U形切口的有限断裂准则

有限断裂力学准则综合了应力和能量参数,假设裂纹或切口端部有限裂纹长度的增长．特别地,该有限裂纹的长度不是材料的基本常数,而是与构件的结构有关．基于U形切口两种形式：点方式和线方式有限断裂准则,对文献中的铝合金U形切口三点弯曲断裂实验进行了分析验证．一方面基于材料的断裂韧度和抗拉强度,预测切口件断裂载荷;另一方面根据几组不同的切口根部半径及其对应的临界切口应力强度因子,同时估算材料的断裂参数：断裂韧度和抗拉强度．将点方式和线方式两种不同形式有限断裂准则的预测结果,与平均周向应力准则、最大周向应力准则以及文献中相关结果进行了比较得出：无论是预测断裂载荷还是估算材料断裂参数,线方式有限断裂准则,与文献中相关结果比较吻合,尤其是估算的断裂韧度精度较高．     

Finite Fracture Mechanics model for mixed mode fracture in adhesive joints

Up to now the failure load assessment of bonded joints is still not fully understood. This work provides a new approach for assessing the crack initiation load of bonded joints. A failure model for single lap joints is proposed that is based on Finite Fracture Mechanics. Only two basic fracture parameters are required: the tensile strength and the fracture toughness of the adhesive. A coupled stress and energy criterion proposed in 2002 by Leguillon is used to model crack initiation in the adhesive layer. The theory of this criterion is outlined in detail, its relationship to other failure criteria is discussed and an overview of applications found in literature is given. An enhanced weak interface model that predicts a linear variation of the shear stresses in the adhesive layer is utilized to model the single lap joint. To compare joint designs and to reveal the limitations of the given approach a dimensionless brittleness number for mixed-mode loading is proposed. Along with a detailed discussion of the results for exemplary joint designs a comparison to experimental results from literature is performed. The two necessary fracture parameters are each taken from standard test results published in literature. A good agreement of the failure load predictions with the experimental results is observed. A remarkable outcome is that the presented failure model renders the adhesive thickness effect correctly. The paper concludes with a discussion of the limitations of the approach and the effect of material parameters.     

Non-local criteria for the borehole problem: Gradient Elasticity versus Finite Fracture Mechanics

Two nonlocal approaches are applied to the borehole geometry, herein simply modelled as a circular hole in an infinite elastic medium, subjected to remote biaxial loading and/or internal pressure. The former approach lies within the framework of Gradient Elasticity (GE). Its characteristic is nonlocal in the elastic material behaviour and local in the failure criterion, hence simply related to the stress concentration factor. The latter approach is the Finite Fracture Mechanics (FFM), a well-consolidated model within the framework of brittle fracture. Its characteristic is local in the elastic material behaviour and non-local in the fracture criterion, since crack onset occurs when two (stress and energy) conditions in front of the stress concentration point are simultaneously met. Although the two approaches have a completely different origin, they present some similarities, both involving a characteristic length. Notably, they lead to almost identical critical load predictions as far as the two internal lengths are properly related. A comparison with experimental data available in the literature is also provided.

     

Tangential continuity of elastic/plastic curvature and strain at interfaces

The continuity vs discontinuity of the elastic/plastic curvature & curvature rate, and strain & strain rate tensors is examined at non-moving surfaces of discontinuity, in the context of a field theory of crystal defects (dislocations and disclinations). Tangential continuity of these tensors derives from the conservation of the Burgers and Frank vectors over patches bridging the interface, in the limit where such patches contract onto the interface. However, normal discontinuity of these tensors remains allowed, and Kirchhoff-like compatibility conditions on their normal discontinuities across the concurring interfaces are derived at multiple junctions. In a simple plane case and in the absence of surface-disclinations, the compatibility of the normal discontinuities in the elastic curvatures assumes the form of a Young’s law between the grain-to-grain disorientations and the sines of the dihedral angles. Complete continuity of the plastic strain rate tensor at triple junctions also derives from the compatibility of the normal discontinuities in the plastic strain rates in such conditions.     

Two-dimensional unstructured elastic model for acoustic pulse scattering at solid-liquid interfaces

Abstract. A numerical model to simulate elastic waves and acoustic scattering in two spatial dimensions has been developed and thoroughly tested. The model universally includes elastic solids and liquids. The equations of motion are written in terms of stresses, displacements and displacement velocities for control volumes constructed about the nodes of a triangular unstructured grid. The latter conveniently supports various geometries with complex external and internal boundaries separating sub-domains of different elastic properties. Theoretical dispersion for zero mode symmetric () and antisymmetric () waves in a plate has been reproduced numerically with high accuracy, thus verifying the method and code. Comparison of simulated acoustic pulse scattering at water-immersed steel plate with the respective experiments reveals a very good agreement in such delicate features as excitation of the surface (A) wave. The numerical results explain the peculiar location of the surface wave relative to the other ones in experimental registrations. Examples of acoustic pulse interactions with curvilinear metallic shells in water demonstrate flexibility of the method with respect to complex geometries. Potential applications as well as some directions for further improvement to the technique are briefly discussed. Received 5 September 2002 / Accepted 25 November 2002 Published online 4 February 2003 RID="*" ID="*"Permanent address: Ioffe Physical-Technical Institute, 26 Polytekhnicheskaya, 194021 St. Petersburg, Russia Correspondence to: P. Voinovich (e-mail: vpeter@scc.ioffe.ru)     

