A posteriori error estimates of discontinuous Galerkin methods for the Signorini problem

A reliable and efficient a posteriori error estimator is derived for a class of discontinuous Galerkin (DG) methods for the Signorini problem. A common property shared by many DG methods leads to a unified error analysis with the help of a constraint preserving enriching map. The error estimator of DG methods is comparable with the error estimator of the conforming methods. Numerical experiments illustrate the performance of the error estimator. (C) 2015 Elsevier B.V. All rights reserved.

General framework for acoustic emission during plastic deformation

Despite the long history, so far there is no general theoretical framework for calculating the acoustic emission spectrum accompanying any plastic deformation. We set up a discrete wave equation with plastic strain rate as a source term and include the Rayleigh-dissipation function to represent dissipation accompanying acoustic emission. We devise a method of bridging the widely separated time scales of plastic deformation and elastic degrees of freedom. While this equation is applicable to any type of plastic deformation, it should be supplemented by evolution equations for the dislocation microstructure for calculating the plastic strain rate. The efficacy of the framework is illustrated by considering three distinct cases of plastic deformation. The first one is the acoustic emission during a typical continuous yield exhibiting a smooth stress-strain curve. We first construct an appropriate set of evolution equations for two types of dislocation densities and then show that the shape of the model stress-strain curve and accompanying acoustic emission spectrum match very well with experimental results. The second and the third are the more complex cases of the Portevin-Le Chatelier bands and the Luders band. These two cases are dealt with in the context of the Ananthakrishna model since the model predicts the three types of the Portevin-Le Chatelier bands and also Luders-like bands. Our results show that for the type-C bands where the serration amplitude is large, the acoustic emission spectrum consists of well-separated bursts of acoustic emission. At higher strain rates of hopping type-B bands, the burst-type acoustic emission spectrum tends to overlap, forming a nearly continuous background with some sharp acoustic emission bursts. The latter can be identified with the nucleation of new bands. The acoustic emission spectrum associated with the continuously propagating type-A band is continuous. These predictions are consistent with experimental results. More importantly, our study shows that the low-amplitude continuous acoustic emission spectrum seen in both the type-B and type-A band regimes is directly correlated to small-amplitude serrations induced by propagating bands. The acoustic emission spectrum of the Luders-like band matches with recent experiments as well. In all of these cases, acoustic emission signals are burstlike, reflecting the intermittent character of dislocation-mediated plastic flow.

Stability analysis of thick piezoelectric metal based FGM plate using first order and higher order shear deformation theory

This paper presents the stability analysis of functionally graded plate integrated with piezoelectric actuator and sensor at the top and bottom face, subjected to electrical and mechanical loading. The finite element formulation is based on first order and higher order shear deformation theory, degenerated shell element, von-Karman hypothesis and piezoelectric effect. The equation for static analysis is derived by using the minimum energy principle and solutions for critical buckling load is obtained by solving eigenvalue problem. The material properties of the functionally graded plate are assumed to be graded along the thickness direction according to simple power law function. Two types of boundary conditions are used, such as SSSS (simply supported) and CSCS (simply supported along two opposite side perpendicular to the direction of compression and clamped along the other two sides). Sensor voltage is calculated using present analysis for various power law indices and FG (functionally graded) material gradations. The stability analysis of piezoelectric FG plate is carried out to present the effects of power law index, material variations, applied mechanical pressure and piezo effect on buckling and stability characteristics of FG plate.

A FRAMEWORK FOR THE ERROR ANALYSIS OF DISCONTINUOUS FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS AND APPLICATIONS TO C-0 IP METHODS

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posteriori error estimator. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. Subsequently, the applications of C-0 interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings.

Effect of Nb orientation and deformation on the growth of Nb3Sn intermetallic superconductor by bronze technique

The growth of Nb3Sn by bronze technique on single crystals and deformed Nb is studied. The grain boundary diffusion-controlled growth rate is found to be higher for Nb-(0 1 3) than Nb-(0 1 1) because of smaller grain size of Nb3Sn. The difference in grain size is explained with the help of surface energies leading to different nucleation barrier. Significantly finer grains and higher growth rate of the product phase is found for rolled Nb because of available defects acting as potential nucleation sites.

