Mixed Mode

ELSEVIER Finite Elements in Analysis and Design 27 (1997) 1940 FINITE ELEMENTS IN ANALYSIS AND DESIGN Some aspects of the nonlinear finite element method MA Crisfield*, G. Jelenic, Y. Mi, HG Zhong, Z. Fan Department of Aeronautics, Imperial College of Science, ...

A detailed analytical and experimental investigation is presented to understand the dynamic fracture behavior of functionally graded materials (FGMs) under mode I and mixed mode loading conditions. Crack-tip stress, strain and displacement fields for a mixed mode crack propagating at an angle from the direction of property gradation were obtained through an asymptotic analysis coupled with a displacement potential approach. This was followed by a comprehensive series of experiments to gain further insight into the behavior of propagating cracks in FGMs. Dynamic photoelasticity coupled with high-speed photography was used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the FGMs. Dynamic fracture experiments were performed using different specimen geometries to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor (K ID ) and crack-tip velocity ( ${\mathop a\limits^ \cdot }$ ) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar ${\mathop a\limits^ \cdot }$ -K ID relation was also obtained for matrix material (polyester) for comparison purposes. The results obtained show that crack propagation velocities in FGMs were about 80% higher than the polyester matrix. Crack arrest toughness was found to be about 10% lower than the value of local fracture toughness in FGMs.

The desire to establish a three-dimensional framework for use in analyzing problems of stable mixed-mode crack propagation has received lately a considerable attention. The study of predicting crack paths under the most general possible hypotheses (three dimensions, arbitrary geometry of the body and of the crack, arbitrary loading) is an ambitious objective. Recently, Leblond [1] and Leblond et al. [2] established formulae which specify the general functional form of the successive terms of the expansions of the SIFs along the front of the extended crack and, as they underline, the formulation of the propagation criterion is an open problem only in the presence of mode III. Therefore, in a mode I+II situation, the widely accepted “principle of local symmetry” of Goldstein and Salganik [3] receives a general recognition. In numerical experiments the FRANC3D code uses new concepts with a model that allows for the implementation of 3D crack growth mechanics [4] with the support of both finite and boundary elements. Keeping in mind such beneficial developments, one should emphasize that for a specific geometry and loading we may obtain various experimental crack paths which are dependent on the local position of the initial crack, as any deviation from “symmetry” influences the future crack trajector

The phenomenon of mixed-mode is one of the most important characteristics of switched delay systems. If a networked control system (NCS) with network induced delays and packet dropouts (NIDs & PDs) is recast as a switched delay system, it is imperative to consider the effects of mixed-modes in the stability analysis for an NCS. In this paper, with the help of the interpolatory quadrature formula and the average dwell time method, stabilization of NCSs using a mixed-mode based switched delay system method is investigated based on a novel constructed Lyapunov-Krasovskii functional. With the Finsler's lemma, new exponential stabilizability conditions with less conservativeness are given for the NCS. Finally, an illustrative example is provided to verify the effectiveness of the developed results.

Drying for agricultural and marine products are one of the most attractive and cost-effective application of solar energy. Numerous types of solar dryers have been designed and developed in various parts of the world, yielding varying degrees of technical performance. Basically, there are four types of solar dryers; (1) direct solar dryers, (2) indirect solar dryers, (3) mixed-mode dryers and (4) hybrid solar dryers. This paper is a review of these types of solar dryers with aspect to the product being dried, technical and economical aspects. The technical directions in the development of solar-assisted drying systems for agricultural produce are compact collector design, high efficiency, integrated storage, and long-life drying system. Air-based solar collectors are not the only available systems. Water-based collectors can also be used whereby water to air heat exchanger can be used. The hot air for drying of agricultural produce can be forced to flow in the water to air heat exchanger. The hot water tank acts as heat storage of the solar drying system.

Transmission line port de-embedding is critical in characterization and modeling for high-speed digital systems. De-embedding technique for single-ended transmission lines has been developed and widely used. However, few de-embedding techniques for coupled transmission lines have been reported in the literature. In this paper, a de-embedding technique for coupled transmission lines using a single-ended TRL (Thru-Reflect-Line) calibration pattern is proposed. It

Recent high-resolution GPS and seismological data reveal that tectonic faults exhibit complex, multi-mode slip behavior including earthquakes, creep events, slow and silent earthquakes, low-frequency events and earthquake afterslip. The physical processes responsible for this range of behavior and the mechanisms that dictate fault slip rate or rupture propagation velocity are poorly understood. One avenue for improving knowledge of these mechanisms involves coupling direct observations of ancient faults exhumed at the Earth's surface with laboratory experiments on the frictional properties of the fault rocks. Here, we show that fault zone structure has an important influence on mixed-mode fault slip behavior. Our field studies depict a complex fault zone structure where foliated horizons surround meter- to decameter-sized lenses of competent material. The foliated rocks are composed of weak mineral phases, possess low frictional strength, and exhibit inherently stable, velocity-strengthening frictional behavior. In contrast, the competent lenses are made of strong minerals, possess high frictional strength, and exhibit potentially unstable, velocity-weakening frictional behavior. Tectonic loading of this heterogeneous fault zone may initially result in fault creep along the weak and frictionally stable foliated horizons. With continued deformation, fault creep will concentrate stress within and around the strong and potentially unstable competent lenses, which may lead to earthquake nucleation. Our studies provide field and mechanical constraints for complex, mixed-mode fault slip behavior ranging from repeating earthquakes to transient slip, episodic slow-slip and creep events.► Heterogeneous fault zone with phyllosilicate-rich horizons and competent lenses. ► The competent lenses deform by cataclasis and slip localization. ► The phyllosilicate-rich horizons are weak and velocity strengthening. ► The lenses are strong and velocity weakening with increasing sliding velocity. ► Fault heterogeneities favor a mixed-mode fault-slip behaviour.

In this paper, three methods for the measuring common-mode and differential-mode S-parameters of common mode chokes are presented. The three methods involved: (1) ABCD chain matrix; (2) using hybrid couplers; and (3) modal decomposition. Each measurement method provides a specific level of accuracy. The modal decomposition method can work up to 10 GHz. Given a full characterization of a common