The relationship between stress rates and tangent stiffness values with special orthogonal group SO (3) for finite-element formulation was shown in Part1, and stiffness elements of finite beam element using SO (3) were shown in Part2. Those stress rates are the Truesdell stress rate, the Jaumann stress rate, the Neo-Green stress rate and the Ishihara stress rate, a nonsymmetric stress rate that will be defined by this author in this report. In this study, the constitutive equation of the Ishihara stress rate will be considered. It will be shown that although the stress rate and the strain rate are nonsymmetric, the material stiffness matrix is symmetric. Next, it is shown that although the geometric stiffness of a rigid rotation is nonsymmetric, even if only the symmetric part of the stiffness is used, the second-order convergent rate determined by the Newton-Raphson method is conserved. Finally, it will be shown that the tangent stiffness formulated with SO (3) is different from that of the conventional formulation with linear rotation.
A string of series-connected Hill-type bars is proposed for modeling the effect of muscle tension on human body kinematics in a car collision. The preliminary results indicated that such strings exhibit oscillations and instabilities when subjected to a large and transient stretch. A new algorithm for calculation of the force-velocity of the deformation relationship and the concept of the Hill-type multi-bar muscle element are introduced as countermeasures against these instabilities. In the Hill-type multi-bar muscle element, muscle force is computed from the sum of the deformations and the velocities of deformation of all the series-connected bars applied to model a given muscle. When the Hill-type multi-bar muscle element was applied to model experiments on fast stretching of an activated muscle, the calculated force well corresponded with the results published in the literature. Moreover, the current approach to muscle modeling yielded results consistent with the literature data on volunteers subjected to transient acceleration when it was utilized in simulations of the effect of muscle tension on the head-neck kinematics in a frontal car collision.
In this paper, the Finite Element Method(FEM)is proposed for application to a real-time parallel control system of connected piezoelectric actuators, assuming an actuator as finite elements, wich are mainly used in the field of computational mechanics. The conventional control system requires change of state equations depending on the shape of a system or the quanTITY of the linked members. On the other hand, the FEM is capable of expressing the behaviors of each discrete element, as well as the whole continuous system, by evaluating the stiffness equations. It also can cope flexibly with lack or disability of constituent members of the system by controlling stiffness matrices. An inverse theory to calculate the required electric potential for obtaining target displacements is applied to the control algorithm of connected actuators. A noncompatible finite element, which allows the in-plane bending mode by using a fewer number of elements, is used in the FEM control program to enable real-time control. As a result, the possibility of controlling piezoelectric actuators by the newly proposed methodology has been confirmed.
In this study, molecular dynamics (MD) is used to simulate adhesive wear, where the simulation model is simplified as a single α-Fe (bcc material) under shear deformation. The adhesive plane is assumed to be the (001) plane and the slip(shear)direction, the  direction. First, MD analysis is carried out with/without periodic boundary conditions in the  and  directions to clarify the influence of periodic boundary condition. Next, the shear deformation speed is varied and its influence on the behavior of adhesive wear is examined. The results are summarized as follows: (a) The periodic boundary condition significantly affects the deformation of adhesive wear. That is, the existence of free boundary plays a very important role in wear. (b) The deformation speed does not affect the type of structural destruction of adhesive wear, and only the time from the start of shear deformation to the beginning of adhesive wear becomes short as the deformation speed becomes high.
The fundamental solutions were obtained for a fluid-saturated, elastically isotropic, porous, infinite solid with transversely isotropic permeability under an instantaneous fluid point source and instantaneous point forces acting in mutually orthogonal directions, by superposing the dislocation line segments. These solutions include those for both porous solids of zero permeability in one direction and isotropic permeability as limiting cases. These solutions are intended to be used to derive the integral equations for a plane crack of arbitrary shape;these equations in turn will be implemented in a hydraulic fracturing simulator for the gas/oil production.
A general model with arbitrary bonding angles for the edge of a fiber/matrix interface is developed. Many practical problems in composite materials can be included in this model. Based on the elastic basic equations for the spatial axisymmetric problem, the stress singularity at the interface edge is investigated. The singular stress field is also deduced theoretically in detail. It is found that the eigenequation determining the stress singular order coincides with that of the corresponding plane strain problem, while the singular stress distribution does not. Moreover, three composite parameters are required to describe the effect of material combinations on the stress field in the present axisymmetric interface problem, but only two are needed in a two-dimensional plane problem.
An injection-molded short fiber composite often contains some fiber clusters due to a poor mixing. An analytical model for a composite with such clusters was developed to estimate a composite stiffness and stresses inside and just outside a fiber of the composite. In this paper, first the stiffness of the cluster is predicted by applying the Eshelby's equivalent inclusion method. Secondly the stiffness of the overall composite and the stress inside a fiber are assessed by applying the Eshelby's method to two kinds of inhomogeneities, i. e. cluster and fiber. Finally the stress just outside the fiber, namely the fiber-end stress, is evaluated using the Hill-Walpole-Mura's jump condition. It is concluded from this parametric study that the effective stiffness of a short fiber composite tends to decrease as the volume fraction of clusters increases, and cracks at fiber ends are more likely to occur at a lower applied stress level as the volume fraction of clusters increases since the magnitude of the fiber-end stress increases. It is found that a carbon fiber composite with higher stiff reinforcement is more sensitive to the negative effects of fiber clustering than a composite with less stiff reinforcement.
