Active Control of Fan Noise-Feasibility Study. Volume 2: Canceling Noise Source-Design of an Acoustic Plate Radiator Using Piezoceramic Actuators

The feasibility of using acoustic plate radiators powered by piezoceramic thin sheets as canceling sources for active control of aircraft engine fan noise is demonstrated. Analytical and numerical models of actuated beams and plates are developed and validated. An optimization study is performed to identify the optimum combination of design parameters that maximizes the plate volume velocity for a given resonance frequency. Fifteen plates with various plate and actuator sizes, thicknesses, and bonding layers were fabricated and tested using results from the optimization study. A maximum equivalent piston displacement of 0.39 mm was achieved with the optimized plate samples tested with only one actuator powered, corresponding to a plate deflection at the center of over 1 millimeter. This is very close to the deflection required for a full size engine application and represents a 160-fold improvement over previous work. Experimental results further show that performance is limited by the critical stress of the piezoceramic actuator and bonding layer rather than by the maximum moment available from the actuator. Design enhancements are described in detail that will lead to a flight-worthy acoustic plate radiator by minimizing actuator tensile stresses and reducing nonlinear effects. Finally, several adaptive tuning methods designed to increase the bandwidth of acoustic plate radiators are analyzed including passive, active, and semi-active approaches. The back chamber pressurization and volume variation methods are investigated experimentally and shown to be simple and effective ways to obtain substantial control over the resonance frequency of a plate radiator. This study shows that piezoceramic-based plate radiators can be a viable acoustic source for active control of aircraft engine fan noise

Control-oriented modelling of three-way catalytic converter for fuel-to-air ratio regulation in spark ignited engines

