homogenization method (AHM). The imperfect interface is modeled as a generalization of the well‐known spring model; that is, the homogeneous imperfect interface is described by the following conditions: tractions and coupled stress are continuous, but displacements and microrotations are discontinuous across the imperfect interface. The jumps in displacements and microrotations are proportional to the interface traction and coupled stress components, respectively. In particular, micropolar multilaminated nanocomposites with centro‐symmetric isotropic constituents and imperfect contact conditions are studied. From AHM, the solutions for the displacement and microrotation fields are found by means of two‐scale series expansions depending on a local (microscopic) variable and a global (macroscopic) variable. The local problem statements and the corresponding effective properties are explicitly described. The formulation depends on the constituent physical properties, the imperfection parameters, the cell length in the y3‐direction, and the phase's volume fractions. Numerical results are illustrated and discussed. We concluded that the effective moduli are affected by the imperfections and the cell length in the y3‐direction. [ABSTRACT FROM AUTHOR]

In this paper, we study a porous thermoelastic system with microtemperature and strong time delay acting on the volume fraction equation. The thermal effect of microtemperature is based on the Lord–Shulman theory (J Mech Phys Solids. 15(5) (1967), 299–309.), while the strong delay is motivated by Makheloufi's et al. recent work (Math Meth Appl Sci. 44 (2021), 6301–6317.). To prove the well‐posedness of the system, lack of exponential stability and the polynomial decay with optimal rate, we use the semigroup theory of linear operators. [ABSTRACT FROM AUTHOR]

The paper presents the features of solutions to nonlocal elasticity problems in domains with stepped transitions and elliptical notches. A comparative analysis of the solutions obtained in the classical and nonlocal elasticity theories was carried out, as well as an analysis of the influence of the main parameters of the model on the final results. The presented solutions for the region with a step transition are in qualitative agreement with the experimental data and have similar portraits of deformations and resultant stresses along the loading axis. In regions with elliptical notches, similar effects are observed. In addition to qualitative agreement with experiments, solutions in the nonlocal formulation have lower stress values in the concentrators and exhibit edge effects, which are characterized by sharp stress and strain gradients at the domain boundaries. The solutions were carried out numerically by the finite element method. [ABSTRACT FROM AUTHOR]

The paper presents the derivation and analysis of a poroelasticity model in a domain with fracture represented by a codimension‐one manifold. The system of saturated flow and linear elasticity both in the rock matrix and in the fracture coupled through an appropriate interface condition is obtained from a continuum description by integration and semi‐discretization in the normal direction of the fracture. The existence and uniqueness of a weak solution are proved with the help of an iterative splitting, whose convergence rate is analyzed. The analysis is complemented by a numerical example. [ABSTRACT FROM AUTHOR]

Utilization of symmetrical or anti‐symmetrical condition could improve the calculation efficiency. In this paper, a mathematical formulation is proposed to deal with the symmetrical or anti‐symmetrical condition in an integral nonlocal stress gradient model (INSGM), which is transformed equivalently into differential form with constitutive boundary condition as well as constitutive symmetrical or anti‐symmetrical condition. Unlike general constitutive boundary conditions, an integral item is introduced to constitutive symmetrical and anti‐symmetrical conditions, and they are opposite to each other. Based on INSGM with symmetrical or anti‐symmetrical conditions, static bending of simply‐supported (SS) and clamped‐clamped (CC) functionally graded porous Timoshenko nanobeams is investigated for symmetrical loads, including uniformly distributed load (UDL) and middle point force, as well as anti‐symmetrical loads, including anti‐symmetrical UDL and middle point moment. The exact solutions are deduced and expressed in explicit form for different boundary and loading conditions. Calculation shows that, under UDL, bending deflections of half Timoshenko nanobeams based on current model agree well with those for whole Timoshenko nanobeams based on general INSGM for both SS and CC boundary conditions. Numerical study is performed to show the effectiveness of current model. [ABSTRACT FROM AUTHOR]

In this paper, we show that within the class of isotropic Mindlin‐Toupin gradient theories there exist a particular variant of the theory, which allows a completely simplified form of traction boundary value problems. This theory can be obtained assuming that the high‐grade part of the strain energy density depends only on the vector‐type quantities, that are the gradient of dilatation and the curl of small rotation. Such incomplete gradient theory becomes positive semi‐definite and at the same time it obeys the strong ellipticity conditions of the general Mindlin‐Toupin first strain gradient elasticity. Based on the variational approach it is shown that the equilibrium equations of the developed theory and its definition for the surface traction can be given only in terms of the total stresses (like in classical elasticity). Such formulation can be useful for derivation of the closed form solutions for the problems with traction‐type boundary conditions. Examples of the solutions for the problem of cylindrical bending and for the inplane crack tip fields are presented. It is shown that considered theory allows to obtain a regularized solution for the crack problems and at the same time it does not predict a non‐physical infinite increase of the material's rigidity under bending. [ABSTRACT FROM AUTHOR]

