Absorbing boundary conditions for elastic waves in transversely isotropic media

In the numerical simulation of elastic wave propagation in the solid, it is essential to introduce absorbing boundary conditions to limit the large or unbounded domain of computation. In this paper, the absorbing boundaries for transversely isotropic media are composed of simple first-order partial differential operators, and each of the operators can perfectly absorb a plane wave outgoing at a certain angle. To test the absorbing ability, the reflection coefficient formulas for the quasi-P and quasi-S wave on the absorbing boundary are derived based on the potential functions theory of the elastic wave. Numerical examples show that the absorbing effect is good. The boundary conditions given here have a practical meaning.Supported by National Natural Science Foundation of China.     

General solution for the coupled equations of transversely isotropic magnetoelectroelastic solids

IntroductionMechanicsandphysicsofmediapossessingsimultaneouslypiezoelectric ,piezomagneticandmagnetoelectriceffects ,namely ,magnetoelectroelasticsolids,haveattractedmoreandmoreattentionduetotheirgreatpotentialapplicationsinthetechnologiesofsmartandadaptivematerialsystem[1] .Sometheoreticalinvestigationsappearedintheliteratureinclude :1)Theexistenceproblemofsurfacewavesinsemi_infiniteanisotropicmagnetoelectroelasticmediawithvariousboundaryconditions[2 ,3 ] ;2 )Green’sfunctions[4～ 7] ;3)Inho…     

Axisymmetric thermoelastoplastic stress-strain state of transversely isotropic laminated shells

The method of successive approximations is used to determine the thermoelastoplastic stress-strain state of isotropic and transversally isotropic laminated shells of revolution under axisymmetric loading. Hill’s theory of plasticity with isotropic hardening is used to describe the deformation of transversely isotropic materials, while the theory of deformation along paths of small curvature is used to describe the deformation of isotropic materials. The elastoplastic stress-strain state of a two-layer cylindrical shell under mechanical and thermal loads is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 71–80, June 2006.     

General solution technique for transient thermoelasticity of transversely isotropic solids in Cartesian coordinates

Summary In the present paper we propose a new general solution technique for transient thermoelastic problems of transversely isotropic solids in Cartesian coordinates. The solution technique consists of five fundamental solutions. By considering the relations among the material constants of transverse isotropy, the solution technique is classified into five groups. One among those corresponds to Goodier's thermoelastic potential function as well as the generalized Boussinesq solutions and the Michell function. For an application of the solution technique, an inverse problem of transient thermoelasticity in a transversely isotropic semi-infinite solid is analyzed.

---

Ein allgemeines Lösungsverfahren in kartesischen Koordinaten für transiente Thermoelastizität transversal-isotroper Körper

Übersicht Vorgeschlagen wird ein neues, allgemeines Verfahren zur Lösung transienter thermoelastischer Probleme transversal-isotroper Körper in kartesischen Koordinaten. Das Lösungsverfahren besteht aus fünf Fundamentallösungen und kann unter Berücksichtigung der Beziehungen zwischen den Materialkonstanten der Transversal-Isotropie in fünf Gruppen eingeteilt werden Eine Gruppe entspricht dem Goodierschen thermoelastischen Potential bzw. der verallgemeinerten Boussinesq-Lösung und der Mitchell-Funktion. Als Anwendung dieses Lösungsverfahrens wird ein inverses transient thermoelastisches Problem des transversal-isotropen, unendlichen Halbraumes untersucht.

     

冲击载荷下猪后腿肌肉的横向同性本构模型

基于纤维增强复合材料连续介质力学理论及粘弹性理论,提出了猪后腿肌肉的率相关本构模型。 通过拟合以往研究中猪后腿肌肉的SHPB和SHTB实验应力应变曲线,确定了本构模型的相关参数。结果 表明:提出的本构模型既能描述猪后腿肌肉沿纤维方向的动态压缩力学性能又能描述其动态拉伸性能,理论 模型与实验模型有较好的一致性。该结果可为安全防护数值模拟提供一定的理论依据。     

Dynamic behavior of piles embedded in transversely isotropic layered media

Dynamic behavior of single pile embedded in transversely isotropic layered media is investigated using the finite element method combined with dynamic stiffness matrices of the soil derived from Green's function for ring loads. The influence of soil anisotropy on the dynamic behavior of piles is examined through a series of parametric studies     

Chargements axisymétriques d'un bicouche transversalement isotropeAxisymmetric loading on a transversely isotropic two-layered medium

An exact three-dimensional analysis is developped for an axisymmetric loading acting on the surface of a semi-infinite medium composed by two transversely isotropic materials. The loading is assumed to be parallel to the elastic symmetry axis of the upper layer. The solutions of a concentrated force and a uniform loading distributed on a circle are obtained by exact integral expressions. The numerical results are performed to show the anisotropic effect with isovalue curves of stress. To cite this article: C. Ruimy, M. Dahan, C. R. Mecanique 330 (2002) 469–473.     