Quantitative In Situ Analysis of Deformation in Sliding Metals: Effect of Initial Strain State

Using in situ, high-speed imaging of a hard wedge sliding against pure aluminum, and image analysis by particle image velocimetry, the deformation field in sliding is mapped at high resolution. This model system is representative of asperity contacts on engineered surfaces and die-workpiece contacts in deformation and machining processes. It is shown that large, uniform plastic strains of 1-5 can be imposed at the Al surface, up to depths of 500 mu m, under suitable sliding conditions. The spatial strain and strain rate distributions are significantly influenced by the initial deformation state of the Al, e.g., extent of work hardening, and sliding incidence angle. Uniform straining occurs only under conditions of steady laminar flow in the metal. Large pre-strains and higher sliding angles promote breakdown in laminar flow due to surface fold formation or flow localization in the form of shear bands, thus imposing limits on uniform straining by sliding. Avoidance of unsteady sliding conditions, and selection of parameters like sliding angle, thus provides a way to control the deformation field. Key characteristics of the sliding deformation such as strain and strain rate, laminar flow, folding and prow formation are well predicted by finite element simulation. The deformation field provides a quantitative basis for interpreting wear particle formation. Implications for engineering functionally graded surfaces, sliding wear and ductile failure in metals are discussed.

High temperature deformation behavior of Nb-1 wt.%Zr alloy

The hot deformation behavior of Nb-1 wt.%Zr alloy was studied using uniaxial compression tests carried out in vacuum to a true strain of 0.6 in the temperature range of 900 to 1700 degrees C and the strain rate range of 3 x 10(-3) to 10 s(-1). The optimum regime of hot workability of Nb-1Zr alloy was determined from the strain rate sensitivity (m) contour plots. A high m of about 02 was obtained in the temperature and strain rate range of 1200-1500 degrees C and 10(-3) to 10(-1) s(-1) and 1600-1700 degrees C and 10(-1) to 1 s(-1). Microstructure of the deformed samples showed features of dynamic recrystallization within the high strain rate sensitivity domain. Compared to the study on Nb-1Zr-0.1C alloy, Nb-1Zr showed a lower flow stress and an optimum hot working domain at lower temperatures. In the 1500 to 1700 degrees C range the apparent activation energy of deformation for Nb-1Zr was 259 kJ mol(-1), the stress exponent 5, and the activation volume about 200 to 700 b(3). (C) 2015 Elsevier Ltd. All rights reserved.

Deformation pathways and breakup modes in acoustically levitated bicomponent droplets under external heating

Controlled breakup of droplets using heat or acoustics is pivotal in applications such as pharmaceutics, nanoparticle production, and combustion. In the current work we have identified distinct thermal acoustics-induced deformation regimes (ligaments and bubbles) and breakup dynamics in externally heated acoustically levitated bicomponent (benzene-dodecane) droplets with a wide variation in volatility of the two components (benzene is significantly more volatile than dodecane). We showcase the physical mechanism and universal behavior of droplet surface caving in leading to the inception and growth of ligaments. The caving of the top surface is governed by a balance between the acoustic pressure field and the restrictive surface tension of the droplet. The universal collapse of caving profiles for different benzene concentration (<70% by volume) is shown by using an appropriate time scale obtained from force balance. Continuous caving leads to the formation of a liquid membrane-type structure which undergoes radial extension due to inertia gained during the precursor phase. The membrane subsequently closes at the rim and the kinetic energy leads to ligament formation and growth. Subsequent ligament breakup is primarily Rayleigh-Plateau type. The breakup mode shifts to diffusional entrapment-induced boiling with an increase in concentration of the volatile component (benzene >70% by volume). The findings are portable to any similar bicomponent systems with differential volatility.

Deformation, Phase Transformation and Recrystallization in the Shear Bands Induced by High-Strain Rate Loading in Titanium and its Alloys

alpha-titanium and its alloys with a dual-phase structure (alpha+beta) were deformed dynamically under strain rate of about 10(4) s(-1). The formation and microstructural evolution of the localized shear bands were characterized by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The results reveal that both the strain and strain rate should be considered simultaneously as the mechanical conditions for shear band formation, and twinning is an important mode of deformation. Both experimental and calculation show that the materials within the bands underwent a superhigh strain rate (9 x 10(5) s(-1)) deformation, which is two magnitudes of that of average strain rate required for shear band formation; the dislocations in the bands can be constricted and developed into cell structures; the phase transformation from alpha to alpha(2) within the bands was observed, and the transformation products (alpha(2)) had a certain crystallographic orientation relationship with their parent; the equiaxed grains with an average size of 10 mu m in diameter observed within the bands are proposed to be the results of recrystallization.