Finite elastic straining

Summary Finite elastic straining is analysed with all quantities referred consistently to the deformed body taken as the function domain. The straining-displacement of a typical point is relative to a set of axes imbedded in the body at one arbitrary point and rotating in fixed space with that neighborhood if necessary in a particular problem. The resulting |plane stress' equations have precisely the same form as in the classical theory but relate to |true' quantities in the deformed body.The solution of a circular hole in a deformed sheet under simple tension is given and checks closely with experiment on rubber. Cauchy strains of order 65% and local rotation of order 30° are found to occur at the hole boundary.The solution of a deformed quadrantal cantilever is given. Cauchy strains of several hundred percent and local rotation of order 90° occur.Any boundary value problem already solved for the classical infinitesimal strains theory can be applied directly as a finite strains solution for the deformed body.Notation x, y, z, r, , z Cartesian and polar co-ordinates respectively - , Normal and shear true stresses respectively - , Normal and shear true strains respectively - r Position vector - Airy stress function - S Simple tensile stress applied to sheet - a Radius of circular hole in deformed sheet - a, b Inner and outer radii of quadrantal cantilever - u Straining-displacement vector - u, v Straining-displacement scalar components - E, True Young's modulus and Poisson's ratio respectively - c ₁, c ₂ Local unit vectors in principal normal strains directions - i, j Cartesian axes constant unit vectors - Stress dyadic or tensor - First stress invariant - I Idemfactor or spherical tensor - P Shear load per unit thickness applied to quadrantal cantilever - A, B, D, N, H, K, L Arbitrary constants of integration     

Reflection and transmission of elastic waves at five types of possible interfaces between two dipolar gradient elastic half-spaces

Reflection and transmission of an incident plane wave at five types of possible interfaces between two dipo-lar gradient elastic solids are studied in this paper. First, the explicit expressions of monopolar tractions and dipolar trac-tions are derived from the postulated function of strain energy density. Then, the displacements, the normal derivative of displacements, monopolar tractions, and dipolar tractions are used to create the nontraditional interface conditions. There are five types of possible interfaces based on all possible combinations of the displacements and the normal derivative of displacements. These interfacial conditions with consid-eration of microstructure effects are used to determine the amplitude ratio of the reflection and transmission waves with respect to the incident wave. Further, the energy ratios of the reflection and transmission waves with respect to the incident wave are calculated. Some numerical results of the reflection and transmission coefficients are given in terms of energy flux ratio for five types of possible interfaces. The influences of the five types of possible interfaces on the energy parti-tion between the refection waves and the transmission waves are discussed, and the concept of double channels of energy transfer is first proposed to explain the different influences of five types of interfaces.     

多参量断裂力学广义杂交/混合裂纹有限元法

通过研究广为人知的断裂力学单变量八节点位移裂纹QPE元和Akin族奇异单元法，本文运用经典局部裂纹解析解，与非协调假设应力杂交-混合元列式方法相结合，提出用于分层各向异性材料的多变量半解析假设应力奇异广义杂交／混合裂纹有限元法，能克服现有位移裂纹元法的域应力分布精度低和高次单元所需计算容量大的局限性，互为补充，更有利于结构裂纹扩展分析和应用研究。文中设计了一个半解析奇异裂纹平面单元，各向同性材料板算例验证了退化二次八节点协调位移裂纹元及六节点非协调奇异应力裂纹元，说明采用稀疏及加密单元网格，两类裂纹单元分别从上下逼近收敛于实验和理论参考解，可得到吻合程度较好的1／√r奇异应变和应力分量以及应力强度因子值，表明了本文奇异裂纹单元理论的优越性。     

Scattering of elastic waves in an elastic matrix containing an inclusion with interfaces

Based on the theory of elastic dynamics, the scattering of elastic waves and dynamic stress concentration in fiber-reinforced composite with interfaces are studied. Analytical expressions of elastic waves in different medium areas are presented and an analytic method of solving this problem is established. The mode coefficients are determined by means of the continuous conditions of displacement and stress on the boundary of the interfaces. The influence of material properties and structural size on the dynamic stress concentration factors near the interfaces is analyzed. It indicates that they have a great influence on the dynamic properties of fiber-reinforced composite. As examples, numerical results of dynamic stress concentration factors near the interfaces are presented and discussed. This paper provides reliable theoretical evidence for the study of dynamic properties in fiber-reinforced composite. Project supported by the National Natural Science Foundation of China (No. 19972018).     

Mechanics and thermodynamics of fluid-saturated highly elastic materials

We consider a mixture that consists of a highly elastic material and a liquid dissolved in this material. Using the laws of classical thermodynamics, we state a variational principle describing the mixture equilibrium under static loading conditions. From this principle, we derive equilibrium equations and a system of constitutive relations characterizing the mixture elastic and thermodynamic properties. We state problems describing the stress-strain state of a swollen material and a statically loaded material in thermodynamic equilibrium with the liquid. We consider the case of incompressible mixture. The general theory is illustrated by examples concerned with the deformation behavior of inhomogeneously swollen cross-linked polymers and with their thermodynamics of strains and swelling in solvent media.     

