Dynamic stress intensity factor due to concentrated loads on a propagating semi-infinite crack in orthotropic materials

The elastodynamic response of an infinite orthotropic material with a semi-infinite crack propagating at constant speed under the action of concentrated loads on the crack faces is examined. Solution for the stress intensity factor history around the crack tip is found for the loading modes I and II. Laplace and Fourier transforms along with the Wiener-Hopf technique are employed to solve the equations of motion. The asymptotic expression for the stress near the crack tip is analyzed which lead to a closed-form solution of the dynamic stress intensity factor. It is found that the stress intensity factor for the propagating crack is proportional to the stress intensity factor for a stationary crack by a factor similar to the universal function k(v) from the isotropic case. Results are presented for orthotropic materials as well as for the isotropic case.     

A point heat source on the surface of a semi-infinite transversely isotropic electro-magneto-thermo-elastic material

We use the compact mono-harmonic general solutions of transversely isotropic electro-magneto-thermo-elastic material to construct the three-dimensional Green’s function for a steady point heat source on the surface of a semi-infinite transversely isotropic electro-magneto-thermo-elastic material by five newly introduced mono-harmonic functions. All components of coupled field are expressed in terms of elementary functions and are convenient to use. Numerical results are given graphically by contours.     

The frictionless rolling contact of a rigid circular cylinder on a semi-infinite granular material

The resulting flow and deformation of a semi-infinite granular material under a rolling, smooth rigid circular cylinder is investigated using a perturbation method. Based on the double-shearing theory of granular flow, complete stress and velocity fields, resistance to rolling and the permanent displacement of surface particles are determined to first order; when the internal friction angle is zero, the solutions reduce to those obtained in the corresponding analysis for Tresca or von-Mises materials. The solution scheme and the double-shearing model for granular flow both find their origins in the work of A.J.M. Spencer.     

Fundamental solution of a circular rigid punch problem for a half plane

A fundamental solution (a Green's function) of a circular rigid punch problem is derived. The punch on a half plane contacts smoothly at both ends of the contact region and a concentrated force or a point dislocation apply at an arbitrary point. Two cases where the punch is kept vertically and the punch is inclined are considered. Complex stress functions and a mapping function are used and a closed form solution is derived. Some results of stress distribution, contact length and resultant moment on the contact region are shown in figures.     

The Cauchy stress tensor for a material subject to an isotropic internal constraint

The Cauchy stress tensor, T_{_ij}, is considered for an elastic material which is subject to any internal isotropic constraint, apart from the constraint of incompressibility. For a given strain, it is seen that if in a given basis one of the eigenvectors of the stress tensor has a zero component, say the th component, and if the arbitrary scalar term in the stress may be chosen so that T_{_}() shear stress component is zero, then the stress tensor has a double eigenvalue. This means that there is a great simplification in the stress field. The given strain may be maintained experimentally by a simple tension superimposed upon a hydrostatic stress field. Examples are presented for Bell-constrained and Ericksen-constrained materials.     

Numerical solution of two-dimensional inverse force function in the wave equation with nonlocal boundary conditions

In this paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the inverse time-dependent force function in the wave equation on regular and irregular domains. The SMRPI is developed for identifying the force function which satisfies in the wave equation subject to the integral overspecification over a portion of the spatial domain or to the overspecification at a point in the spatial domain. This method is based on erudite combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which play as basis functions in the frame of SMRPI. Since the problem is known to be ill-posed, Thikhonov regularization strategy is employed to solve effectively the discrete ill-posed resultant linear system. Three numerical examples are tested to show that numerical results are accurate for exact data and stable with noisy data.     

Elastodynamic stress intensity factors for a semi-infinite crack due to three-dimensional concentrated shear loadings on the crack faces

The dynamic stress intensity factors for a semi-infinite crack in an otherwise unbounded elastic body is investigated. The crack is subjected to a pair of suddenly-applied shear point loads on its faces at a distance l away from the crack tip. This problem is treated as the superposition of two problems. The first problem considers the disturbance by a concentrated shear force acting on the surface of an elastic half space, while the second problem discusses a half space with its surface subjected to the negative of the tangential surface displacements induced by the first problem in the front of the crack edge. A fundamental problem is proposed and solved by means of integral transforms together with the application of the Wiener–Hopf technique and Cagniard–de Hoop method. Exact expressions are then derived for the mode II and III dynamic stress intensity factors by taking integration over the fundamental solution. Some features of the solutions are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analytical solution for the singular stress distribution due to V-notch in an orthotropic plate material

On the basis of general solutions of two-dimensional linear elasticity, displacement and singular stress fields near the singular point in orthotropic materials are derived in closed form expressions. According to the presented expressions, analysis formulas of displacement and singular stress fields near the tip of a V-notch under the symmetric and the anti-symmetric modes are obtained subsequently. The open literatures devoted to developing stress singularity near the tip of the V-notch in anisotropic or orthotropic materials. In this study, however, not only direct eigenequations were derived, but also the explicit solutions of displacement and singular stress fields were obtained. At the end, the correctness of the formulas of the singular stress field near the tip of the V-notch has been verified by FEM analysis.     

