The present work is inspired by Anderson et al. (Phys. D Nonlinear Phenom. 2000; 135(1¯2):175¯194) and Noll (http://www.math.cmu.edu/wn0g/noll) and falls in the conceptual line of the Ginzburg-Landau class of first-order phase-transition models based on the concept of phase-field parameter. Trying to keep the exposition as much general as possible, we develop below a thermodynamically consistent rationalization of the physical process of (anisotropic) deposition of pyrolytic carbon from a gas phase. The derivation line we follow is well established in the field of the modern continuum physics. From the covariance of the first principle of thermodynamics, the second Newton's law and the Liouville's theorem with respect to the one-dimensional Lie groups of transformations, the balance laws for the temperature, linear momentum and density are formulated. This system of partial differential equations is comprehended further by the constitutive laws for the phase field, the stress, and the heat and entropy fluxes obtained in a form consistent with the Clausius-Duhem understanding of the second law. The result referred to as a local, strongly coupled initial boundary value problem of chemical vapor deposition (IBVP-CVD) constitutes the general mathematical description of the CVD process. The weak form of isotropic IBVP-CVD is then derived and discretized by means of the discontinuous Galerkin method. At the end of the paper, we also derive the weak formulations for the local lifting operators that provide the stabilization mechanism for the discontinuous Galerkin discretization scheme.
{"title":"Diffuse interface method for simulation of the chemical vapor deposition of pyrolytic carbon: Aspects of the mathematical formulation","authors":"S. Dimitrov, Alexander Ekhlakov, T. Langhoff","doi":"10.1002/CNM.1083","DOIUrl":"https://doi.org/10.1002/CNM.1083","url":null,"abstract":"The present work is inspired by Anderson et al. (Phys. D Nonlinear Phenom. 2000; 135(1¯2):175¯194) and Noll (http://www.math.cmu.edu/wn0g/noll) and falls in the conceptual line of the Ginzburg-Landau class of first-order phase-transition models based on the concept of phase-field parameter. Trying to keep the exposition as much general as possible, we develop below a thermodynamically consistent rationalization of the physical process of (anisotropic) deposition of pyrolytic carbon from a gas phase. The derivation line we follow is well established in the field of the modern continuum physics. From the covariance of the first principle of thermodynamics, the second Newton's law and the Liouville's theorem with respect to the one-dimensional Lie groups of transformations, the balance laws for the temperature, linear momentum and density are formulated. This system of partial differential equations is comprehended further by the constitutive laws for the phase field, the stress, and the heat and entropy fluxes obtained in a form consistent with the Clausius-Duhem understanding of the second law. The result referred to as a local, strongly coupled initial boundary value problem of chemical vapor deposition (IBVP-CVD) constitutes the general mathematical description of the CVD process. The weak form of isotropic IBVP-CVD is then derived and discretized by means of the discontinuous Galerkin method. At the end of the paper, we also derive the weak formulations for the local lifting operators that provide the stabilization mechanism for the discontinuous Galerkin discretization scheme.","PeriodicalId":51245,"journal":{"name":"Communications in Numerical Methods in Engineering","volume":"24 1","pages":"2155-2193"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/CNM.1083","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51533886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SUMMARY This work investigates partitioned iterative solution of coupled multiphysics systems including subcycling time-stepping strategies for decoupled subsystems in conjunction with a proportional-integral-derivative feedback control algorithm for adaptive time-step selection. Some basic algorithms are proposed and the total computational effort to integrate to steady state is compared for a representative coupled flow and heat transfer problem to illustrate the approach and assess performance efficiency. Copyright 2008 John Wiley & Sons, Ltd.
{"title":"On decoupled time step/subcycling and iteration strategies for multiphysics problems","authors":"A. Valli, G. Carey, A. Coutinho","doi":"10.1002/CNM.1085","DOIUrl":"https://doi.org/10.1002/CNM.1085","url":null,"abstract":"SUMMARY This work investigates partitioned iterative solution of coupled multiphysics systems including subcycling time-stepping strategies for decoupled subsystems in conjunction with a proportional-integral-derivative feedback control algorithm for adaptive time-step selection. Some basic algorithms are proposed and the total computational effort to integrate to steady state is compared for a representative coupled flow and heat transfer problem to illustrate the approach and assess performance efficiency. Copyright 2008 John Wiley & Sons, Ltd.","PeriodicalId":51245,"journal":{"name":"Communications in Numerical Methods in Engineering","volume":"24 1","pages":"1941-1952"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/CNM.1085","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51533966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SUMMARY The present study investigated the mechanical properties of human Achilles tendon (AT) during different forms of human locomotion, by combining biomechanical tests and numerical modelling. A Pedar-X plantar pressure measurement system and Mega multichannel SEMG system were used to measure the dynamic data of a female athlete during hopping and walking. The human Achilles tendon force (ATF) was determined through inverse muscle force calculation. A 3D finite element (FE) model was developed using subject-specified CT images to simulate the deformation of AT during hopping and walking. The stress/strain within the AT during different subphases (e.g. heel strike, midstance, forefoot contact, push off and toe off) was successfully predicted. Results showed that the muscle forces in hopping were much higher than in normal gait. The maximum stress in hopping was three times of that in walking. The tendon stress increased with external load over different subphases and the maximum ATF was found to be in the push-off phase. Copyright q 2008 John Wiley & Sons, Ltd.