Two-dimensional time-harmonic dynamic Green’s functions in transversely isotropic piezoelectric solids

The two-dimensional time-harmonic dynamic Green’s functions in an infinite transversely isotropic piezoelectric solid are obtained. After introduction of a new function, the original problem is reduced to the determination of the Green’s function for the two-dimensional Helmholtz equation and that for the two-dimensional Laplace equation. The explicit expressions of all the field components are presented. It is verified that the obtained dynamic Green’s functions can reduce to the corresponding static ones by letting the circular frequency be zero. The asymptotic expansions for Green’s functions at far-field are also given.     

On complex potentials for finite plane deformation of a transversely isotropic material

We consider the finite deformation of plane equilibrium problem for a transversely isotropic layer, using the complex variable approach. We give the general expression for the pertinent complex potentials and state the corresponding fundamental problems. We discuss in detail the boundary value problem for fundamental problem-one. As an application of the espoused method, an analytical solution of “Lame's problem” for an infinite layer is obtained. The nonlinear effect of this is highlighted in the obtained figure.     

Penny-shaped and half-plane cracks in a transversely isotropic piezoelectric solid under arbitrary loading

Summary The problem of a penny-shaped crack in a transversely isotropic piezoelectric material loaded by both normal and tangential tractions and by electric charges is analyzed. Closed-form solutions are obtained for the full electroelastic fields as well as for the stress and electric displacement intensity factors. Solutions are also obtained for the (non-trivial) limiting case of a half-plane crack. The results are illustrated on the example of piezoceramics PZT-6B. Received 12 July 1999; accepted for publication 20 July 1999     

Elastoplastic stress-strain state of flexible layered shells made of isotropic and transversely isotropic materials with different moduli and subjected to axisymmetric loading

The paper proposes a numerical technique for analysis of the elastoplastic stress-strain state of flexible layered shells of revolution under axisymmetric loading. It is assumed that the shells are made of isotropic and transversely isotropic materials with different moduli in tension and compression. The technique is based on a geometrically nonlinear theory of shells that takes into account the squared angles of rotation and the Kirchhoff-Love hypotheses for a layer stack. The deformation of isotropic materials is described using the theory of deformation along paths of small curvature. The deformation of transversely isotropic materials is described using the theory of elasticity with different moduli in tension and compression. The problem is solved by the method of successive approximations. A numerical example is given __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 31–42, November 2007.     

Analytical thermo-elastodynamic solutions for a nonhomogeneous transversely isotropic hollow sphere

Summary  The spherically symmetric dynamic thermoelastic problem for a special nonhomogeneous transversely isotropic elastic hollow sphere is formulated by introduction of a dependent variable and separation of variables technique. The derived solution can be degenerated into that for a homogeneous transversely isotropic hollow sphere, a nonhomogeneous isotropic hollow sphere or a solid sphere. The present method, allow to avoid integral transforms, is suited for a hollow sphere of arbitrary thickness subjected to arbitrary spherical symmetric thermal and mechanical loads, and is convenient in dealing with different boundary conditions of dynamic thermoelasticity . The numerical calculation involved is easy to be performed and its results are also presented. Received 30 October 2001; accepted for publication 21 February 2002 The work was supported by the National Natural Science Foundation of China (No. 10172075 and No. 10002016)     

The stress intensity factor history for an advancing crack in a transversely isotropic solid under 3-D loading

The mode I extension of a half plane crack in a transversely isotropic solid under 3-D loading is analyzed. Firstly, the fundamental problem that the crack is subjected to a pair of unit point loads on its faces is considered. Transform methods are used to reduce the boundary value problem to a single integral equation that can be solved by the Wiener–Hopf technique. The Cagniard–de Hoop method is employed to invert the transforms. An exact expression is derived for the mode I stress intensity factor as a function of time and position along the crack edge. Based on the fundamental solution, the stress intensity factor history due to general loading is then obtained. Some features of the solutions are discussed through numerical results.     