[EN] The purpose of this paper is to introduce a grey-box model of three-way catalytic converter, which is capable of estimating the oxygen storage level to aid the fuel-to-air ratio control in spark ignited engines. As it is well-known, the prime parameter that drives the transient dynamics in current three-way catalytic converter is their capability to store a certain amount of oxygen, then allowing to oxidize some pollutant species such as carbon monoxide or hydrocarbons even at rich conditions during short periods of time. Since oxygen storage level is considered a good indicator of the catalyst state but it cannot be directly measured, a model based real-time capable estimation like the one proposed in this paper could be valuable. The model accounts for oxygen storing as well as oxidation and reduction of the main species involved, taking as inputs fuel-to-air equivalence ratio, air mass flow, temperature and gas composition at three-way catalyst inlet. From these inputs, oxygen storage level and brick temperature are calculated as model states, which finally provide the gas composition downstream of the catalyst as output. In addition, a simplified model of narrowband lambda sensor is included, it provides a voltage from gas composition at the outlet of the catalyst and allows to assess the model behaviour by comparison with the on-board lambda sensor measurements. Finally, the validation of the model performance by means of experimental test as well as different practical cases, where the benefits of oxygen storage level estimation plays a key role, are introduced.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors acknowledge the support of Spanish Ministerio de Economía, Industria y Competitividad through project TRA2016-78717-R.Guardiola, C.; Climent, H.; Pla Moreno, B.; Real, M. (2019). Control-oriented modelling of three-way catalytic converter for fuel-to-air ratio regulation in spark ignited engines. Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering. 233(14):3758-3774. https://doi.org/10.1177/0954407019833822S3758377423314Auckenthaler, T. S., Onder, C. H., & Geering, H. P. (2004). Aspects of Dynamic Three-Way Catalyst Behaviour Including Oxygen Storage. IFAC Proceedings Volumes, 37(22), 331-336. doi:10.1016/s1474-6670(17)30365-8Yang, H., Shu, G., Tian, H., Ma, X., Chen, T., & Liu, P. (2018). Optimization of thermoelectric generator (TEG) integrated with three-way catalytic converter (TWC) for harvesting engine’s exhaust waste heat. Applied Thermal Engineering, 144, 628-638. doi:10.1016/j.applthermaleng.2018.07.091Koltsakis, G. C., Konstantinidis, P. A., & Stamatelos, A. M. (1997). Development and application range of mathematical models for 3-way catalytic converters. Applied Catalysis B: Environmental, 12(2-3), 161-191. doi:10.1016/s0926-3373(96)00073-2Zygourakis, K. (1989). Transient operation of monolith catalytic converters: a two-dimensional reactor model and the effects of radially nonuniform flow distributions. Chemical Engineering Science, 44(9), 2075-2086. doi:10.1016/0009-2509(89)85143-7Coxeter, H. S. M. (1993). Cyclotomic integers, nondiscrete tessellations, and quasicrystals. Indagationes Mathematicae, 4(1), 27-38. doi:10.1016/0019-3577(93)90049-5Konstantas, G., & Stamatelos, A. M. (2007). Modelling three-way catalytic converters: An effort to predict the effect of precious metal loading. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 221(3), 355-373. doi:10.1243/09544070jauto329Pontikakis, G. N., Konstantas, G. S., & Stamatelos, A. M. (2004). Three-Way Catalytic Converter Modeling as a Modern Engineering Design Tool. Journal of Engineering for Gas Turbines and Power, 126(4), 906-923. doi:10.1115/1.1787506Kumar, P., Gu, T., Grigoriadis, K., Franchek, M., & Balakotaiah, V. (2014). Spatio-temporal dynamics of oxygen storage and release in a three-way catalytic converter. Chemical Engineering Science, 111, 180-190. doi:10.1016/j.ces.2014.02.014Auckenthaler, T. S., Onder, C. H., Geering, H. P., & Frauhammer, J. (2004). Modeling