Abstract: This is our third and last exegetic essay on the fundamental review article DIE ALLGEMEINEN ANSÄTZE DER MECHANIK DER KONTINUA in the Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Bd. IV‐4, Hft. 5 (1913) by Ernst Hellinger which contains the translation and the commentary of the remaining text starting from p. 663. The six subsections, No. 9–15, deal with the applications of the previously developed conceptual tools to formulate: an effective theory of elasticity, the dynamics of ideal fluids, models for internal friction and elastic hysteresis, a theory of capillarity, optics, the fundamental equations of electrodynamics, an introduction of the thermodynamical foundations and the relationship between the theory of continua and the theory of relativity. Hellinger refers to relevant literature while consolidating in an effective way the contemporary knowledge in 1913. Considering notational differences as being irrelevant for the characterization of the presented scientific content, Hellinger's article shows that an effective compendium of a large part of the insights given in Truesdell and Toupin and Truesdell and Noll has already been available in 1913. We include in this paper an assessment of the different roles played by pioneers, who are innovating their scientific discipline, and by erudite scholars whose role consists in re‐ordering existent knowledge and advertising to a wider audience the most important technical results already obtained in a given discipline. [ABSTRACT FROM AUTHOR]

The paper presents the dynamic solution of a Mode-I crack in an orthotropic medium by use of the non-local theory, the generalized Almansi's theorem and the Schmidt method. By using Fourier transform, this problem is converted to a pair of dual integral equations. Different from the classical elasticity solution, the present solution exhibits no stress singularity at the crack tips because of the incorporation of non-local effects. Numerical examples are provided to show the effects of the crack length, the circular frequency of the incident waves and the lattice parameter on the stress field near the crack tips in an orthotropic medium. [ABSTRACT FROM AUTHOR]

The paper presents the fundamental solutions established for the equilibrium equations written in terms of displacements in the gradient model describing the deformation of two-component elastic composites with stochastic structure. In the paper 2D and 3D problems are constructed on the basis of the theory of generalized functions. [ABSTRACT FROM AUTHOR]

The paper deals with the elastic and cohesive interface behavior of pre-cracked bi-material ceramic-metal structures under dynamic time harmonic load. The shear lag model as well as the Fourier method is applied to find the dynamic response of the considered bi-material structure, assuming the cohesive interface behaviour, accompanied before of the elastic-brittle one. In both cases, the growth of debond length is not considered, e.g. at a given loading condition the only corresponding debond length is found. The inertia forces of the already elastic debond parts of the bi-material structure are neglected. Appropriate contact conditions are proposed in order to fit together both elastic and cohesive solutions. The numerical predictions for the cohesive debond length of the bi-material structures is calculated by the aid of the corresponding value of the elastic debond length at the same loading condition. The influence of loading characteristics i.e. frequencies and amplitude fluctuations on the debond length and the interface shear stress distribution is discussed. The parametric analysis of the results obtained is illustrated by examples of the modern ceramic-metal composites on metal substrates and is depicted in figures. [ABSTRACT FROM AUTHOR]

Structures made of Functionally Graded Materials (FGMs) show a gradual variation of material properties in one, two, or three directions. In this paper, an efficient low-order shell element with six nodal degrees of freedom (including the drill rotation) is presented, supplemented with a proper method for calculating effective elastic properties. This new FGM shell element can be coupled with 3D FGM beam elements on a single node. The numerical results indicate high effectiveness and accuracy of the proposed approach. [ABSTRACT FROM AUTHOR]