Evaluation of the Effectiveness of Representative Methods for Determining Young's Modulus and Hardness from Instrumented Indentation Data

The effectiveness of Oliver & Pharr's (O&P's) method, Cheng & Cheng's (C&C's) method, and a new method developed by our group for estimating Young's modulus and hardness based on instrumented indentation was evaluated for the case of yield stress to reduced Young's modulus ratio (sigma(y)/E-r) >= 4.55 x 10(-4) and hardening coefficient (n) <= 0.45. Dimensional theorem and finite element simulations were applied to produce reference results for this purpose. Both O&P's and C&C's methods overestimated the Young's modulus under some conditions, whereas the error can be controlled within +/- 16% if the formulation was modified with appropriate correction functions. Similar modification was not introduced to our method for determining Young's modulus, while the maximum error of results was around +/- 13%. The errors of hardness values obtained from all the three methods could be even larger and were irreducible with any correction scheme. It is therefore suggested that when hardness values of different materials are concerned, relative comparison of the data obtained from a single standard measurement technique would be more practically useful. It is noted that the ranges of error derived from the analysis could be different if different ranges of material parameters sigma(y)/E-r and n are considered.

Formation of Fivefold Deformation Twins in Nanocrystalline Face-Centered-Cubic Copper Based on Molecular Dynamics Simulations

Fivefold deformation twins were reported recently to be observed in the experiment of the nanocrystalline face-centered-cubic metals and alloys. However, they were not predicted previously based on the molecular dynamics (MD) simulations and the reason was thought to be a uniaxial tension considered in the simulations. In the present investigation, through introducing pretwins in grain regions, using the MD simulations, the authors predict out the fivefold deformation twins in the grain regions of the nanocrystal grain cell, which undergoes a uniaxial tension. It is shown in their simulation results that series of Shockley partial dislocations emitted from grain boundaries provide sequential twining mechanism, which results in fivefold deformation twins. (c) 2006 American Institute of Physics.

Twinning and Stacking Fault Formation during Tensile Deformation of Nanocrystalline Ni

Deformation twins and stacking faults have been observed in nanocrystal line Ni, for the first time under uniaxial tensile test conditions. These partial dislocation mediated deformation mechanisms are enhanced at cryogenic test temperatures. Our observations highlight the effects of deformation conditions, temperature in particular, on deformation mechanisms in nanograins.

Formation, Thermal Stability and Deformation Behavior of Graphite-Flakes Reinforced Cu-based Bulk Metallic Glass Matrix Composites

Graphite-flake reinforced Cu47Ti34Zr11 Ni-8 bulk metallic glass matrix composite was fabricated by water-cooled copper mould cast. Most of the graphite flakes still keep unreacted and distribute uniformly in the amorphous matrix except that some reactive wetting occurs by the formation of TiC particles around the flakes. It reveals that the presence of graphite flakes does not affect the onset of the glass transition temperature, crystallization reaction and liquidus of the metallic glass. The resulting material shows obvious serrated flow and higher fracture strength under room temperature compressive load, comparing with the monolithic bulk metallic glass (BMG). Three types of interaction between the shear bands and graphite flakes, namely, shear band termination, shear bands branching and new shear bands formation near the graphite flakes can be observed by quasi-static uniaxial compression test and bonded interface technique through Vickers indentation.

A quality-guided displacement tracking algorithm for ultrasonic elasticity imaging.

Displacement estimation is a key step in the evaluation of tissue elasticity by quasistatic strain imaging. An efficient approach may incorporate a tracking strategy whereby each estimate is initially obtained from its neighbours' displacements and then refined through a localized search. This increases the accuracy and reduces the computational expense compared with exhaustive search. However, simple tracking strategies fail when the target displacement map exhibits complex structure. For example, there may be discontinuities and regions of indeterminate displacement caused by decorrelation between the pre- and post-deformation radio frequency (RF) echo signals. This paper introduces a novel displacement tracking algorithm, with a search strategy guided by a data quality indicator. Comparisons with existing methods show that the proposed algorithm is more robust when the displacement distribution is challenging.

Experimental Study of Pore Pressure and Deformation of Suction Bucket Foundations Under Horizontal Dynamic Loading

Centrifuge experiments are carried out to investigate the responses of suction bucket foundations under horizontal dynamic loading. The effects of loading amplitude, the size of the bucket and the structural weight on the dynamic responses are investigated. It is shown that, when the loading amplitude is over a critical value, the sand at the upper part around the bucket softens or even liquefies. The liquefactio...