of a Three-Way Catalytic Converter with Respect to Fast Transients of λ-Sensor Relevant Exhaust Gas Components. Industrial & Engineering Chemistry Research, 43(16), 4780-4788. doi:10.1021/ie034242uNievergeld, A. J. L., Selow, E. R. v., Hoebink, J. H. B. J., & Marin, G. B. (1997). Simulation of a catalytic converter of automotive exhaust gas under dynamic conditions. Dynamics of Surfaces and Reaction Kinetics in Heterogeneous Catalysis, Proceedings of the International Symposium, 449-458. doi:10.1016/s0167-2991(97)80431-4Oh, S. H., & Cavendish, J. C. (1982). Transients of monolithic catalytic converters. Response to step changes in feedstream temperature as related to controlling automobile emissions. Industrial & Engineering Chemistry Product Research and Development, 21(1), 29-37. doi:10.1021/i300005a006Chan, S. H., & Hoang, D. L. (1999). Heat transfer and chemical reactions in exhaust system of a cold-start engine. International Journal of Heat and Mass Transfer, 42(22), 4165-4183. doi:10.1016/s0017-9310(99)00064-2Sabatini, S., Gelmini, S., Hoffman, M. A., & Onori, S. (2017). Design and experimental validation of a physics-based oxygen storage — thermal model for three way catalyst including aging. Control Engineering Practice, 68, 89-101. doi:10.1016/j.conengprac.2017.07.007Schürholz, K., Brückner, D., Gresser, M., & Abel, D. (2018). Modeling of the Three-way Catalytic Converter by Recurrent Neural Networks. IFAC-PapersOnLine, 51(15), 742-747. doi:10.1016/j.ifacol.2018.09.166Brandt, E. P., Yanying Wang, & Grizzle, J. W. (2000). Dynamic modeling of a three-way catalyst for SI engine exhaust emission control. IEEE Transactions on Control Systems Technology, 8(5), 767-776. doi:10.1109/87.865850Shaw, B. T., Fischer, G. D., & Hedrick, J. K. (2002). A SIMPLIFIED COLDSTART CATALYST THERMAL MODEL TO REDUCE HYDROCARBON EMISSIONS. IFAC Proceedings Volumes, 35(1), 307-312. doi:10.3182/20020721-6-es-1901.01519Bickel, J., Odendall, B., Eigenberger, G., & Nieken, U. (2017). Oxygen storage dominated three-way catalyst modeling for fresh catalysts. Chemical Engineering Science, 160, 34-53. doi:10.1016/j.ces.2016.11.016Kiwitz, P., Onder, C., & Guzzella, L. (2012). Control-oriented modeling of a three-way catalytic converter with observation of the relative oxygen level profile. Journal of Process Control, 22(6), 984-994. doi:10.1016/j.jprocont.2012.04.014Kumar, P., Makki, I., Kerns, J., Grigoriadis, K., Franchek, M., & Balakotaiah, V. (2012). A low-dimensional model for describing the oxygen storage capacity and transient behavior of a three-way catalytic converter. Chemical Engineering Science, 73, 373-387. doi:10.1016/j.ces.2011.12.001Gong, J., Wang, D., Li, J., Currier, N., & Yezerets, A. (2017). Dynamic oxygen storage modeling in a three-way catalyst for natural gas engines: A dual-site and shrinking-core diffusion approach. Applied Catalysis B: Environmental, 203, 936-945. doi:10.1016/j.apcatb.2016.11.005Ramanathan, K., & Sharma, C. S. (2011). Kinetic Parameters Estimation for Three Way Catalyst Modeling. Industrial & Engineering Chemistry Research, 50(17), 9960-9979. doi:10.1021/ie200726jOlsson, L., & Andersson, B. (2004). Kinetic Modelling in Automotive Catalysis. Topics in Catalysis, 28(1-4), 89-98. doi:10.1023/b:toca.0000024337.50617.8eMöller, R., Votsmeier, M., Onder, C., Guzzella, L., & Gieshoff, J. (2009). Is oxygen storage in three-way catalysts an equilibrium controlled process? Applied Catalysis B: Environmental, 91(1-2), 30-38. doi:10.1016/j.apcatb.2009.05.003Rink, J., Meister, N., Herbst, F., & Votsmeier, M. (2017). Oxygen storage in three-way-catalysts is an equilibrium controlled process: Experimental investigation of the redox thermodynamics. Applied Catalysis B: Environmental, 206, 104-114. doi:10.1016/j.apcatb.2016.12.052Auckenthaler, T. S., Onder, C. H., & Geering, H. P. (2002). CONTROL-ORIENTED INVESTIGATION OF SWITCH-TYPE AIR/FUEL RATIO SENSORS. IFAC Proceedings Volumes, 35(1), 331-336. doi:10.3182/20020721-6-es-1901.0152