The paper is concerned with wrinkling of thin facings in sandwich structures with a bi‐modular elastic core. Bi‐modularity of core implies a different stiffness in tension and compression. The solution to the wrinkling problem is obtained by an extension of the Hoff method. One of two bounding cases are the classical Hoff solution where the stiffness of the core in tension is equal to that in compression. In the second case demonstrated in the paper the mismatch in the stiffness of the core in tension and compression is so large that the higher stiffness can be assumed infinite. The solution for intermediate cases where the ratio of the core stiffness in tension to that in compression is finite is also presented in the paper. In addition, the approach to the analysis of wrinkling utilizing the stresses in the core derived by the theory of elasticity is discussed and the closed‐form solution obtained in the particular case of equal tensile and compressive moduli. It is shown that a mismatch in the elastic moduli of the core in tension and compression results in the change in the mode shape of wrinkling as compared to the core with equal tensile and compressive stiffness. An increase in the stiffness of the facing or using a stiffer bi‐modular core results in a higher wrinkling stress. It is also demonstrated that a higher stiffness of a bi‐modular core in either tension or compression causes only a limited reduction in the energy absorbed prior to wrinkling. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we present new closed‐form solutions for functionally graded longitudinally vibrating bar. The modulus of elasticity is represented as a continuous function varying along the axial coordinate. It is postulated that the mode shape represents the sixth order polynomial. Six closed form solutions are presented: four for clamped‐clamped bar, and two for clamped‐free bar. [ABSTRACT FROM AUTHOR]

The majority of processes in composite materials involve a wide range of scales. Because of the scale disparity in multi scale problem, it's often impossible to resolve the effect of small scales directly. In this paper we perform multi scale modeling in order to analyze properties of composite materials with periodical structure under temperature and stresses influence. Each component has its own thermal and mechanical (elastic) properties. We replace differential equations with rapidly oscillating coefficients by homogenized equations having effective parameters, incorporating multi scale structure and properties of any component. The influence of any component's properties and of the layer thickness on the effective properties of whole sample has been studied. We perform comparison of results, obtained with and without account for thermostresses. [ABSTRACT FROM AUTHOR]

The paper is devoted to the construction of an iterative procedure of calculation of mechanical properties of water saturated porous materials subject to freezing and thawing processes. The procedure consists of two steps. The first is the solution of equations for the linear poroelastic medium with material parameters depending on current porosity which measures the frost damage. The second one, based on the Gurson-Tvergaard-Needleman model of plastic deformations with porosity as a measure of damage, yields, among other quantities, the relation for porosity changes caused by freezing. Relations between material parameters and varying porosity follow from the micro-macro procedure which yields Gassmann and Epstein relations for compressibilities and permeability in the classical linear poroelasticity. [ABSTRACT FROM AUTHOR]

The paper focuses on the development of a mathematical model connecting penetration profile of a rigid circular indenter with elastic properties of a functionally graded coating (FGC). We introduce the concept of stiffness function dependent on the radius of the contact zone for FGC coupled with a homogeneous half-space. This approach allows one to determine the properties variation across the coating. Several most typical numerical examples are discussed in detail to illustrate effect of the Young's modulus variation on the stiffness function. These examples also show that the proposed methodology allows one to identify and experimentally distinguish between different types of variation of FGC elastic properties. The paper focuses on the development of a mathematical model connecting penetration profile of a rigid circular indenter with elastic properties of a functionally graded coating (FGC). We introduce the concept of stiffness function dependent on the radius of the contact zone for FGC coupled with a homogeneous half-space. This approach allows one to determine the properties variation across the coating. Several most typical numerical examples are discussed in detail to illustrate effect of the Young's modulus variation on the stiffness function. These examples also show that the proposed methodology allows one to identify and experimentally distinguish between different types of variation of FGC elastic properties. [ABSTRACT FROM AUTHOR]

In the present paper a two-scale approach for the description of anisotropies in sheet metals is introduced, which combines the advantages of a macroscopic and a microscopic modeling. While the elastic law, the flow rule, and the hardening rule are formulated on the macroscale, the anisotropy is taken into account in terms of a micro-mechanically defined 4th-order texture coefficient. The texture coefficient specifies the anisotropic part of the elasticity tensor and the quadratic yield condition. The evolution of the texture coefficients is described by a rigid-viscoplastic Taylor type model. The advantage of the suggested model compared to the classical v. Mises-Hill model is first, that macroscopic anisotropy parameters can be identified based on a texture measurement, and second, that the anisotropy of the elastic and the plastic behavior is generally path-dependent and that this path-dependence is related to a micro-mechanical deformation mechanism. An explicit modeling of the plastic spin is circumvented by the aforementioned micro-mechanical approach. The model is implemented into the FE code ABAQUS and applied to the simulation of the deep drawing process of aluminum. [ABSTRACT FROM AUTHOR]

This paper examines the problem of symmetric indentation of a penny-shaped crack by a smoothly embedded rigid circular disc inclusion in a thick layer. Expressions for the resultant pressure applied to the inclusion and for the stress intensity factor at the boundary of the penny-shaped crack are obtained. The mathematical form of the expressions for the resultant stress fields and the tractions along the inclusion are also derived. Numerical results for the resultant pressure and stress intensity factor, resultant stress fields and the resultant tractions along the inclusion are obtained and displayed graphically. [ABSTRACT FROM AUTHOR]

