Papers by Keyword: Body Force Method

Abstract: Based on the principle of a Body Force Method (BFM), any inclusion problem can besolved only by using a Kelvin solution which corresponds to a stress field caused by a point forceacting in a homogeneous infinite plate, regardless of the mechanical properties of the inclusion. Thischaracteristic is true even for an anisotropic inclusion in which the number of independent elasticconstants are larger than that of a homogeneous material. In the present study, some problems among anisotropic inclusions were analyzed numerically to demonstrate the validity.

Abstract: A method of analysis for calculating a precise distribution of a stress intensity factor alonga front of 3D crack was improved by introducing a closed-form integral. In the present study, the crackface is discretized with number of triangular boundary elements on which the weighting function ofbody force doublet varies linearly with coordinate variables. A closed form solution of a resultant forceover an arbitrary planar-triangular area due to a presence of an isolated point force was derived andused to satisfy a stress boundary condition of a creased crack problem. In principle, arbitrary shaped3D cracks which may contain asperities and multiple creased lines in its face can be solved by presentapproach.

Abstract: In recent years, due to a remarkable progress of qualified mesh generation algorithms combinedwith computational image processing technologies, a complex shaped 3D crack analysis has been carried out more and more easily by finite element method. Generally speaking, in order to assess thereliability of numerical solution, existence of a closed-form solution or a practically exact numericalsolution is important and thank-worthy. In contrast with 2D problems, however, there are very fewnumber of closed form solutions regarding to 3D crack problems. In the present analysis, we examineda highly accurate body force method (BFM) analysis for a partially cylindrical 3D surface crackin which a suitable basic density function can be supposed reasonably by taking account the crackgeometry. The present SIF solution could be used effectively for the purpose of benchmark the finiteelement solution for general non-planar crack problems.

Abstract: In a standard body force method analysis, a mesh division is required to define the boundary of a problem and to solve a governing equation using discretization procedure. However, in the present study, a moving least square strategy is introduced to define a weight function for the density of body force doublet and therefore a crack analysis is carried out without providing a standard mesh-division. Hence, the standard crack face elements are not required at all. A variety of 3D crack problems can be analyzed simply by providing a data that only de nes a crack front. Besides the nodal points for crack front, several internal nodes are generated on the crack face to represent a distribution of unknown function. At the internal nodes, an unknown variable is assigned which uniquely de ne a distribution of the relative crack face displacement. In the present approach, a crack problem is formulated as a singular integral equation whose unknown is a value of the weight function at the internal nodal points. A crack growth can be simulated directly by changing the shape of crack front, by means of adding a new nodal point in the vicinity of the current crack front. In the present paper, the proposed method is used to simulate a coalescence of interacting planar cracks.

Abstract: Residual stresses due to excessive internal pressure applied to an array of semi-circular surface notches is analyzed by body force method. The treated problem corresponds to a simple model of the Stealth Dicing (SD) which is expected as an alternative splitting technology applicable to brittle materials. In SD, laser beam of specific wave length is focused and scanned inside of the material to produce a SD-process zone which includes an array of microvoids. Each microvoid is thought to be received an excessive internal pressure due to thermal expansion and then material is split along a plane which contains an array of microvoids. After the mechanical splitting process, there expected to present a considerable residual stresses in the vicinity of an array of microvoids exposed at the splitting surface. In the present study, by analyzing the elastic-plastic stress fields near the array of surface microvoids, the mechanical characteristics of the SD induces surface is discussed.

Abstract: A new methodology that enables us to compute the arbitrary shaped 3D crack problems is studied. In the present method, it is possible to analyze the 3D crack problems without preparing mesh data as in ordinary boundary elements but with defining a sequence of nodal points representing the crack front and the internal nodal points that define a crack surface as well as a shape function used for determining unknown variables. The present method has special potential for analyzing a complicated 3D crack geometry which is generally difficult to treat in usual element based methods. In the present research, we apply mesh-free body force method to analyze the growth of 3D planar cracks. In concrete, a crack growth analysis for initially rectangular or elliptical crack existing in an infinite solid under uniform tensile stress perpendicular to the crack surface at infinity is demonstrated

Abstract: In this paper, the interference between arbitrary shaped 3D planar crack and cavity existing in the vicinity of the crack front is evaluated. It is assumed that the treated region is unbounded and subjected to uniaxial tension at infinity. The interaction between crack and cavity is treated by body force method. The surface of the crack and cavity is modeled by number of small triangular elements and the density of body force and weight function of the force doublet is assumed at a constant on each triangle. Numerical stress analyses are examined by changing the radius of cavity and the distance between the cavity and crack front systematically. Numerical results are presented for the stresses along the centerline between cavity and crack. To validate the current analysis, numerical results are compared with the results in the literature and found good agreement.

Abstract: Practically exact solutions of stress intensity factor for several two-dimensional standard specimens were calculated and shown in numeric tables. The solutions were confirmed to converge until 6 significant figures through a systematical computation of discretization analysis. The convergence analyses were carried out by using a general purpose program based on a body force method.

Abstract: The occurrence of small scale plasticity can be modeled physically by force doublets embedded in an elastic medium and therefore the plasticity problem can be treated by the superposition of elastic solutions. This idea for the treatment of an inelastic strain is reviewed and generalized to develop a versatile program for two-dimensional elastic-plastic problems based on Body Force Method. In the present study, a treatment of an elastic-perfect plastic body is discussed in detail. The increment of the density of force doublets, which has one to one correspondence to the increment of plastic strain, can be determined from Prandtl-Reuss equation. It was also found the Delaunay triangulation is useful and convenient for the automated elastic-plastic analysis.