EGR transient operations in highly dynamic driving cycles

[EN] EGR is one of the proven and well tested strategies within the specific operating range of the engine. Necessity of an implementation of this exhaust gas recirculation all over the engine operating range is emerging. Therefore, a systematic study has been carried out to identify the specific and frequent transient operations on newly developed dynamic cycles like WLTC and RDE. To perform detailed observations, these transients are imitated individually on the diesel engine test bench. High frequency gas analyzers are used to track the instantaneous CO2 and NOx concentration respectively at the intake and exhaust lines of the engine. A parametric study has been carried out using different valve movement profiles of the LPEGR and HPEGR during severe engine load change operations. An analysis is presented suggesting the best suited valve control during these harsh transients which can be helpful for transient calibration of a turbocharged diesel engine. The effect of length of Long route LPEGR line is also acknowledged. This study reveals the dynamic behavior of a diesel engine during transient operation with exhaust gas recirculation. It outlines the trade-off between performance and NOx emission and opacity for the initial phase of the transient before acquiring the steady state situation.Galindo, J.; Climent, H.; Pla Moreno, B.; Patil, CY. (2020). EGR transient operations in highly dynamic driving cycles. International Journal of Automotive Technology. 21(4):865-879. https://doi.org/10.1007/s12239-020-0084-xS865879214Asad, U., Tjong, J. and Zheng, M. (2014). Exhaust gas recirculation–Zero dimensional modelling and characterization for transient diesel combustion control. Energy Conversion and Management, 86, 309–324.Balau, A., Kooijman, D., Vazquez Rodarte, I. and Ligterink, N. (2015). Stochastic real-world drive cycle generation based on a two stage Markov chain approach. SAE Int. J. 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United States.Buchwald, R., Lautrich, G., Maiwald, O. and Sommer, A. (2006). Boost and EGR system for the highly premixed diesel combustion. SAE Paper No. 2006-01-0204.Chung, J., Kim, H. and Sunwoo, M. (2018). Reduction of transient NOx emissions based on set-point adaptation of real-time combustion control for light-duty diesel engines. Applied Thermal Engineering, 137, 729–738.Darlington, A., Glover, K. and Collings, N. (2006). A simple diesel engine air-path model to predict the cylinder charge during transients: Strategies for reducing transient emissions spikes. SAE Paper No. 2006-01-3373Daya, R., Hoard, J., Chanda, S. and Singh, M. (2017). Insulated catalyst with heat storage for real-world vehicle emissions reduction. Int. J. Engine Research18, 9, 886–899.Donateo, T. and Giovinazzi, M. (2017). Building a cycle for real driving emissions. Energy Procedia, 126, 891–898.European Parliament & Council of the European Union (2016). Commission Regulation (EU) 2016/427 of 10 March 2016 Amending Regulation (EC) No 692/2008 as Regards Emissions from Light Passenger and Commercial Vehicles (Euro 6) (Text with EEA Relevance). Official J. European Union, 82(31/03/2016), 1–98.Giakoumis, E. G., Rakopoulos, C. D., Dimaratos, A. M. and Rakopoulos, D. C. (2012). Exhaust emissions of diesel engines operating under transient conditions with biodiesel fuel blends. Progress in Energy and Combustion Science38, 5, 691–715.Gong, Q., Midlam-Mohler, S., Marano, V., Rizzoni, G. and Guezennec, Y. (2010). Statistical analysis of PHEV fleet data. Proc. IEEE Vehicle Power and Propulsion Conf., Lille, France.Heuwetter, D., Glewen, W., Meyer, C., Foster, D. E., Andrie, M. and Krieger, R. (2011). Effects of low pressure EGR on transient air system performance and emissions for low temperature diesel combustion. SAE Paper No. 2011-24-0062.Khalef, M. S., Soba, A. and Korsgren, J. (2016). Study of EGR and turbocharger combinations and their influence on diesel engine’s efficiency and emissions. SAE Paper No. 2016-01-0676.Kooijman, D. G., Balau, A. E., Wilkins, S., Ligterink, N. and Cuelenaere, R. (2015). WLTP random cycle generator. Proc. IEEE Vehicle Power and Propulsion Conf. (VPPC), Montreal, Quebec, Canada.Lakshminarayanan, P. A. and Aswin, S. (2017). Estimation of particulate matter from smoke, oil consumption and fuel sulphur. SAE Paper No. 2017-01-7002.Lana, C. A., Kappaganthu, K., Kothandaraman, G. and PerfettoKarthik, D. J. S. C. G. H. D. K. (2016). US20160237928A1. United States.Leach, F. C. P., Davy, M. and Peckham, M. (2019). Cyclic NO2: NOx ratio from a diesel engine undergoing transient load steps. Int. J. Engine Research.Leach, F., Davy, M. and Peckham, M. (2018). Cycle-tocycle NO and NOx emissions from a HSDI diesel engine. Proc. ASME Internal Combustion Engine Division Fall