This paper analyses the regularity of the weak solution of the linear elasticity system in three-dimensional axisymmetric domains with reentrant edges under prescribed traction on the boundary by means of Fourier series. Using partial Fourier analysis with respect to one space direction (rotational angle), the three-dimensional boundary value problem (BVP) is decomposed into a sequence of decoupled two-dimensional boundary value problems on the meridian of the axisymmetric domain. The splitting of the 2D solutions near corners of the meridian domain into regular and singular parts provides coefficients from which the 3D edge singularity functions (generalized stress intensity factors) are derived. Two types of singularity functions are presented, namely, a tensorial type, which needs more smoothness assumption on the right hand side and a non-tensorial type, which does not demand any further smoothness assumptions. [ABSTRACT FROM AUTHOR]

Most solid bodies are porous and in such bodies we expect the material properties to vary with porosity and hence with the density. Such bodies whose properties depend on the density cannot be described by the classical linearized elastic constitutive relation when they are undergoing small deformations, as the material moduli cannot depend on density. A constitutive relation which is valid in the small displacement gradient range wherein the material moduli are dependent on the density can be developed by linearizing implicit constitutive relations for describing elastic bodies introduced recently by Rajagopal [1]. In this paper, we determine the stress concentration due to a hole in a slab that is subject to biaxial loading in a body described by such a constitutive relation. We find that the stress concentration can be much as 147% higher than that for classical linearized elasticity for the range of loadings considered in the study. [ABSTRACT FROM AUTHOR]

In this paper the fundamentals of the asymmetric elasticity theory are used to consider one- and two-dimensional boundary-value problems: shear deformation of elastic infinite plane layer(plate): torsion of a ring rigidly fixed at the external contour due to rotation of the inner one; deformation of a plane washer caused by a rigid displacement of the internal contour relative to the external one: the Kirsch problem on unilateral extension of a plate loosened by a circular hole. The solution of each problem is compared with the corresponding solution obtained in the framework of the classical theory of elasticity. The comparison is made in terms of macro-parameters introduced to characterize the degree of difference between these solutions. The analysis of the obtained results show that for each problem under consideration this difference is not essential. It is worthy of note that the macro-parameters used for comparison can he constructively measured by experiment. The obtained results can be used to outline a key diagram of experiments enabling one to detect the effects of "couple" response of the examined medium. [ABSTRACT FROM AUTHOR]

This paper investigates the large displacement post-buckling behavior of a column with central brace using the elastica solution. The method is able in predicting the buckling load and in tracing the exact post-buckling paths, both primary and secondary paths. Depending on the brace stiffness, different shapes of symmetrical and anti-symmetrical post-buckling paths can be shown to exist. Whilst previous work reported only one threshold value of brace stiffness, the results also show the existence of infinite number of threshold values, each indicates a change in the post-buckling behavior. [ABSTRACT FROM AUTHOR]

The paper considers the boundary value problems of elasticity for an ellipse and ellipse with a crack when tangential stress is applied to the ellipse boundary. The mathematical models of these problems are obtained by setting the relevant problems for a semi-ellipse: a) the continuity conditions for the problem solution are given at the linear border, b) the continuity conditions for the problem solution are given at the portion of the linear boundary, beyond the focuses, with the tangential stresses given on the section between the focuses. So, a semi-ellipse can be bound as a whole ellipse, with the continuity conditions of the solution on the section between its focuses met in one case (when there is no crack) and not met in another case (when there is a crack, which is affected by the tangential stress). The problem solution for the cracked ellipse is reduced to the solution of the internal and external problems of elasticity, which are solved quite simply by the method of separation of variables. [ABSTRACT FROM AUTHOR]

This paper addresses the initial stresses and rotation effects on the wave reflection in the pyroelectric half-plane using inhomogeneous wave approach. The rotation in the governing pyroelectric equation is characterized by considering the Coriolis and centrifugal accelerations, and the initial stresses are included by modifying the elasticity tensor. A scenario is modelled where a quasi-longtitudinal wave is incident on free boundary surface, resulting into reflected waves like temperature wave, quasi-transverse wave, quasi-longitudianal wave, and surface wave. Attenuation angle, initial stresses, and rotation's impacts on the velocity, attenuation, and energy coefficients of reflected wave are presented. [ABSTRACT FROM AUTHOR]

