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Tempered martensitic steels with a high chromium content are used for power plant components at elevated temperatures under creep-fatigue conditions. In order to model the complex mechanical behavior of the alloy X20CrMoV12-1, a phase mixture model is used. This model is based on the distinction of hard and soft constituents, which are connected via an iso-strain approach. Nonlinear kinematic hardening and softening effects are taken into account by introducing a backstress and a softening variable. This paper focuses on the numerical implementation of the phase mixture model, i.e., the stress update algorithm and the consistent tangent operator. For implicit time integration of the governing equations, the backward EULER method in combination with NEWTON-RAPHSON iterations is applied. The model is implemented as user material subroutine into the commercial finite element code ABAQUS. For verification, several benchmarks considering uniaxial and multi-axial stress states are presented and analyzed. Furthermore, a thermo-mechanical fatigue test based on a typical sequence of start-ups and shutdowns of power plants is simulated. [ABSTRACT FROM AUTHOR]

A crack initiates frequently at a vertex in three-dimensional joints under an external load and a thermal load. In the present paper, the stress distributions near a very small crack occurring at the vertex of the interface in a three-dimensional joint are analyzed under a tensile load using a boundary element method, and the stress intensity factor of mode II is investigated along the crack front. The joint model is composed of silicon and resin, which is modeled on a material combination in electronic devices. Three kinds of crack shape, triangular, quarter circular, and concave shapes, are supposed as a crack shape. First, the stress distributions near the vertex in the model without a crack are obtained and are used for normalizing the singular stress at the front of the crack. Dimensionless stress intensity factor for an interface crack is defined and determined from the distribution of the normalized stress. Next, the stress distribution near the intersection point of the crack front and the side surface is precisely investigated. An eigenanalysis at the intersection point is conducted, and eigenvalues yielding the stress singularity are obtained. Then, it is found that there are two values yielding the stress singularity. The stress distributions near the intersection point are expressed using the angular functions for each value yielding the singularity. Finally, it is shown that the stress intensity factor for mode II along the crack front varies following the summation of functions composed of the distance from the intersection point with the power indices of ( $${0.5 - {\lambda _1}}$$ ) and ( $${0.5 - {\lambda _2}}$$ ), where $${\lambda _1}$$ and $${\lambda _2}$$ are the orders of stress singularity at the intersection point. [ABSTRACT FROM AUTHOR]

Surface tension plays an important role in nanosized materials. In this paper, the stress field induced by surface tension around an arbitrarily shaped nanosized hole is investigated through complex variable method using truncated series, with an emphasis on the relationship between the hoop stress and the curvature of the hole's boundary curve. Our numerical results for various shapes of holes show that maximum hoop stress always appears nearby, but not exactly at the point of maximum curvature on the hole's boundary. Surprisingly, for elliptical holes with certain aspect ratios and typical non-elliptical holes (such as triangular, square and rectangular holes), our results show that hoop stress can even attain a local minimum (not a local maximum) or even the overall minimum at the point of maximum curvature. In particular, surface tension-induced hoop stress can be very large around nanosized holes. On the other hand, the surface tension-induced stress field is always localized for nanosized holes of arbitrary shapes and fades away with increasing distance from the hole. [ABSTRACT FROM AUTHOR]

In this paper, the mechanical behavior of micro-rotating disks is investigated utilizing the strain gradient theory. The governing equation and boundary conditions are derived utilizing the variational method. The analytical solution for the derived equation is also presented. As a case study, some numerical results are presented to emphasize the importance of utilization of non-classical theories such as the strain gradient elasticity instead of the classical continuum theory in dealing with micro-rotating disks. [ABSTRACT FROM AUTHOR]

