Hiroshi Okada

Non-hyper-singular integral-representations for velocity (displacement) gradients in elastic/plastic solids (small or finite deformations)

New integral representations for deformation (velocity) gradients in elastic or elasto-plastic solids undergoing small or large deformations are presented. Compared to the cases wherein direct differentiation of the integral representations for displacements (or velocities) were carried out to obtain displacement (or velocity) gradients (which gave rise to hyper-singularity when the source point was taken to the boundary), the present integral representations have lower order singularities which are quite tractable from a numerical point of view. Moreover, the present representations, allow the source point to be taken in the limit, to the boundary, without any difficulties. This obviates a need for a two tier system of evaluation of deformation gradients in the interior of the domain on one hand and at the boundary of the domain on the other. It is expected that the present formulations would yield more accurate and stable deformation gradients in problems dominated by geometric and material nonlinearities.

An elastic-plastic finite element alternating method for analyzing wide-spread fatigue damage in aircraft structures

In this paper, a new analytical technique to study the effect of wide-spread fatigue damage in ductile panels is presented. The main purpose of the study is to develop an efficient methodology to predict the maximum load carrying capacity of panels with cracks. The problem arises especially in the fuselage skin of aging airplanes, in which cracks initiate from a row of rivet holes. This problem is known as Multi Site Damage (MSD) in aging aircraft. It is very important to estimate the load carrying capacity. Usually, the approach based on elastic fracture mechanics may overestimate the load capacity. It is very important for the aircraft structure with MSD to estimate the load carrying capacity of such damaged structures. Approaches based on elastic fracture mechanics often lead to a considerable error. In this paper, the Elastic Finite Element Alternating Method (EFEAM) has been extended to the case of elastic-plastic fracture of panels with MSD cracks. In EFEAM, analytical solutions to crack problems in an infinite plate are employed. In this study, we adopted an analytical solution for a row of cracks in an infinite panel. Furthermore, the plastic deformation is accounted for, by using the initial stress algorithm. The Tinfεsup*integral is employed for the fracture criterion. The methodology developed in the present study can be called as Elastic-Plastic Finite Element Alternating Method (EPFEAM) for MSD problems. A series of studies on the maximum load capacity of panels with a row of cracks has been conducted.

Homogenization method for heterogeneous material based on boundary element method

Abstract In this paper, formulations for homogenization method based on the boundary element method, for heterogeneous elastic materials having periodic microstructure, are presented. The formulations are developed using a novel use of the method of weighted residuals. Both the trial and test functions are expressed by asymptotic expansions with respect to the size e of the unit cell. Two types of boundary element formulations for the analysis of unit cell, are proposed; single-region boundary element method with volume integrals and multi-region boundary element method. Convenient formulae to compute effective (homogenized) elastic constants, are presented.

Nonlinear transient dynamic analysis of soil-pavement interaction under moving load: a coupled BEM-FEM approach

Abstract The nonlinear transient dynamic analysis of a 3-D linear elastic pavement placed on an elastoplastic soil medium, subject to a moving load, is presented. The time domain nonlinear boundary element method for the soil medium is combined with the finite element method for the pavement. The nonlinear BEM is based on an initial stress approach. The accuracy of the algorithm is verified by comparison with available analytical solutions and published numerical results.

Some recent developments in finite-strain elastoplasticity using the field-boundary element method

A new boundary integral equation is derived directly for velocity gradients in a finite strain elasto-plastic solid. These integral equations for velocity gradients do not involve hyper-singularities (when the source point is taken to the boundary) of the type found in the alternate case when the integral equations for velocities are differentiated to derive an integral relation for velocity gradients. Hence the new formulation obviates the need for a two tier system of computing the velocity gradients, which existed in the alternate case. A generalized mid-point radial return algorithm is presented for determining the objective increments of stress from the computed velocity gradients. Moreover, a mid-point evaluation of the generalized Jaumann integral is used to determine the material increments of stress. The constitutive equation employed is based on an endochronic model of combined isotropic/kinematic hardening finite plasticity using the concepts of a material director triad and the associated plastic spin.

On shear band formation. II: Simulation using finite element method

Abstract A dual yield constitutive model involving both the J 2 -flow and a threshold-shear-stress based flow, described in the accompanying article, is incorporated in a finite element program, and a simulation of shear band localization occurring in a uniaxially loaded plane strain specimen is carried out. The FEM takes into account the finite strains and the rotations involved in the formation of the shear band. These numerical experiments not only validate the postulated constitutive equation, but also aid in investigating the effect of the material hardening exponent, the aspect ratio of the specimen, and the mesh morphology on the formation of the shear band.