This paper studies deformation of homogeneous elastic isotropic ball under the action of non-stationary axially symmetrical volume forces. Displacements at the boundary of the ball equal to zero. We used expansion in series of Legendre polynomials and their derivatives, as well as the Laplace transform by time. The solution is represented in integral form with kernels in form of Green functions. We have established the structure of such kernels and found their original functions. The present study presents examples of calculations of kernels and deformation of a ball under various external forces. [ABSTRACT FROM AUTHOR]

With the miniaturization of structures, such as MEMS/NEMS, the sizedependent effect has become an issue and attracted much attention. The wellknown theories describing the size-dependent effect mainly include the nonlocal elasticity theory, the strain gradient theory and the modified coupled stress theory. Based on these theories, a number of works have been conducted to explore the size-dependent behaviors of structures or devices in micro/nanoscale, among them, majorities are on elastic performances, while, minorities are on thermoelastic performances. It is inevitable for structures suffering changeable temperature, as a consequence, thermal-induced stress and deformation occur in structures and they are worth being fully concerned. For thermoelastic behaviors limited to small scale problems, the classical Fourier's heat conduction law may fail, meanwhile, new models, for example, fractional order heat conduction model, have been developed to modify Fourier's law. In present paper, the transient thermoelastic response of a nanobeam subjected to a ramp heating is investigated by combining the nonlocal elasticity theory and the fractional order heat conduction model. The governing equations are formulated and then solved by Laplace transform and its numerical inversion. The non-dimensional temperature, displacement, stress, and deflection in the nanobeam are obtained and illustrated graphically. In calculation, the effects of the ramp-heating time parameter, the nonlocal parameter and the fractional order parameter on the considered physical quantities are examined and discussed in detail. [ABSTRACT FROM AUTHOR]

Inequality (unilateral) constraints may introduce various types of singularities in differential-algebraic systems ([5]). In the present paper we consider contact conditions that are formulated as unilateral constraints for position and velocity coordinates in a mechanical multibody system. If the surfaces of the bodies being in contact are worn then the contact conditions result often in constraints that are only piecewise differentiable. We discuss a regularization that considers qualitatively the elastic deformation of the bodies. [ABSTRACT FROM AUTHOR]

In the present paper on the basis of the linear theory of thermoelasticity of homogeneous isotropic bodies with microtemperatures the zeroth order approximation of hierarchical models of elastic prismatic shells with microtemperatures in the case of constant thickness (but, in general, with bent face surfaces) is considered. The existence and uniqueness of solutions of basic boundary value problems when the projections of the bodies under consideration are bounded and unbounded domains with closed contours are established. The ways of solving boundary value problems in explicit forms and of their numerical solution are indicated. [ABSTRACT FROM AUTHOR]

Within the framework of linear elasticity of anisotropic solids, the strong ellipticity (SE) condition is discussing. In this paper, the SE-condition is deriving for 19 classes of 32 known ones of anisotropy. For each class SE-condition reduces to a finite set of elementary inequalities. As a special case, incompressible materials are also considered. [ABSTRACT FROM AUTHOR]

The present paper deals with the magnetoelectroelastic composites containing a doubly periodic array of multicoated fibers under anti-plane shear loads and in-plane electromagnetic loads. By introducing the generalized eigenstrain, the heterogeneous magnetoelectroelastic medium is equivalent to a homogeneous magnetoelectroelastic medium with the periodically distributed generalized eigenstrains. Then the homogeneous magnetoelectroelastic medium with the generalized eigenstrain is solved analytically under the applied load conditions, the generalized stresses and strains in the fibers, coatings and matrix are derived. Based on the average-field theory, the solutions of the generalized stresses and strains are applied to determine the anti-plane effective magnetoelectroelastic properties of the composites. Two-phase (fiber/matrix) and three-phase (fiber/coating/matrix) magnetoelectroelastic composites are examined, and the comparison between the obtained results and the existing results shows the accuracy of the proposed method. Several four-phase magnetoelectroelastic composites with epoxy matrix are studied, and the influences of the composites microstructures on the effective magnetoelectric coefficient are discussed. [ABSTRACT FROM AUTHOR]

The paper deals with numerical realization of discretized, frictionless static contact problems for elastic-perfectly plastic materials and the computational limit analysis. Two numerical methods based on the variational formulation in terms of stresses are analyzed: the semi-smooth Newton method with damping and the alternating direction method of multipliers. These methods are used for tracking the loadings path to determine the discretized limit loading parameter and for solving elastic-perfectly plastic problems. [ABSTRACT FROM AUTHOR]