On the modeling of hardening in metals during non-proportional loading

The purpose of the current work is the formulation and initial application of a phenomenological model for hardening effects in metals subject to non-proportional loading histories characterized by one or more loading-path changes. This model is closely related to the incremental model of Teodosiu and Hu [Teodosiu, C., Hu, Z., 1995. Evolution of the intragranular microstructure at moderate and large strains: modelling and computational significance. In: Shen, S.F., Dawson, P.R. (Eds.), Simulation of Materials Processing: Theory, Methods and Applications. Balkema, Rotterdam, pp. 173–182; Teodosiu, C., Hu, Z., 1998. Microstructure in the continuum modelling of plastic anisotropy. In: Proceedings of 19th Risø International Symposium on Material’s Science: Modelling of Structure and Mechanics of Materials from Microscale to Product. Risø National Laboratory, Roskilde, Denmark, pp. 149–168]. Like their model, the current model captures in particular hardening stagnation after a load reversal as well as cross-hardening after orthogonal loading-path changes. On the other hand, the two models predict qualitatively different behavior during loading-path changes which take place purely in the inelastic range. Such is the case for example during orthogonal loading-path changes from uniaxial tension to simple shear without release, or during monotonic simple shear, or during deep-drawing. As shown by the experimental results reported on in the current work for the mild steel DC06, significant cross-hardening can occur during continuous orthogonal loading-path changes. Beyond this, the current model accounts in an approximate way for the possible effects of texture development on the material behavior with the help of the plastic spin. After investigating the behavior of the current model for various ideal two-stage loading histories (e.g., tension-shear), the current work ends with a comparison of standard combined hardening and current approaches in the context of the simulation of internal stress development and residual stresses during deep-drawing and the resultant springback after ring-splitting.     

Characteristic analysis for stress wave propagation in transversely isotropic fluid-saturated porous media

According to generalized characteristic theory, a characteristic analysis for stress wave propagation in transversely isotropic fluid-saturated porous media was performed. The characteristic differential equations and compatibility relations along bicharacteristics were deduced and the analytical expressions for wave surfaces were obtained. The characteristic and shapes of the velocity surfaces and wave surfaces in the transversely isotropic fluid-saturated porous media were discussed in detail. The results also show that the characteristic equations for stress waves in pure solids are particular cases of the characteristic equations for fluid-saturated porous media.     

The method of weighted residuals for transversely isotropic axisymmetric problems and its applications to engineering

A method with two harmonic functions is proposed for solving transversely isotropic axisymmetric problems by applying the theorems of Refs. [1] and [5]. A series of simple formulas of the boundary least square collocation method is derived. Two engineering examples show that the present method is much more convenient than Lekhniskii's with biharmonic functions. Some useful conclusions are finally obtained.     

Size-dependent sharp indentation—I: a closed-form expression of the indentation loading curve

In this paper, a closed-form expression of the size-dependent sharp indentation loading curve has been proposed based on dimensional analysis and the finite deformation Taylor-based nonlocal theory (TNT) of plasticity (Int. J. Plasticity 20 (2004) 831). The key issue is to link the results of FEM based on TNT plasticity with those obtained using conventional FEM by taking as the effective strain gradient, η, that presented in the work of Nix and Gao (J. Mech. Phys. Solids 46 (1998) 411), thus avoiding large-scale finite element computations using strain gradient plasticity theories. Two experiments carried out on 316 stainless-steel and pure titanium have been used to verify the effectiveness of the present analytical model; the results demonstrate that the present analytical expression of the size-dependent indentation loading curve corresponds very well to the experimental indentation loading curve. The empirical constant, α, in the Taylor model estimated from the experimental data has the correct order of magnitude. Also, the results presented in this part can be further applied to establish an analytical framework to extract the plastic properties of metallic materials with sharp indentation on a small scale where the size effect caused by geometrically necessary dislocations is significant. This will be discussed in detail in the second part of the paper.     

A minimum principle for microstructuring in rigid-viscoplastic crystalline solids

A minimum plastic power principle is proposed for a rigid-viscoplastic crystalline domain subdivided into two sets of lath-shaped regions, called bands. The lattice orientation in each band is assumed uniform and to differ infinitesimally from that in the other band. The proposed minimum principle yields the slip activity in the bands and semi-analytical expressions for the misorientation axis and orientation of band boundaries. These band boundary characteristics are predicted for f.c.c. lattice orientations near the ideal rolling texture components. Surprisingly, it found that the predicted band boundary characteristics closely match those of microstructural features called cell block boundaries reported in the experimental literature, except when the dislocations of activated slip systems are known to interact very strongly. This suggests that except when precluded by strong dislocation interactions, continuum extremum principles may also govern microstructural characteristics.