Application of the material force method to isotropic continuum damage

 The objective of this work is the exploitation of the notion of material forces in computational continuum damage mechanics. To this end we consider the framework of isotropic geometrically non–linear continuum damage and investigate the spatial and material settings that lead to either spatial or material forces, respectively. Thereby material forces essentially represent the tendency of material defects to move relative to the ambient material. In this work we combine an internal variable approach towards damage mechanics with the material force method. Thus the appearance of distributed material volume forces that are conjugated to the damage field necessitates the discretization of the damage variable as an independent field in addition to the deformation field. Consequently we propose a monolithic solution strategy for the corresponding coupled problem. The underlying kinematics, strong and weak forms of the coupled problem will be presented and implemented within a standard Galerkin finite element procedure. As a result in particular global discrete nodal quantities, the so–called material node point (surface) forces, are obtained and are studied for a number of computational examples. Received: 19 August 2002 / Accepted: 16 October 2002     

The Boltzmann equation approach to the shear flow of a granular material

An exact solution of the Boltzmann equation for the shear flow of granular materials is discussed and compared with some related solutions.     

激励力作用位置对圆柱壳辐射声功率影响研究

潜艇上的机械设备不平衡运转会产生激励力,不平衡运转设备引起的艇体噪声是辐射噪声的主要成分。因此研究激励力的位置与声功率的关系是非常具有意义。文章建立了环肋圆柱壳结构声振动分析模型,基于力辐射模态从激励力作用位置变化方面对环肋圆柱壳进行数值计算和分析,研究激励力作用在不同位置处时,辐射声功率的变化规律。为了给出激励力作用位置与壳体辐射声功率的关系,运用力辐射模态概念,依据力辐射模态形态特征,分析判断激励力作用位置对辐射声功率的影响,为有效地减少圆柱壳辐射声功率提供了更为方便的技术手段。     

Fracture of austenitic steel subject to a wide range of stress triaxiality ratios and crack deformation modes

The stress triaxiality ratio (hydrostatic pressure divided by von Mises equivalent stress) strongly affects the fracture behaviour of materials. Various fracture criteria take this effect into consideration in their effort to predict failure. The dependency of the fracture locus on the stress triaxiality ratio has to be investigated in order to evaluate these criteria and improve the understanding of ductile fracture.This was done by comparing the experimental results of austenitic steel specimens with a strong variation in their stress triaxiality ratios. The specimens had cracks with varying depths and crack tip deformation modes; tension, in-plane shear, and out-of-plane shear. The crack growth in fracture mechanics specimens was compared with the failure of standard testing specimens for tension, upsetting and torsion. By associating the experimental results with finite element simulations it was possible to compare the critical plastic equivalent strain and stress triaxiality ratio values at fracture. In the investigated triaxiality regime an exponential dependency of the fracture locus on the stress triaxiality ratio was found.     

The effect of material combinations and relative crack size to the stress intensity factors at the crack tip of a bi-material bonded strip

Several types of singular stress fields may appear at the corner where an interface between two bonded materials intersects a traction-free edge depending on the material combinations. Since the failure of the multi-layer systems often originates at the free-edge corner, the analysis of the edge interface crack is the most fundamental to simulate crack extension. In this study, the stress intensity factors for an edge interfacial crack in a bi-material bonded strip subjected to longitudinal tensile stress are evaluated for various combinations of materials using the finite element method. Then, the stress intensity factors are calculated systematically with varying the relative crack sizes from shallow to very deep cracks. Finally, the variations of stress intensity factors of a bi-material bonded strip are discussed with varying the relative crack size and material combinations. This investigation may contribute to a better understanding of the initiation and propagation of the interfacial cracks.     

