Huy Duong Bui

An integral equations method for solving the problem of a plane crack of arbitrary shape

Abstract T he problem of a plane crack of arbibrary shape, subjected to arbitrary loading, is studied. The displacement field is represented by two elastic potentials, the single-layer and the double-layer potential of the second kind. The equations for the crack displacement discontinuities are derived. An approximate analysis of the crack opening displacement under pressure is discussed.

Reciprocity principle and crack identification

In this paper we are concerned with the planar crack identification problem defined by a unique complete elastostatic overdetermined boundary datum. Based on the reciprocity gap principle, we give a direct process for locating the host plane and we establish a new constuctive identifiability result for 3D planar cracks.

Numerical identification of linear cracks in 2D elastodynamics using the instantaneous reciprocity gap

This paper considers the identification problem of a linear crack in a body of finite extension within the framework of linear two-dimensional elastodynamics. In a series of prior papers in electricity, elasticity or acoustics, it has been proved using the reciprocity gap that three different series of adjoint wave fields determine in closed-form solution the normal of the plane of the crack, the position of the plane and finally the complete crack extension. The work developed next within the framework of linear elastodynamics defines a novel instantaneous reciprocity gap as the instantaneous work done by the adjoint tractions on the crack opening displacement. This quantity is then used to identify linear cracks in a two-dimensional problem. It is shown using a numerical example that a unique family of planar shear waves permits the identification of the normal, position and a convex hull of a linear crack through simple interpretations of the instantaneous reciprocity gap. This method is more general in the sense that it applies to three-dimensional problems as well.

Regularization of the Displacement and Traction BIE for 3D Elastodynamics Using Indirect Methods

This paper deals with regularization techniques developed in order to overcome the strongly singular (displacement BIE) or hypersingular (traction BIE) character of the boundary integral equations commonly used for three-dimensional elastodynamics. More specifically, we address indirect regularization techniques, which rely upon singularity exclusion and separate evaluation of strongly singular or hypersingular integrals containing the singular kernel only. In many, but not all, cases, this evaluation can be made using an auxiliary static problem together with the fact that the dynamic and static kernels share the same singular term. In this paper we first give a bibliographical outline of the regularization problem. Then the regularized displacement and traction BIE for general 3D situations in transient elastodynamics, including crack problems, are derived and stated. We also recall related results of interest. Then numerical implementation considerations are considered. For completeness, a brief survey of Galerkin-type and direct approaches is also given. Finally some numerical examples in elastodynamics are given.

Toward a pure shear specimen for KIIc determination

The object of this note is to report on a newly developed specimen which is proposed for use in accurately measuring K . Since it has Ilc been generally assumed that mode I displacement is dominant, most investigations to date have concentrated on this failure mode; it seems clear however, that most cracks will be loaded in a mixed mode field. Moreover, mode II deformations may dominate as for example in the spar web of an airplane wing. Several specimens have appeared in the literature [1,2,3,4] to measure Kiic, each of which has various deficiencies.

Identification of Heat Conduction Coefficient: Application to Nondestructive Testing

Thermographic Non-Destructive Testing methods for the evaluation of materials and structures are of great interest. They are attractive because of rapid-scanning capabilities available today, Balageas et al [1]. The principle of photothermal methods are well known. The heat flux is applied on the sample by a laser pulse. Then, by means of a Infra-Red camera, one makes a full time record of the whole surface temperature field. There are very rich informations saved in the surface time history θ(x, t), which can be used for the reconstruction of unknown thermal conduction coefficient η(x), defects, cracks etc...

The Reciprocity Gap Functional for Identifying Defects and Cracks

The recovery of defects and cracks in solids using overdetermined boundary data, both the Dirichlet and the Neumann types, is considered in this paper. A review of the method for solving these inverse problems is given, focusing particularly on linearized inverse problems. It is shown how the reciprocity gap functional can solve nonlinear inverse problems involving identification of cracks and distributed defects in bounded solids. Exact solutions for planar cracks in 3D solids are given for static elasticity, heat diffusion and transient acoustics.

SECTION 8.5 – A Thermodynamic Analysis of Wear

The interface is a complex medium made of detached particles, eventually a lubricant fluid, and damaged zones. In this chapter, the interface description is based on given macroscopic laws and differs from the one derived from microscopic considerations in Dragon-Louiset. The local approach allows making a distinction between mechanical quantities evaluated on a given geometry and for specific loading conditions and intrinsic ones associated with any moving wear surfaces. The approach to wear criteria in this chapter is based on the energy release rate like quantities, similar to Griffiths theory in fracture mechanics. All these quantifies some of them accessible to experiments, make it possible to better define wear criteria and wear rates. A system consisting of two sliding contacting solids and the contact interface zone, having some mechanical properties which are assumed to be known and described by usual laws of continuous media is considered. Such interface laws is understood in a macroscopic sense, as average or homogenized through the thickness of contact interface zone. The internal entropy production is positive and consists of different kinds of separately positive contributions: volumic thermal conduction, volumic intrinsic mechanical irreversibility, and surface irreversibility terms.

On viscous fluid flow near a moving crack tip

We consider a crack partially filled with a fluid. We show that the presence of a lag avoids the appearance of pressure and velocity singularities. For the static equilibrium, we recall the previous result on the Capillary Stress Intensity Factor which provides a purely mechanical explanation of the Rehbinder effect, according to which the toughness of the material can be lowered by humidity. For the steady state propagation of a crack due to viscous fluid flow, we set the coupled system of non-linear equations.

ON DUALITY, SYMMETRY AND SYMMETRY LOST IN SOLID MECHANICS

The paper recalls the concept of duality in mathematics and extends it to solid mechanics. One important application of duality is to restore some symmetry between current fields and their adjoint ones. This leads to many alternative schemes for numerical analyses, different from the classical one as used in classical formulation of boundary value problems (finite element method). Usually, conservation laws in fracture mechanics make use of the current fields, displacement and stress. Many conservation laws of this type are not free of the source term. Consequently, one cannot derive path-independent integrals for use in fracture mechanics. The introduction of variables and dual or adjoint variables leads to true path-independent integrals. Duality also introduces some anti-symmetry in current fields and adjoint ones for some boundary value problems. The symmetry is lost between fields and adjoint fields. The last notion enables us to derive new variational formulation on dual subspaces and to exactly solve inverse problems for detecting cracks and volume defects.