Chen Yiheng

Bueckner's work conjugate integrals and weight functions for a crack in anisotropic solids

The Bueckner work conjugate integrals are studied for cracks in anisotropic elastic solids. The difficulties in separating Lekhnitskiis two complex arguments involved in the integrals are overcome and explicit functional representations of the integrals are given for several typical cases. It is found that the pseudoorthogonal property of the eigenfunction expansion forms presented previously for isotropic cases, isotropic bimaterials, and orthotropic cases, are proved to be also valid in the present case of anisotropic material. Finally, Some useful path-independent integrals and weight functions are proposed.

Weight functions for interface cracks in dissimilar anisotropic materials

Bueckners work conjugate integral customarily adopted for linear elastic materials is established for an interface crack in dissimilar anisotropic materials. The difficulties in separating Strohs six complex arguments involved in the integral for the dissimilar materials are overcome and then the explicit function representations of the integral are given and studied in detail. It is found that the pseudo-orthogonal properties of the eigenfunction expansion form (EEF) for a crack presented previously in isotropic elastic cases, in isotopic bimaterial cases, and in orthotropic cases are also valid in the present dissimilar arbitrary anisotropic cases. The relation between Bueckners work conjugate integral and theJ-integral in these cases is obtained by introducing a complementary stress-displacement state. Finally, some useful path-independent integrals and weight functions are proposed for calculating the crack tip parameters such as the stress intensity factors.

A method for conformal mapping of a two-connected region onto an annulus

This paper presents a method for conformal of a two-connected region onto an annulus. The philosophy of the method is to convert the problem into a Dirichlet problem and to prove the real part of the analytic function transformation should be a harmonic function satisfying certain boundary conditions. According to the theory of harmonic function we can determine the inner radius of the annulus from the condition that the harmonic function defined in two-connected region should be single-valued. It is then easy to see that the imaginary part can directly be obtained with the aid of Cauchy-Riemann conditions. The unknown constants of integration only influence the argument of image points and can easily be derived by using the one-to-one mapping of region onto an annulus. Without loss of generality, the method can be used to conformally map other two-connected regions onto an annulus if they can be subdivided into several rectangulars. The method has been programmed for a digital computer. It is demonstrated that the method is efficient and economical. The corresponding numerical results are shown in the Table.This paper presents a method for conformal of a two-connected region onto an annulus. The philosophy of the method is to convert the problem into a Dirichlet problem and to prove the real part of the analytic function transformation should be a harmonic function satisfying certain boundary conditions. According to the theory of harmonic function we can determine the inner radius of the annulus from the condition that the harmonic function defined in two-connected region should be single-valued. It is then easy to see that the imaginary part can directly be obtained with the aid of Cauchy-Riemann conditions. The unknown constants of integration only influence the argument of image points and can easily be derived by using the one-to-one mapping of region onto an annulus. Without loss of generality, the method can be used to conformally map other two-connected regions onto an annulus if they can be subdivided into several rectangulars. The method has been programmed for a digital computer. It is demonstrated that the method is efficient and economical. The corresponding numerical results are shown in the Table.

The Finite Element Method of Viscoelastic Large Deformation Plane Problem with Kirchhoff Stress Tensors-Green Strain Tensors Constitutive Relation

The stress analysis of viscoelastic large deformation plane problem had been completed in [1]. Because the Eular stress tensors are used in the viscoelastic differential constitutive relation, when the rigid-body rotation can not be negligible the accuracy of results is relatively poor.

Interaction between an interface crack and a parallel subinterface crack in dissimilar anisotropic composite materials

In this paper, the pseudo-traction method is combined with the edge-dislocation method (i.e. PTDM) to solve the interaction problem between an interface crack and a parallel subinterface crack in dissimilar anisotropic materials. After deriving the fundamental solutions for an interface crack loaded by normal or tangential tractions on both crack surfaces and the fundamental solutions for an edge dislocation beneath the interface in the lower anisotropic material, the interaction problem is reduced to a system of a singular integral equations by adopting the well-known superposition technique. The equations are then solved numerically with the aid of the Chebyshev numerical integration and the Chebyshev polynomial expansion technique. Several typical examples are calculated and numerical results are shown in figures and tables from which a series of valuable conclusions is obtained. Since the present results should be verified and since no previous results exist to compare them with a consistency check in introduced which starts from the conservation law of the J-integral in anisotropic cases. It is shown that the check provides a powerful tool to examine the results, although it really presents a necessary condition rather than a sufficient way to the crack-tip parameters of the interface crack and the subinterface crack in the dissimilar anisotropic materials.

FURTHER INVESTIGATION OF" INTERACTION BETWEEN INTERFACE MACROCRACK AND PARALLEL MICROCRACKS IN BIMATERIAL ANISOTROPIC SOLIDS*

In this paper, with the aid of superimposing technique and the Pseudo Traction Method (PTM), the interaction problem between an interface macrocrack and parallel microcracks in the process zone in bimaterial anisotropic solids is reduced to a system of integral equations. After the integral equations are solved numerically, a conservation law among three kinds ofJ-integrals is obtained which are induced from the interface macrocrack tip, the microcrack and the remote field, respectively. This conservation law reveals that the microcrack shielding effect in such materials could be considered as the redistribution of the remoteJ-integral.

Some Faults in the Stress Analysis of Power-Hardening Materials With Pseudo-Stress Function Method

A new analytic method was suggested and described by Lee(1987), which is known as the pseudo-stress function method similar to the Airy stress function method in linear elasticity. Here the serious errors of Lees theory are presented

New description of microcrack damage based on conservation laws

This paper presents a new description for brittle solids with microcracks under plane strain assumption. The basic idea is to extend the conservation laws such as theJj-vector andM-integral analysis used in single crack problems to strongly interacting crack problems. TheM-integral contains two distinct parts. One of them is a summation from the well-known relation between theM-integral and the stress intensity factors (SIF) at both tips of each crack. The other, called as the additional contribution, is obtained from the two components of theJj-vector and the coordinates of each microcrack center in a global system. Of great significance is the clarification of the confusion about the dependence of theM-integral on the origin selection of global coordinates, provided that the vector vanishes at infinity and that the closed contour chosen to calculate the integral and the vector encloses all the microcracks completely. TheM-integral is equivalent to the decrease of the total potential energy of the microcracking solids with the strong interaction being taken into account. TheM-integral analysis, from a physical point of view, does play an important role in evaluating the damage level of brittle solids with strongly interacting microcracks.

On the torsional rigidity for bars with L- and +-cross-section

This paper is a continuation of the senior authors previous papers[1–3]. Using the harmonic continuation technique, the torsional rigidity for bars with L- and +-cross-section can be easily found. Numerical results are shown in Tables 1–3 respectively.This paper is a continuation of the senior authors previous papers[1–3]. Using the harmonic continuation technique, the torsional rigidity for bars with L- and +-cross-section can be easily found. Numerical results are shown in Tables 1–3 respectively.