Compliance based assessment of stress intensity factor in cracked hollow cylinders with finite boundary restraint: Application to thermal shock part I

The evaluation of mode I stress intensity factor associated with the creep-free thermal shock (TS) of finite length elastically/thermo-elastically restrained cracked hollow cylinders is a problem of interest. Among existing evaluation methodologies, the mechanical weight function approach is often perceived to be an optimal compromise between simplicity and accuracy for and more generalised K_I evaluation. However, to confidently apply a mechanical weight function methodology in such circumstances requires the derivation of different weight functions for each potential boundary restraint configuration, i.e. free, flexible or rigid boundary conditions. In this article, the traditional mechanical weight function philosophy is complimented with an elastic compliance analysis, enabling the mechanical weight function and geometry factors for an equivalent semi-infinite cracked hollow cylinder to be used to evaluate associated with a wide range of finite length elastically/thermo-elastically restrained cracked hollow cylinders. The need for deriving different weight functions is therefore removed and the proposed Compliance Adjusted Weight Function (CAWF) approach becomes more ‘user-friendly’. The targeted cracked hollow cylinders are assumed to exhibit an exterior circumferential edge crack or an exterior circumferential semi-elliptical surface crack.     

Use of CFD-DEM to evaluate the effect of intermediate stress ratio on the undrained behaviour of granular materials

This study investigates the effect of intermediate stress ratio (b) on the mechanical behaviour of granular soil in true triaxial tests. A CFD-DEM solver with the ability to model compressible fluid and moving mesh has been developed and calibrated based on existing experimental test results on Nevada sand. The effect of b on the undrained true triaxial test, which has been neglected in the literature, was investigated using a reasonable number of models. The effects of the initial confining stress and initial void ratio also have been studied. The developed model was used to calculate the hydrodynamic forces on the particles and evaluate the ratio of the particle–fluid interaction force to the resultant force on the particles. It has been demonstrated that, in numerical studies, the effect of these forces cannot be neglected.     

数值模拟大气边界层中解决壁面函数问题的方法研究

在雷诺平均N-S方程湍流模型框架内,壁面函数常用来模型化壁面附近的低雷诺数流动。探讨基于标准湍流模型数值模拟大气边界层中出现的壁面函数问题。在已有标准壁面函数基础上,通过增加一个附加项来模型化地表上面建筑结构等粗糙元由于大小不一、错乱分布对地表附近空气流动产生的附加影响。通过模拟缩尺比为1∶300的具有较大空气动力学粗糙长度的中性大气边界层,以及缩尺比为1∶50的TTU低矮建筑模型在中性大气边界层内的绕流,对附加项的有效性和使用场合进行评估和说明。结果表明:附加项对于解决壁面函数问题,即在计算域内保持来流边界条件是必要的。     

Deriving the dynamic stress function using complex function and its application to the analysis of the stress distribution around an elliptical hole

In the engineering field, analyzing the stress distribution of an elastic body to which an impact force is applied at its boundary is one of the most interesting problems. However, owing to the absence of a useful and easy method of analyzing the stress distribution of an arbitrarily shaped body, it is difficult to grasp the strength of an elastic body. Therefore, we first devise an easy and useful method employing the complex stress function and then analyze the stress distribution of a body that has an elliptical hole.     

Plastic stress singularity near the tip of a V-notch

In this study, a new practical method is proposed to analyze the plastic stress singularity at a V-shaped notch tip. By dividing the domain around the notch tip into a number of wedge-shaped elements, the problem is reduced to determining the stress singularity in a wedge composed of multiple materials with different stiffness matrix. The results so obtained appear to be quite satisfactory. Based on the numerical results, the effects of the notch geometry and the hardening exponent on the singularity are discussed. In particular, an approximate expression is presented for the evaluation of the plastic stress singularity.     

The adhesive contact of a flat punch on a hyperelastic substrate subject to a pull-out force or a bending moment

In the last decade, instrumented macro- and nano-indentation tests have become useful tools for probing mechanical properties of materials. In this context, little in-depth work has been done for soft bio-materials like biofilms, tissues, gels, cells, etc. Such materials show large elastic strains when subjected to relatively fast loading (excluding viscoelastic phenomena). The present work focuses on the adhesive contact of such materials. Flat punches of circular imprint are used and are subjected to pullout normal forces or bending moments. The materials are modeled as hyperelastic (fast-testing conditions), using the Mooney-Rivlin (M-R) strain energy density function. We examine both incompressibility and compressibility issues. The contact problem of half-space materials interacting with rigid indenters is solved explicitly for moderate deformations and is compared with finite element results. Experiments are conducted with an artificial material (gel, reinforced with talc powder) that is modeled as a hyperelastic material. The present work is expected to extend indentation testing to important technologies like medical applications (health monitoring of tissues) and food industries (quality control of various production stages). It is concluded that the adhesive contact can be used to estimate the initial elastic modulus of soft substrates, but not all the material constants required by the hyperelastic models.