In this paper, a method of local perturbations, previously successfully applied to decompose the problem of elasticity in the system of connected thin rods and beams [24], is used to study the asymptotic behavior of the elasticity problem in connected thin plates. A complete decomposition of the problem, i.e. the separation of the original problem into the two-dimensional problem of the theory of plates and local problems is proposed. The local problems describe the three-dimensional stress-strain state in the connected plates and can be solved by numerical methods. [ABSTRACT FROM AUTHOR]

This paper describes a method for determination of elastic parameters (elastic moduli and Poisson's ratio) of orthotropic composite plate-type structural elements using the results of natural frequency measurements. The identification of parameter values is provided by minimization of weighted squared difference (discrepancy) between physically measured frequencies and natural frequencies calculated by Finite Element Method. The metamodels for the frequency dependence on the elastic parameters and other geometrical and physical parameters of test specimens, including parameters with uncertainty ('noisy constants') are built using experimental designs optimized according to the Mean Squared Error space filling criterion and third-order polynomial approximations. The minimum of weighted squared difference between measured and calculated frequencies is found using the multistart random search method. The expressions for standard deviations of identified parameters depending on deviations of 'noisy constants' are derived using linearized metamodels. The expressions for identification errors allow the statement of the identification task as a robust minimization problem by simultaneous minimization of the discrepancy function and standard deviations of the identified values by varying the values of unknown elastic parameters and weighting coefficients for different frequencies. The partial scaling of natural frequencies is used for the reduction of the uncertainty impact on the identification error. This allows reducing the identification error of elastic moduli about two times and Poisson's ratio about 20 times in comparison with the results obtained by using dimensioned frequencies. [ABSTRACT FROM AUTHOR]

In this work, the interaction between a moving anti-plane crack and a screw dislocation in the magneto-electro-elastic material is studied. The exact solutions are derived by the Muskhelishvili theory and the mechanical-electric-magnetic fields are presented. Comparing with the recent researching status, the present work has three prominent features. Firstly, both the remote loads with eight possible combinations and the coupling of the mechanical-electric-magnetic fields are considered. Secondly, the crack face is assumed to have the general boundary condition which is not the single permeable or impermeable case. Finally, the general solution is derived with the consideration of the crack moving velocity and the screw dislocation. Results presented in this paper would have potential applications on the analysis and design of magneto-electro-elastic structures, especially for the influence of microdefects on the initiation and propagation of cracks. [ABSTRACT FROM AUTHOR]

This paper studies the buckling problem of nanowires (NWs) and carbon nanotubes (CNTs) freely standing on a substrate and subjected to distributed axial loads. NWs and CNTs are modeled as elastic nanocolumns and due to their high Young's modulus, the substrate is reasonably considered as an elastic foundation. The junction between the nanocolumn and substrate is described by a rotational spring. A new approach is suggested to solve the stability of axially-loaded nanocolumns with a rotational spring junction. An approximation expression for the critical load with high accuracy is derived in closed form. The results are confirmed for a rectangular Ag NW by FEM. Numerical results of the critical length of NWs and CNTs under their own weight are presented in graphs and tables. Obtained results indicate that the critical length is sensitive to small Young's modulus of the elastic substrate and becomes insensitive for enough large Young's modulus of the elastic substrate. When the rotational spring stiffness is sufficiently large, the case reduces to a free-standing NW on a rigid foundation. [ABSTRACT FROM AUTHOR]

This paper deals with the electromagnetic theory of microstretch elasticity. The full dynamic theory, which describes the interaction of electromagnetic fields with piezoelectric bodies, called piezoelectromagnetism, is considered. First, we derive the equations governing the bending theory of thin piezoelectromagnetic microstretch plates. Then, the boundary-initial value problem is formulated and a uniqueness result is presented. Finally, the effects of a concentrated charge density in an infinite plate are studied. [ABSTRACT FROM AUTHOR]

Plastic deformation of crystals is mostly mediated by the motion of dislocations. During the last two decades a lot of effort was directed towards including more knowledge about dislocations in continuum descriptions of plasticity. Promising approaches towards building continuum plasticity theories on averages of the behavior of many single dislocations have been formulated under the assumption of small deformations. In the current paper we derive the kinematics of single dislocations moving inside a dislocated crystal simultaneously deforming by the motion of other dislocations in the language of large deformation plasticity. The evolution equation of a single dislocation is connected to the formation of kinks and jogs due to cutting by other dislocations and is shown to parallel the evolution equation of the dislocation density tensor in finite deformation formulation. Implications for dislocation based modeling of plasticity are discussed. [ABSTRACT FROM AUTHOR]