Technical Conf., San Diego, California, USA.Liu, F. and Pfeiffer, J. (2015). Estimation algorithms for low pressure cooled EGR in spark-ignition engines. SAE Paper No. 2015-01-1620.Liu, F., Pfeiffer, J. M., Caudle, R., Marshall, P. and Olin, P. (2016). Low pressure cooled EGR transient estimation and measurement for an turbocharged SI engine. SAE Paper No. 2016-01-0618.Luján, J. M., Climent, H., Ruiz, S. and Moratal, A. (2018a). Influence of ambient temperature on diesel engine raw pollutants and fuel consumption in different driving cycles. Int. J. Engine Research20, 8–9, 877–888.Luján, J. M., Bermúdez, V., Dolz, V. and Monsalve-Serrano, J. (2018b). An assessment of the real-world driving gaseous emissions from a Euro 6 light-duty diesel vehicle using a portable emissions measurement system (PEMS). Atmospheric Environment, 174, 112–121.Luján, J. M., Climent, H., Arnau, F. J. and Miguel-García, J. (2018c). Analysis of low-pressure exhaust gases recirculation transport and control in transient operation of automotive diesel engines. Applied Thermal Engineering, 137, 184–192.Luján, J. M., Guardiola, C., Pla, B. and Reig, A. (2015). Switching strategy between HP (high pressure)- and LPEGR (low pressure exhaust gas recirculation) systems for reduced fuel consumption and emissions. Energy90, Part 2, 1790–1798.Maiboom, A., Tauzia, X. and Hétet, J. F. (2008). Experimental study of various effects of exhaust gas recirculation (EGR) on combustion and emissions of an automotive direct injection diesel engine. Energy33, 1, 22–34.Park, J. and Choi, J. (2016). Optimization of dual-loop exhaust gas recirculation splitting for a light-duty diesel engine with model-based control. Applied Energy, 181, 268–277.Park, J., Song, S. and Lee, K. S. (2015). Numerical investigation of a dual-loop EGR split strategy using a split index and multi-objective Pareto optimization. Applied Energy, 142, 21–32.Park, Y. and Bae, C. (2014). Experimental study on the effects of high/low pressure EGR proportion in a passenger car diesel engine. Applied Energy, 133, 308–316.Reifarth, S. and Angstrom, H.-E. (2009). Transient EGR in a long-route and short-route EGR system. Proc. ASME Internal Combustion Engine Division Spring Technical Conf., Milwaukee, Wisconsin, USA.Reifarth, S. and Angstrom, H.-E. (2010). Transient EGR in a high-speed DI diesel engine for a set of different EGRroutings. SAE Paper No. 2010-01-1271.Serrano, J. R., Climent, H., Guardiola, C. and Piqueras, P. (2009). Methodology for characterisation and simulation of turbocharged diesel engines combustion during transient operation. Part 2: Phenomenological combustion simulation. Applied Thermal Engineering29, 1, 150–158.Shutty, J. (2009). Control strategy optimization for hybrid EGR engines. SAE Paper No. 2009-01-1451.Soltis, R., Hilditch, J., Clark, T., House, C., Gerhart, M. and Surnilla, G. (2016). Intake oxygen sensor for EGR measurement. SAE Paper No. 2016-01-1070.Sutela, C., Collings, N. and Hands, T. (2000). Real time CO2 measurement to determine transient intake gas composition under EGR conditions. SAE Paper No. 2000-01-2953.Thunis, P., Lefebvre, W., Weiss, M., Vranckx, S., Clappier, A., Degraeuwe, B. and Janssen, S. (2017). Impact of passenger car NOX emissions on urban NO2 pollution–Scenario analysis for 8 European cities. Atmospheric Environment, 171, 330–337.Triantafyllopoulos, G., Katsaounis, D., Karamitros, D., Ntziachristos, L. and Samaras, Z. (2018). Experimental assessment of the potential to decrease diesel NOx emissions beyond minimum requirements for Euro 6 real drive emissions (RDE) compliance. Science of the Total Environment, 618, 1400–1407.Tutuianu, M., Bonnel, P., Ciuffo, B., Haniu, T., Ichikawa, N., Marotta, A., Pavlovic, J. and Steven, H. (2015). Development of the World-wide harmonized Light duty Test Cycle (WLTC) and a possible pathway for its introduction in the European legislation. Transportation Research Part D: Transport and Environment, 40, 61–75.Yamada, H., Misawa, K., Suzuki, D., Tanaka, K., Matsumoto, J., Fujii, M. and Tanaka, K. (2011). Detailed analysis of diesel vehicle exhaust emissions: Nitrogen oxides, hydrocarbons and particulate size distributions. Proc. Combustion Institute33, 2, 2895–2902.Yang, L., Franco, V., Mock, P., Kolke, R., Zhang, S., Wu, Y. and German, J. (2015). Experimental assessment of NOx emissions from 73 Euro 6 diesel passenger cars. Environmental Science and Technology49, 24, 14409–14415.Zamboni, G. and Capobianco, M. (2012). Experimental study on the effects of HP and LP EGR in an automotive turbocharged diesel engine. Applied Energy, 94, 117–128.Zamboni, G., Moggia, S. and Capobianco, M. (2017). Effects of a dual-loop exhaust gas recirculation system and variable nozzle turbine control on the operating parameters of an automotive diesel engine. Energies10, 1, 47

