含双周期不等长刚性线材料有效反平面剪切模量研究

研究无限介质中含双周期刚性线夹杂复合材料的反平面问题,其基本胞元含有四条不同长度的刚性线夹杂。运用椭圆函数和保角变换理论,获得了该问题严格的闭合解。利用微结构的周期性和平均应力/应变定理得到了复合材料有效反平面剪切模量的精确公式。由结果的特殊情形可以得到一系列有意义的解答。数值结果给出了该类非均匀材料有效反平面剪切模量随微结构参数变化的规律。精确解可以为其它数值和近似方法提供有价值的参考。     

Property of eigenvalues and eigenfunctions for an interface V-notch in antiplane elasticity

The so-called pseudo-orthogonal property of the eigenfunction expansion form is proved to be valid for the case of an antiplane interface V-notch and the corresponding path-independent integral is derived. The relation between the path-independent integral and the stress intensity factor of the notch is found. The influence of loads on the related integral is also presented.     

压电材料中反平面渗透裂纹的解

用复变函数的保角映射法,采用可渗透边界条件,研究了含裂纹的无限大压电材料在平面内电场和反平面荷载作用下的耦合场,得到了精确的解和场强度因子以及能量释放率。结果表明,电场强度在裂尖没有奇异性,应变、应力、电位移具有1/2阶的奇异性,能量释放率总是正的。     

Determination of high‐order fields for multianisotropic material antiplane V‐notches and inclusions by the asymptotic expansion technique and an overdeterministic method

In this paper, the singular behavior for anisotropic multimaterial V‐notched plates is investigated under antiplane shear loading condition. Firstly, the elastic governing equations are transformed into eigen ordinary differential equations through introducing the asymptotic expansions of displacements near the notch tip. The stress singularity exponents, including the higher‐order terms, and the corresponding eigen angular functions are then obtained by solving the established equations by using the interpolating matrix method. Thus, using the combination of the results from finite element analyses and the derived asymptotic expansion, an overdeterministic method is employed to calculate the amplitudes of the coefficients in the asymptotic expansions. Finally, the stress and displacement fields in the vicinity of the notch tip, consisting of both singular terms and higher‐order terms, are determined. The effects of material properties and geometry characteristic on the singular behaviour of the notch tip are discussed in detail.     

Nonlinear mode III crack stress fields for materials obeying a modified Ramberg‐Osgood law

In this paper, an analytical study is carried out on the work‐hardening, elastic‐plastic stress distributions in a cracked body under antiplane shear deformation. A modified Ramberg‐Osgood law is introduced to describe the material behaviour, and stress and strain fields are derived in closed form. Compared with the conventional Ramberg‐Osgood formulation, the new law includes the effect of a new parameter, κ, which allows the transition from the ideally elastic behaviour (low stress regime) to the power law behaviour (large stress regime) to be controlled, thus providing 1 more degree of freedom to better fit the actual behaviour of engineering materials. A discussion is carried out on the features of stresses and strains close to and far away from the crack tip.     

非均匀复合材料中反平面裂纹的动态断裂力学研究

对于非均匀复合材料中多个裂纹的动态断裂力学问题, 提出了一种分析方法, 假设复合材料为正交各向异性并含有多个垂直于厚度方向的裂纹, 材料参数沿厚度方向为变化的, 沿该方向将复合材料划分为许多单层, 假设单层材料参数为常数, 应用柔度矩阵/刚度矩阵方法及Fourier变换法, 在L aplace 域内推导出了控制问题的奇异积分方程组, 并用虚位移原理求解, 给出了应力强度因子及能量释放率的表达式, 然后利用Laplace 数值反演, 得出了裂纹尖端的动态应力强度因子和能量释放率。作为算例, 研究了带有两个裂纹的功能梯度结构, 分析了材料参数的优化对降低应力强度因子的意义。      

Regularized meshless method for antiplane piezoelectricity problems with multiple inclusions

In this paper, solving antiplane piezoelectricity problems with multiple inclusions are attended by using the regularized meshless method (RMM). This is made possible that the troublesome singularity in the MFS disappears by employing the subtracting and adding-back techniques. The governing equations for linearly electro-elastic medium are reduced to two uncoupled Laplace's equations. The representations of two solutions of the two uncoupled system are obtained by using the RMM. By matching interface conditions, the linear algebraic system is obtained. Finally, typical numerical examples are presented and discussed to demonstrate the accuracy of the solutions.     

集中载荷作用下的不同压电材料反平面应变状态的共圆弧界面裂纹问题

本文应用复变函数解析延展原理，得到了集中载荷作用下的不同压电材料反平面应变状态的共圆弧界面裂纹问题的一般解；对单个圆弧界面裂纹，给出了复函数封闭解和场强度因子。     

Analytical study on the mode III stress fields due to blunt notches with cracks

This work presents an analytical study on the stress fields induced by cracks nucleated at the tip of radiused notches under antiplane shear and torsion loadings. Closed‐form solutions for both shallow and deep notches are derived leveraging a combination of proper curvilinear coordinate systems and the complex potential method for antiplane elasticity. Based on the exact stress field solutions, convenient expressions for the stress intensity factors are derived. The accuracy of all the analytical formulations is verified by comparison with the results from a bulk of numerical analyses.     

Dynamics steady crack propagation of antiplane shear in an elastic perfectly plastic material

Abstract

A theoretical analysis of steady‐state crack growth in an elastic ideally‐plastic material under small‐scale yielding conditions has been carried out for anti‐plane shear. Asymptotic expansion method is used to construct the solutions for the region near the crack line. Exact solutions for the distribution of strain on the crack line within the primary active plastic zone is obtained. It is shown that the solution reduces to the correct asymptotic form as the crack speed approaches zero (quasi‐static) for any point on the crack line. The results are used to discuss the applicability of quasi‐static solutions to moving steady‐state situations. It is found that if the crack propagation speed is less than 0.1 of the shear wave speed, the quasi‐static solutions can be accurately approximated for the steady state solutions.