Homogenization methods utilizing classical elasticity-based Eshelby tensors cannot capture the particle size effect experimentally observed in particle-matrix composites at the micron and nanometer scales. In this paper, a new homogenization method for predicting effective elastic properties of multiphase composites is developed using Eshelby tensors based on a simplified strain gradient elasticity theory (SSGET), which contains a material length scale parameter and can account for the size effect. Based on the strain energy equivalence, a homogeneous comparison material obeying the SSGET is constructed, and two sets of equations for determining an effective elastic stiffness tensor and an effective material length scale parameter for the composite are derived. By using Eshelby's eigenstrain method and the Mori-Tanaka averaging scheme, the effective stiffness tensor based on the SSGET is analytically obtained, which depends not only on the volume fractions and shapes of the inhomogeneities (i.e., phases other than the matrix) but also on the inhomogeneity sizes, unlike what is predicted by the existing homogenization methods based on classical elasticity. To illustrate the newly developed homogenization method, sample cases are quantitatively studied for a two-phase composite filled with spherical, cylindrical, or ellipsoidal inhomogeneities (particles) using the averaged Eshelby tensors based on the SSGET that were derived earlier by the authors. Numerical results reveal that the particle size has a large influence on the effective Young's moduli when the particles are sufficiently small. In addition, the results show that the composite becomes stiffer when the particles get smaller, thereby capturing the particle size effect. [ABSTRACT FROM AUTHOR]

In the present paper, the mixed-mode Dugdale model is applied to investigate the plastic zone size and the crack tip opening displacement of an interface crack between two dissimilar layers. In the analysis, both normal and shear stresses are assumed to exist in the plastic zones and satisfy the Von Mises yield criterion. The plastic zone sizes can be determined on condition that the stress intensity factors caused by the stresses in the plastic zones and applied loading are zero. Then, the crack tip opening displacement can be obtained by dislocation theories. In numerical examples, the plane stress condition is considered. The plastic zone size and the crack tip opening displacement of an interface crack between two dissimilar layers under a uniform load are examined. The effects of Dundurs' parameters and the thickness of materials on the plastic zone size and the crack tip opening displacement are investigated in detail. Numerical results show that in the case of small thickness, the values of the normalized plastic zone size and the normalized crack tip opening displacement decrease with increasing Dundurs' parameters, α and β, while, in the case of infinite thickness, the value of the normalized plastic zone size is independent of α, and the value is symmetric about the axis on which β = 0. [ABSTRACT FROM AUTHOR]

A description of brick/block masonry by continua equivalent to discrete systems made of blocks of different geometry and texture is proposed in this paper. Here, the reasons for the selection of a micropolar continuum with respect to the classical continuum are discussed. As recent research in various micromorphic multifield formulations shows, the problem of the choice of the most appropriate continuum to model masonry mechanical behavior is still open, and the advantages of non-classical continuum modeling are not yet completely ascertained. Earlier analyses performed on masonry panels in the presence of load and geometrical singularities pointed out the significant role of the additional degree of freedom of the micropolar continuum (microrotation) and of its gradient. The present study aims to expand the investigation into the consequences of changes in blocks' shape, size and arrangement on the response of block masonry panels under shear forces. This analysis points out the greater effectiveness of micropolar models in capturing the gross structural response of masonry, with respect to the classical modeling. The cases analyzed herein show that apart from the very peculiar case of orthotetragonal symmetry, not only the gradient of microrotation but also the relative rotation between the local rigid rotation and the microrotation, to which relevant non-symmetric strains correspond, are predominant in the majority of the performed numerical tests. Models lacking in these strain measures are therefore inappropriate. The results obtained, ascertained by analyses performed on discrete block assemblies, point out that the micropolar continuum provides a proper description of the masonry behavior. Moreover, the differences between micropolar and classical models remain when the internal lengths vanish. [ABSTRACT FROM AUTHOR]

This paper proposes a new simple derivation of bilateral bounds for the strain energy-based shear and torsion factors, χ, of an elastic beam together with some comments about the coherence of the current formulations. A rearrangement of the definition as a mean over the cross-section and an original decomposition of the shear stress in two parts- τ that is equivalent to the external force and a residual Δ τ-allow ( i) to interpret ( χ − 1) as the mean quadratic deviation of the shear field with respect to the distribution τ and ( ii) to easily evaluate an upper bound, using minimal information about the stress field. In this formulation, the lower bound becomes trivial. Several numerical examples illustrate the accuracy and suitability of the results obtained. [ABSTRACT FROM AUTHOR]