This paper presents a simple and effective method of solving the 3D elasticity problems for thick shells. It is based on the new concept of sampling surfaces (S-surfaces) inside the shell body. According to this concept, we introduce N not equally located S-surfaces parallel to the midsurface and choose displacements of these surfaces as basic shell unknowns. Such choice allows one to represent the governing equations of the proposed higher order shell model in a very compact form and to solve the 3D static problems for thick plates and shells efficiently. [ABSTRACT FROM AUTHOR]

In this paper, the strong sampling surfaces (SaS) formulation developed earlier by the authors to solve the statics problems for plates and shells is extended to the three‐dimensional (3D) vibration analysis of laminated composite shells. The SaS formulation is based on choosing the arbitrary number of SaS parallel to the middle surface in order to introduce the displacements of these surfaces as basic shell unknowns. Such choice of unknowns with the use of Lagrange polynomials in approximations of displacements and strains through the layer thicknesses leads to a robust laminated shell formulation. The feature of the proposed strong SaS formulation is that all SaS are located inside the layers at Chebyshev polynomial nodes. The use of outer surfaces and interfaces is avoided that makes possible to minimize uniformly the error due to Lagrange interpolation. Therefore, the strong SaS formulation based on direct integration of equations of motion of the elastic body can be applied efficiently for the 3D vibration analysis of laminated cylindrical shells and panels. In this paper, the strong sampling surfaces (SaS) formulation developed earlier by the authors to solve the statics problems for plates and shells is extended to the three‐dimensional (3D) vibration analysis of laminated composite shells. The SaS formulation is based on choosing the arbitrary number of SaS parallel to the middle surface in order to introduce the displacements of these surfaces as basic shell unknowns. Such choice of unknowns with the use of Lagrange polynomials in approximations of displacements and strains through the layer thicknesses leads to a robust laminated shell formulation. The feature of the proposed strong SaS formulation is that all SaS are located inside the layers at Chebyshev polynomial nodes. The use of outer surfaces and interfaces is avoided that makes possible to minimize uniformly the error due to Lagrange interpolation. Therefore, the strong SaS formulation based on direct integration of equations of motion of the elastic body can be applied efficiently for the 3D vibration analysis of laminated cylindrical shells and panels. [ABSTRACT FROM AUTHOR]

Scale-transition models, such as Eshelby-Kröner self-consistent framework, which are often used for predicting the effective behavior of heterogeneous materials or estimating the distribution of local states from the knowledge of the corresponding macroscopic quantities, require the extensive use of set averages. The present paper is devoted to the comparison of the numerical results provided in pure elasticity by Eshelby-Kröner model depending on the average type chosen for achieving set average operations: either the traditional arithmetic mean or the geometric average. Various numerical applications of the model to the case of predicting either the effective stiffness or the lattice strains of single-phase polycrystals will be provided. The particular case when an extreme grain-shape occurs will also be investigated. [ABSTRACT FROM AUTHOR]

In this paper we study wave propagation through a composite material built up of a periodically repeated one-dimensional structure of coated inclusions and matrix material by the application of the asymptotic homogenization method. We take into account geometrical nonlinearity, which is described by the Cauchy-Green strain tensor and physical nonlinearity by the Murnaghan elastic potential. We take into account structural nonlinearity by considering the bonding between two materials to be imperfect. As a result we obtain homogenized equations for the low-frequency range. The authors study wave propagation through a composite material built up of a periodically repeated one-dimensional structure of coated inclusions and matrix material by the application of the asymptotic homogenization method. They take into account geometrical nonlinearity, which is described by the Cauchy-Green strain tensor and physical nonlinearity by the Murnaghan elastic potential. They take into account structural nonlinearity by considering the bonding between two materials to be imperfect. As a result the authors obtain a homogenized equation for the low-frequency range. [ABSTRACT FROM AUTHOR]

In this paper we consider the control of cracks in elastic bodies with rigid inclusion. We first describe the problem statement, provide an equivalent formulation as a variational inequality and prove existence and uniqueness of solutions. Furthermore, we consider this problem as a limiting problem when the elasticity parameters of the inclusion tend to infinity. Then we formulate the optimal control problems and derive an explicit formula for the crack sensitivity and for the energy release rate. We show existence of optimal solutions. The authors consider the control of cracks in elastic bodies with rigid inclusion. They first describe the problem statement, provide an equivalent formulation as a variational inequality and prove existence and uniqueness of solutions. Furthermore, the authors consider this problem as a limiting problem when the elasticity parameters of the inclusion tend to infinity. Then they formulate the optimal control problems and derive an explicit formula for the crack sensitivity and for the energy release rate. It is shown the existence of optimal solutions. [ABSTRACT FROM AUTHOR]