In order to describe the relationship of mesoscopic phenomena of interfacial debonding and breakage of fiber and matrix to the macroscopic stress-strain curve of unidirectional composites, an approximate nondimensional solution method was presented using a two-dimensional model. By applying this method to several examples in which the species and locations of broken components were varied, the following features were revealed: (a) fiber-breakage-induced debonding occurs at a lower strain than the matrix-breakage-induced one; (b) the overall debonding is hastened due to mechanical intractions under the existence of many broken fibers and matrices; (c) the progress of overall debonding is dependent on the species of the broken components and on the geometrical location of broken components and debonded interfaces;and (d) the stress-strain curve shows drops in stress due to the progress of debonding. As an extended application of the present method, a nondimensional Monte Carlo simulation method was presented to describe the behavior of the composite in which the number and location of broken components and debonded interface vary with increasing strain.
The response and stability of titanium alloy tubes subjected to cyclic bending are presented in this paper. The curvature-ovalization measurement apparatus, designed by Pan et al., is used for conducting the present curvature-controlled experiments. It is observed from the moment-curvature curve that the titanium alloy tube is cyclically harden and becomes steady after a few cycles for symmetric curvature-controlled bending. However, from the ovalization-curvature curve, the ovalization of the tube cross-section increases in a ratchetting manner with the number of cycles. Owing to the progressive accumulation of the ovalization of the tube cross-section during the cyclic bending, the titanium alloy tubes buckle eventually. Theoretical formulation, proposed by Kyriakides and Shaw, is used for investigating the relationship between the magnitude of the controlled curvature range and the number of cycles to produce buckling. Good agreement between the experimental and theoretical results is achieved. Furthermore, experimental data of the titanium alloy tubes from present study are compared with the experimental results of 6061-T6 aluminum and 1018 steel tubes tested by Kyriakides and Shaw. It is shown that for similar outer diameter/wall thickness ratio, the stronger metal tube exhibits a shorter number of cycles to produce buckling.
In this paper, we describe the quasi-static lateral compression tests of high-strength, high-elastic-modulus fibers. The fibers examined were γ-alumina fiber (Altex) by Sumitomo Chemical Co., Ltd., two types of carbon fibers by Mitsubishi Rayon Co., Ltd., and four types of aramid fibers by Du Pont and Teijin Ltd. Special attention was paid to environmental influences such as water absorption and electron or ultraviolet radiation on the lateral compression behavior of aramid fibers. A specially designed testing machine (load range:0.1mN-5N, accuracy:0.02mN) that enables mechanical testing, including fatigue of microelements, was employed. Using the testing machine, lateral compression of fibers whose diameter ranged from 7 to 17 μm was achieved with sufficient precision. The transverse compression behavior of carbon fibers and alumina fiber exhibited brittle nature:most of the load-displacement curve followed the elastic deformation, with a final catastrophic fracture into small pieces. However, that of the aramid fibers showed a more ductile nature:the very early stage of the load-displacement curve was elastic, and the rest was plastic. The final catastrophic fracture observed in ceramic and carbon fibers did not occur with a large amount of plastic deformation. The influence of electron radiation on the transverse elastic modulus of aramid fibers was not observed. However, water absorption or ultraviolet radiation lowered the transverse elastic modulus. The fiber surface was closely examined using an atomic force microscope, and the influence of environment on surface degradation and deformation behavior is discussed.
The present paper a new damage monitoring system that employs luminance of EL backlight for semi-transparent composites. For the semi-transparent composites, damage is easily found by visual inspections. In the cases that the structures are sealed or huge structures, however, the visual inspections are difficult. The present paper adopts a system using change of luminance of transmitted light. When the composite structures are damaged, the damage reduces luminance of the transmitted light from the backside. The present study adopts an Electro Luminescent device (EL) as the backlight. The EL device can emit uniform-plane-light and is a very flexible device. The EL device can be mounted on a curved surface. Fatigue tests are conducted using rectangular specimens with an open hole fabricated from fabric glass/epoxy composites. The monitoring system is applied to the fatigue tests, and it is experimentally shown that the method can detect the fatigue damage without loading.
This paper deals with the criterion and mechanical characteristics of the initial critical softening point of porous materials under different loading triaxiality. First, the concept of the initial critical softening point (hereafter abbreviated by ICSP) is defined. The close relations between the ICSP and other important phenomena, such as the failure initiation, void coalescence, localization, instability and ductile fracture in a porous material element are carefully annotated. Second, a criterion for predicting the ICSP is suggested and examined on the basis of a new rigid plastic constitutive model published previously. Third, the mechanical characteristics at or around the ICSP are systematically analyzed by numerical calculations. This research reveals the potentiality of applying the ICSP and corresponding criterion to control the fracture initiation and strength distribution in porous materials and prevent the materials from ductile fracture during plastic forming.
The bending properties of composites made of aramid short fiber and unsaturated polyester resin are investigated. The strength of the composite increases with the length and content of the fiber. The fibers are considered to be oriented randomly in the composite. In order to analyse the strength of the composite, we consider a simple model of the composite, that is, the classical single-fiber pull-out test. We modify the conventional equation by considering the results of the pull-out test in the calculation of the strength of the short-fiber composite. The experimental results show good agreement with the results provided by the theoretical model.