Morphometric Discriminant Analysis of isolated chondrichthyan scales for palaeoecological inferences: the Middle Triassic of the Iberian Chain (Spain) as a case of study

Palaeontological studies on exosqueletal disarticulated remains of chondrichthyans have focused on teeth and only less interest has been paid to scales due their limited taxonomic and systematic significance. However, classical works linking the morphology and the function of the squamation in extant sharks suggest that, despite their limited taxonomic value, the study of isolated scales can be a useful tool for palaeoenvironmental and palaeoecological inferences. Following this idea, we have analyzed the fossil record of shark scales from two Middle Triassic sections of the Iberian Chain (Spain), identifying different functional types by means of a morphometric discriminant analysis. From a total of 1136 isolated chondrichthyan scales, 25% were identified as abrasion resistant scales, 62% as drag reduction scales and 13% as scales of generalized functions. The elevated proportion of abrasion resistant scales suggests that this chondrichthyan palaeocommunity was highly dominated by benthic sharks that lived over a hard sea floor. However, one of the stratigraphical levels studied (He-20), presents statistically significant differences from the others, showing a lower percentage of abrasion resistant scales and a larger percentage of drag reduction scales. This level can be linked with storm episodes that could introduce remains of bentho-pelagic or pelagic forms in the inner platform.. Finally, partial correlation analysis between relative abundances of functional scale types and tooth-based taxa from the same sections provide positive correlation between teeth of Hybodus and Pseudodalatias and drag reduction scales, and teeth of Prolatodon and abrasion strength scales.Los estudios paleontológicos de restos desarticulados de condrictios se han centrado en los dientes, no prestando prácticamente interésal estudio de sus escamas debido a su limitada importancia taxonómica y sistemática. Sin embargo, algunos trabajos clásicos que hanrelacionado su morfología y función en base al estudio de la escamación de tiburones actuales, sugieren que, a pesar de su limitado valortaxonómico, el estudio de las escamas aisladas puede ser una herramienta útil para obtener inferencias paleoambientales y paleoecológicas.Siguiendo estas ideas, se ha analizado el registro fósil de escamas de tiburón de dos secciones del Triásico Medio de la Cordillera Ibérica(España), identificando diferentes tipos funcionales por medio de un análisis morfométrico discriminante. De un total de 1.136 escamasaisladas de condrictios, el 25% de ellas fueron identificadas como escamas resistentes a la abrasión, el 62% como de reducción de la friccióncon el agua y el 13% de las escamas como de función generalizada. La elevada proporción de las escamas resistentes a la abrasión sugiereque esta paleocomunidad de condrictios estaba claramente dominada por tiburones bentónicos que habitaban sobre un sustrato rocoso. Sinembargo, uno de los niveles estratigráficos estudiados (He-20), presenta diferencias estadísticamente significativas con los demás, mostrandoun porcentaje más bajo de escamas resistentes a la abrasión y un porcentaje mayor de las escamas de reducción de la fricción con elagua. Este nivel se relaciona con episodios de tormenta que pudieron haber introducido los restos de formas bento-pelágicas o pelágicasen la plataforma interna. Por último, el análisis de correlación parcial entre la abundancia relativa de los tipos funcionales de escamas ytaxones en basado dientes de las mismas secciones proporcionan una correlación positiva entre los dientes de Hybodus y Pseudodalatias yescamas de reducción de la fricción con el agua, y dientes de Prolatodon y escamas resistencia a la abrasión

Energy radiation of moving cracks

The energy radiated by moving cracks in a discrete background is analyzed. The energy flow through a given surface is expressed in terms of a generalized Poynting vector. The velocity of the crack is determined by the radiation by the crack tip. The radiation becomes more isotropic as the crack velocity approaches the instability threshold.Comment: 7 pages, embedded figure

Mean Field Theory of Sandpile Avalanches: from the Intermittent to the Continuous Flow Regime

We model the dynamics of avalanches in granular assemblies in partly filled rotating cylinders using a mean-field approach. We show that, upon varying the cylinder angular velocity $\omega$, the system undergoes a hysteresis cycle between an intermittent and a continuous flow regimes. In the intermittent flow regime, and approaching the transition, the avalanche duration exhibits critical slowing down with a temporal power-law divergence. Upon adding a white noise term, and close to the transition, the distribution of avalanche durations is also a power-law. The hysteresis, as well as the statistics of avalanche durations, are in good qualitative agreement with recent experiments in partly filled rotating cylinders.Comment: 4 pages, RevTeX 3.0, postscript figures 1, 3 and 4 appended

Discrete models of dislocations and their motion in cubic crystals

A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are the elastic stiffness constants of the material and a dimensionless periodic function that restores the translation invariance of the crystal and influences the Peierls stress. Explicit expressions are given for crystals with cubic symmetry: sc, fcc and bcc. Numerical simulations of this model with conservative or damped dynamics illustrate static and moving edge and screw dislocations and describe their cores and profiles. Dislocation loops and dipoles are also numerically observed. Cracks can be created and propagated by applying a sufficient load to a dipole formed by two edge dislocations.Comment: 23 pages, 15 figures, to appear in Phys. Rev.

Fracture driven by a Thermal Gradient

Motivated by recent experiments by Yuse and Sano (Nature, 362, 329 (1993)), we propose a discrete model of linear springs for studying fracture in thin and elastically isotropic brittle films. The method enables us to draw a map of the stresses in the material. Cracks generated by the model, imposing a moving thermal gradient in the material, can branch or wiggle depending on the driving parameters. The results may be used to compare with other recent theoretical work, or to design future experiments.Comment: RevTeX file (9 pages) and 5 postscript figure