We review recent progress on the derivation and analysis of higher order corrections to the classical mean-field theory of Lifshitz, Slyozov, and Wagner for domain coarsening. Most research on this subject in the applied literature has focussed on the effect of screening induced fluctuations, however some of the resulting models lack self-consistency. We discuss here recent work in which a self-consistent model for fluctuations is derived and compare it to a model that has first been suggested in the original paper by Lifshitz and Slyozov. This model takes the effect of encounters between domains into account, but has seemingly gone unnoticed in the literature. Contrary to common expectations self-similar solutions of this model predict a much larger coarsening rate than the models accounting for fluctuations. [ABSTRACT FROM AUTHOR]

In this paper, the problem of an edge crack of finite length, situated in an orthotropic infinite strip of finite thickness h, under normal point loading has been considered. The displacements and stresses for orthotropic elasticity in plane strain condition are expressed in terms of two harmonic functions. The problem is resolved in a simplistic manner by seeking the solution of a pair of simultaneous integral equations with Cauchy type singularities which have finally been solved through finite Hilbert Transform technique. For large h, the analytical expression of the stress intensity factor (SIF) at the crack tip is obtained, which corresponds to the weight function of a crack under normal point loading. The numerical results of the normalized stress intensity factor at different arbitrary locations of the crack surface and various values of crack length have been computed for a particular orthotropic material (Steel-Mylar composite) and the results are depicted graphically. [ABSTRACT FROM AUTHOR]

This paper discusses an existence result for energetic solutions of rate-independent damage processes and the temporal regularity of the solution. We consider a body consisting of a physically nonlinearly elastic material undergoing small deformations and partial damage. The present work is a generalization of [16] concerning the properties of the stored elastic energy density as well as the suitable Sobolev space for the damage variable: While previous work assumes that the damage variable z satisfies z in W1, r(Ω) with r > d for Ω ⊂ ℝd, we can handle the case r > 1 by a new technique for the construction of joint recovery sequences. Moreover, this work generalizes the temporal regularity results to physically nonlinearly elastic materials by analyzing Lipschitz- and Hölder-continuity of solutions with respect to time. [ABSTRACT FROM AUTHOR]

Within the framework of the piecewise homogeneous body model and through the application of the three-dimensional linearized theory of elastic waves in an initially stressed body, the torsional wave dispersion in pre-stretched bi-material compounded cylinders is investigated. It is assumed that the elasticity relations of the materials of the components of the cylinders are given through the Murnaghan potential. The numerical investigations are made for steel (St) (as a material for the solid cylinder) and bronze (Br) (as a material for a hollow covering cylinder). According to the numerical results obtained, the influence of the problem parameters such as the initial stresses in the components of the bi-material compounded cylinder, the values of the mechanical and physical constants of the components, and the geometrical parameters (such as the relation of the thickness of the covering cylinder with the radius of the inner solid cylinder on the dispersion curves) are analyzed. [ABSTRACT FROM AUTHOR]

Problems in elasticity are described by relations between the displacement field u, the strain or deformation tensor ℇ, and the stress tensor σ. In 2D elasticity and if volume forces are absent, one may also consider an elastic potential. We explain these settings for a domain Ω with finitely many holes. On such domains the problem for the displacement and the potential problem are not necessarily equivalent. We will also recall the relation between these quantities. We conclude the paper with the potential setting for some specific problems in semi-periodic domains with infinite many holes. Also the setting for non-smooth domains is addressed. [ABSTRACT FROM AUTHOR]

There are many approaches in continuum mechanics involving incompatible deformations, one well-known example being the polar decomposition of the deformation gradient tensor. Such deformations have in the past been regarded rather in the context of local configurations. In the present paper, we discuss incompatible deformations among others, also from the point of view of material lines. Related covariant derivatives and spatial differential operators are introduced and investigated. In particular, it is shown that components of curvature tensors, present in many gradient constitutive theories, may be expressed in terms of the difference between different connections for the same manifold. These issues are illustrated with reference to multiplicative decompositions of deformation gradient tensors into elastic and plastic parts. Two classes of model materials are addressed, non-polar and micropolar ones. [ABSTRACT FROM AUTHOR]