Differential geometrical method in elastic composite with imperfect interfaces

I.IntroductionWhethertheinterfacesofcompositematerialsareperfectornotwillaffectitsmacromechanicaloreffectivepropertiesimportantly.Butsofar,almostallofthestudiesontheeffectivepropertiesofcompositematerialsarebasedontheassumptionthattheinterfacesareperfectl"2].Infact,thisisnotappropriateforallinterfaces[31.Thusthestudiesonmechanicalpropertyofcompositematerialswithimperfaceintert'acehavebeenconsideredrecentlyinsomeliteratures.Hashin16]hasextendedtheelasticextremumprinciplesofminimumpotentialandm…     

Higher order model for soft and hard elastic interfaces

The present paper deals with the derivation of a higher order theory of interface models. In particular, it is studied the problem of two bodies joined by an adhesive interphase for which “soft” and “hard” linear elastic constitutive laws are considered. For the adhesive, interface models are determined by using two different methods. The first method is based on the matched asymptotic expansion technique, which adopts the strong formulation of classical continuum mechanics equations (compatibility, constitutive and equilibrium equations). The second method adopts a suitable variational (weak) formulation, based on the minimization of the potential energy. First and higher order interface models are derived for soft and hard adhesives. In particular, it is shown that the two approaches, strong and weak formulations, lead to the same asymptotic equations governing the limit behavior of the adhesive as its thickness vanishes. The governing equations derived at zero order are then put in comparison with the ones accounting for the first order of the asymptotic expansion, thus remarking the influence of the higher order terms and of the higher order derivatives on the interface response. Moreover, it is shown how the elastic properties of the adhesive enter the higher order terms. The effects taken into account by the latter ones could play an important role in the nonlinear response of the interface, herein not investigated. Finally, two simple applications are developed in order to illustrate the differences among the interface theories at the different orders.     

Discontinuous wave interaction with interfaces between anisotropic elastic media

The problem about dynamic interaction of discontinuous waves with interfaces between anisotropic elastic media is considered. To investigate this phenomenon accompanied by formation of reflected and refracted quasi-longitudinal and quasi-shear discontinuous waves, a technique based on joint usage of the zero approximation of the ray theory and method of stereomechanical impact is proposed. It is used for the analysis of the wave front transformation, scattering and focusing. The setup problem solutions can be applied to discovering the most seismically hazardous zones in the earth’s crust, interpretation of geophysical data about geological rock structures and the analysis of the causes of dynamic delamination of layered composite and nanomaterials.     

Finite deflection dynamics of elastic beams

Solutions are obtained for the problem of an infinite elastic beam subjected to essentially constant velocity boundary conditions at one point of the beam. The effects of finite deflections, normal force, rotatory inertia and shear deformation are included. The equations of the problem are converted into non-dimensional form and a perturbation approach is used to obtain a consistent approximation. Numerical solutions are obtained for the bending moment, shear force and the normal force for different velocities of impact. It is shown that the solution to the problem depends on a combined geometrical and material parameter which does not vary significantly for compact sections and a loading parameter which determines the amplitude of the response. Finally the linear Timoshenko beam theory is shown to predict the bending moment and shear force extremely well even when the deflections are large enough to cause appreciable stretching of the centroidal axis.     

Finite element system of elastic structure

The article deals with the problems of controllability, observability and stabilizability of an elastic-structural system treated by the finite element method. The results obtained here agree with that obtained in distributed parameter-system model, nevertheless, they are more convenient than those in carrying out the computation with a computer, at the same time the method appears much easier that the conventional one. In section one, the system's controllability and observability are studied and some conditions which are easier to be justified by computer are given. In section two, the problem of stabilizing an elastic object by the use of linear feedback is fully discussed. As the attained results there show that, so far as an elastic-structural system is concerned, it is possible to assign arbitrary frequencies of vibration only by the use of displacement feedback, however, it is impossible to stabilize the system while the system is completely controllable. While the velocity feedback can stabilize the system, but its ability is limited. The case of rigid body motion involved in the system equation has also been discussed. In section three, the control of a straight beam is treated by the finite element method. The whole system of a beam can be decomposed into four irrelevant subsystems of tension-compression, torsion, bending in two directions, their controllability and observability are also analyzed respectively. The controllability and observability of segment-shaped beam are discussed in the end.     

断裂力学的半解析相似边界元法

本文首先对弹性力学的相似边界元法进行了研究，推导了相应的计算公式。与传统的边界元法相比，相似边界元法由于只需在少数单元上进行数值积分，大大减少了计算量。在此基础上，对断裂力学问题，利用裂纹尖端位移场的解析表达式将裂纹尖端节点未知量转化为几个待定常数，提出了半解析相似边界元法，可大大减少最终形成的线性代数方程组的系数矩阵的阶数，进一步减小计算量。最后给出了算例，说明了本文方法的有效性。