A contact model between a homogeneous half-space with a linearly graded layer and a rigid punch is proposed and studied in the present paper. The governing equation, which describes the relation of the displacements and the normal tractions at the contact interface, is obtained by means of Fourier transform and a transfer matrix method. Appropriate collocation methods are used in order to solve the equation numerically. Singular behaviors at the edge of a flat punch are revealed. Compared to the case with a graded surface varying according to an exponential law, stress concentration is relatively weaker in the case with the graded surface varying according to a linear law. Furthermore, stress distributions in cases of a flat or cylindrical punch are given for different varying graded laws, thickness of graded layer, ratios of stiffness, and frictional coefficients. All the results are helpful for the design of strong and wear resistance coating surfaces. [ABSTRACT FROM AUTHOR]

In this paper, systematic approaches to determine the polynomial stress functions for anisotropic plane problems are presented based on the Lekhnitskii's theory of anisotropic elasticity. It is demonstrated that, for plane problems, there are at most four independent polynomials for arbitrary n-th order homogeneous polynomial stress functions: three independent polynomials for n equal to two and four for n greater than or equal to three. General expressions for such polynomial stress functions are derived in explicit forms. Unlike the isotropic case, the polynomials for anisotropic problems are functions of material constants, because the elastic constants cannot be eliminated in the governing equation for general anisotropic cases. The polynomials can be used as analytical trial functions to develop the new 8-node hybrid element (ATF-Q8) for anisotropic problems. This ATF-Q8 element demonstrated excellent performance in comparison with traditional numerical methods through several testing examples. [ABSTRACT FROM AUTHOR]

In this paper, the De Saint-Venant flexure-torsion problem is developed via a technique by means of a novel complex potential function analytic in all the domain whose real and imaginary parts are related to the shear stresses. The latter feature makes the complex analysis enforceable for the shear problem. Taking full advantage of the double-ended Laurent series involving harmonic polynomials, a novel element-free weak form procedure, labelled Line Element-less Method (LEM), is introduced, imposing that the square of the net flux across the border is minimized with respect to expansion coefficients. Numerical implementation of the LEM results in systems of linear algebraic equations involving positive-definite and symmetric matrices solving only contour integrals. Some numerical applications are reported to assess not only the efficiency and accuracy of the method to handle shear stress problems but also the robustness in the sense that exact solutions when available are captured straight away. [ABSTRACT FROM AUTHOR]

The stress and displacement fields for a viscoelastic axisymmetric plane problem involving time-dependent boundary regions under mixed boundary condition are presented in this paper. The viscoelastic fields are determined by solving two unknown functions; one is governed by a resulting second kind Volterra integral equation from the stress condition at the outer radius of an annular region, which is dependent on the other by the displacement condition at the inner radius. The integral equation has an analytical solution for the case of an infinite region with large enough outer radius while it can be solved using a numerical integral method for the case of a finite region. Numerical examples for the Boltzmann viscoelastic model are given, and the responses of the displacement and stresses are presented in detail to illustrate the effects of velocity of change in the inner radius and the magnitude of the outer radius. Meanwhile, the effect of the aspect ratio (void concentration parameter) on the viscoelastic fields is presented. When the ratio of the outer radius to the inner radius is large enough, the responses can be evaluated by directly adopting the resulting analytical solution to avoid a complex numerical procedure. The resulting solutions and computational results are helpful to a better understanding of mechanical behaviors for (large) excavation or finite void growth in viscoelastic media. [ABSTRACT FROM AUTHOR]