Analysis of toughening of magnesia partially stabilized zirconia, due to dilatational transformation

Abstract An analysis of toughening of magnesia partially stabilized zirconia (Mg-PSZ) due to dilatational transformation is presented in this paper. Transformation toughening of Mg-PSZ is attributed to the stress-induced phase transformation of tetragonal zirconia to monoclinic structure in the neighborhood of a macro-crack tip. A trate (incremental) type constitutive model is developed, using a micromechanics approach, wherein the interaction between a transformed zirconia particle and the rest of the material is considered. Problems of stationary and stably propagating cracks are analyzed, using a finite element method. The results of finite element analysis are compared to those of an experimental study by Perry et al. In the comparisoon, of it is found that the displacement and toughness enhancement during stable crack propagation, predicted by the finite element analysis, are very analogous to those obtained in the experimental study. Moreover, the present constitutive model is capable of revealing detailed information, such as the distribution of transformed zirconia in the wake zone.

Direct evaluation of Tε∗ integral from experimentally measured near tip displacement field, for a plate with stably propagating crack

In this paper, a method for quantitatively evaluating the T integral, directly from the measured near-tip displacement field in laboratory specimens made of metallic materials, is presented for the first time. Following Okada and Atluri (Okada, H., Atluri, S.N., 1999. Further studies on the characteristics of the T integral: plane stress stable crack propagation in ductile materials. Computational Mechanics), it is shown that T quantifies the deformation energy dissipated near the crack tip region (an elongating strip of height) per unit crack extension. To directly evaluate the T integral from the measured displacement field near an advancing crack tip, the use of the deformation theory of plasticity (J2-D theory), and the truncation of the near crack T integral path just behind the advancing crack tip, are suggested. This suggestion is validated through some careful numerical computations. The results basedontheexperimental studiesofOmoriet al.(Omori, Y., Okada, H.,Atluri, S.N.,Kobayashi, A.S. T integral analysis for SEN specimen using Moire interferometry. ATEM’95 (International Symposium on Advanced Tecnology in Experimental Mechanics JSME [Japan Society of Mechanical Engineering]), submitted for publication) show good agreement with the results of finite element analysis. The latter T values were computed with a full-finite element analysis based on a J-flow theory, using a full elongating path, as well as with the use of ‘‘cut-oA’’ integral path, and the use of J-D plasticity. # 1999 Elsevier Science Ltd. All rights reserved.

Numerical analysis on near net shape forming of Al-Al3Ni functionally graded material

Abstract The results of numerical studies on the near-net shape forming of Al–Al3Ni functionally graded material (FGM) are presented and are compared with the experiments. FGM billets at an elevated temperature of semi-solid condition are set in a container and are subject to backward extruding, and FGM cups are obtained. Due to the composition gradient of FGM the effective viscosity of semi-melt FGM billet varies spatially. The flow/deformation of semi-melt FGM billet is strongly influenced by the spatial variation of effective viscosity. Some characteristic behaviors of flow/deformation of FGM during the semi-solid process are presented and discussed.

Residual strength prediction for aircraft panels with Multiple Site Damage, using the "EPFEAM" for stable crack growth analysis

In this paper, a new analytical method for solving stable crack propagation problems in a ductile panel with a row of cracks, is presented. The main purpose of the present study is to estimate the maximum load carrying capacity of such panels accurately. The so called Elastic Plastic Finite Element Alternating Method (Pyo et al. (1994) was extended to account for the propagating cracks. The crack propagation algorithm utilizes the analytic crack solution to release the stresses ahead the crack tip. The Tinfεsup*integral is employed as the crack extension criterion. This integral parameter accounts for the near tip stress-strain singularity and its critical values for crack propagation can be extracted from the P-Δa curve of single cracked specimen case. The present method can be applied to the problems of the fuselage skin of aging airplanes, in which a row of cracks develop (MSD; Multiple Site Damage) from rivet holes. The load carrying capacity of such damaged structure reduces by a considerable amount. In order to predict the behavior near the critical load, one must account for plastic deformation, if the material is ductile. Furthermore, the maximum load carried by the structure is often reached after some amount of crack propagation. In this paper, a series of analyses have been conducted and their results compare with the available experimental data.