The dynamic behavior of a clamped-clamped microbeam loaded by a symmetric combined voltage, which is composed of a direct current (DC) voltage and an alternating current (AC), is investigated in this paper. Based on the Euler-Bernoulli hypothesis and the standard anelastic solid model, the equation of motion of this microbeam with considering the material damping is got, and then by using the Galerkin method a reduced-order model is derived. An instability phenomenon named as electromechanical dynamic buckling in this system is shown, and the condition of instability is determined by the averaging method. To validate our results, a numerical simulation model is set up. The effects of the fringing field, residual stress, applied DC voltage, environmental damping and material damping on the electromechanical dynamic buckling are discussed. [ABSTRACT FROM AUTHOR]

In this paper, the mixed-mode fracture problem of a functionally graded piezoelectric material strip with two penny-shaped or annular cracks is considered. It is assumed that the electroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under electric loading. The problem is formulated in terms of a system of singular integral equations, which are solved numerically. Numerical calculations are carried out, and the stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the crack size, the crack location, and the material nonhomogeneity. [ABSTRACT FROM AUTHOR]

In this paper, an efficient method is developed for the formation of null bases of four-node quadrilateral plate bending finite element models, corresponding to highly sparse and banded flexibility matrices. This is achieved by introducing a new four-node quadrilateral plate bending element, and using special graphs associated with the finite element models. The results are compared to those of the previously developed graph theoretical and algebraic force methods, and also the displacement approach. [ABSTRACT FROM AUTHOR]

In this paper a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) and subjected to impact internal pressure is considered. The axisymmetric conditions are assumed for the 2D-FG cylinder. The finite element method with graded material properties within each element is used to model the structure, and the Newmark direct integration method is implemented to solve the time dependent equations. The time histories of displacements, stresses and 2D wave propagation are investigated for various values of volume fraction exponents. Also the effects of mechanical properties distribution in radial and axial direction on the time responses of the FG cylinder as well as the stress distribution are studied and compared with a cylinder made of 1D-FGM. The achieved results show that using 2D-FGM leads to a more flexible design. To verify the presented method and data, the results are compared to published data. [ABSTRACT FROM AUTHOR]

In this paper, a boundary element method is developed for the general flexural–torsional vibration problem of Timoshenko beams of arbitrarily shaped cross section taking into account the effects of warping stiffness, warping and rotary inertia and shear deformation. The beam is subjected to arbitrarily transverse and/or torsional distributed or concentrated loading, while its edges are restrained by the most general linear boundary conditions. The resulting initial boundary value problem, described by three coupled partial differential equations, is solved employing a boundary integral equation approach. Besides the effectiveness and accuracy of the developed method, a significant advantage is that the displacements as well as the stress resultants are computed at any cross-section of the beam using the respective integral representations as mathematical formulae. All basic equations are formulated with respect to the principal shear axes coordinate system, which does not coincide with the principal bending one in a nonsymmetric cross section. To account for shear deformations, the concept of shear deformation coefficients is used. Six boundary value problems are formulated with respect to the transverse displacements, to the angle of twist, to the primary warping function and to two stress functions and solved using the Analog Equation Method, a BEM based method. Both free and forced vibrations are examined. Several beams are analysed to illustrate the method and demonstrate its efficiency and wherever possible its accuracy. [ABSTRACT FROM AUTHOR]

Delamination may reduce the buckling of the laminated plate. In this paper, a semi-analytical, semi-exact method, namely the strip transfer function method based on Mindlin’s first-order shear deformation theory is developed to investigate the buckling of a delaminated plate. First, a composite plate with bulit-in rectangular delamination is divided into two kinds of rectangular super-units, one with a delamination and one without. The variational principle is used to obtain equilibrium equations and boundary conditions. Then, by displacement continuity and force balance of nodes that connect two super-units, the characteristic equation for the buckling analysis of the delaminated plate is derived. Consequently, buckling load and mode are computed. By comparing the results of the plate with through-the-width delamination to the analytic solutions of a beam and the results of the finite element method, the validity of this method is tested. Furthermore, the influence of length, depth and position of the delamination, the boundary condition and the plying angle of the material on the buckling load is analyzed. [ABSTRACT FROM AUTHOR]