{"title":"The mechanical response of Achilles tendon during different kinds of sports","authors":"Y. Gu, J. S. Li, M. Lake, X. Ren, Yanjun Zeng","doi":"10.1002/CNM.1096","DOIUrl":"https://doi.org/10.1002/CNM.1096","url":null,"abstract":"SUMMARY The present study investigated the mechanical properties of human Achilles tendon (AT) during different forms of human locomotion, by combining biomechanical tests and numerical modelling. A Pedar-X plantar pressure measurement system and Mega multichannel SEMG system were used to measure the dynamic data of a female athlete during hopping and walking. The human Achilles tendon force (ATF) was determined through inverse muscle force calculation. A 3D finite element (FE) model was developed using subject-specified CT images to simulate the deformation of AT during hopping and walking. The stress/strain within the AT during different subphases (e.g. heel strike, midstance, forefoot contact, push off and toe off) was successfully predicted. Results showed that the muscle forces in hopping were much higher than in normal gait. The maximum stress in hopping was three times of that in walking. The tendon stress increased with external load over different subphases and the maximum ATF was found to be in the push-off phase. Copyright q 2008 John Wiley & Sons, Ltd.","PeriodicalId":51245,"journal":{"name":"Communications in Numerical Methods in Engineering","volume":"24 1","pages":"2077-2085"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/CNM.1096","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51534753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Piat, I. Tsukrov, T. Böhlke, Norbert Bronzel, Tilottama Shrinivasa, B. Reznik, D. Gerthsen
SUMMARY Carbon/carbon composites produced by chemical vapor infiltration consist of carbon fibers embedded in a matrix of pyrolytic carbon with anisotropic mechanical properties. The matrix around fibers consists of cylindrically shaped pyrolytic carbon layers of coating, which may have different textures with different mechanical properties in the axial, radial and circumferential directions. The goal of the present numerical study is to investigate the influence of the coating microstructure on stress concentrations and possible modes of failure in the carbon composite. Numerical modeling was performed on two length scales. First, the material properties of the differently textured pyrolytic carbon layers were determined on the nanometer scale using methodology based on the Eshelby theory for continuously distributed inclusions. Then, the obtained material parameters for each layer were used as input for the finite element models on the micrometer scale. The numerical simulations were conducted for three basic loading scenarios: uniaxial tension, shear loading and hydrostatic compression. The calculated stress distributions show zones of maximum stress concentrations and provide information on the possible failure regions for each material under all considered loading cases. The numerical results demonstrate good correspondence with experimentally identified failure regions. Copyright q 2008 John Wiley & Sons, Ltd.
{"title":"Numerical studies of the influence of textural gradients on the local stress concentrations around fibers in carbon/carbon composites","authors":"R. Piat, I. Tsukrov, T. Böhlke, Norbert Bronzel, Tilottama Shrinivasa, B. Reznik, D. Gerthsen","doi":"10.1002/CNM.1081","DOIUrl":"https://doi.org/10.1002/CNM.1081","url":null,"abstract":"SUMMARY Carbon/carbon composites produced by chemical vapor infiltration consist of carbon fibers embedded in a matrix of pyrolytic carbon with anisotropic mechanical properties. The matrix around fibers consists of cylindrically shaped pyrolytic carbon layers of coating, which may have different textures with different mechanical properties in the axial, radial and circumferential directions. The goal of the present numerical study is to investigate the influence of the coating microstructure on stress concentrations and possible modes of failure in the carbon composite. Numerical modeling was performed on two length scales. First, the material properties of the differently textured pyrolytic carbon layers were determined on the nanometer scale using methodology based on the Eshelby theory for continuously distributed inclusions. Then, the obtained material parameters for each layer were used as input for the finite element models on the micrometer scale. The numerical simulations were conducted for three basic loading scenarios: uniaxial tension, shear loading and hydrostatic compression. The calculated stress distributions show zones of maximum stress concentrations and provide information on the possible failure regions for each material under all considered loading cases. The numerical results demonstrate good correspondence with experimentally identified failure regions. Copyright q 2008 John Wiley & Sons, Ltd.","PeriodicalId":51245,"journal":{"name":"Communications in Numerical Methods in Engineering","volume":"24 1","pages":"2194-2205"},"PeriodicalIF":0.0,"publicationDate":"2008-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/CNM.1081","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51533811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alexander Ekhlakov, S. Dimitrov, T. Langhoff, E. Schnack
A diffuse interface model for the determination of the evolution of the deposited substrate surface during isobaric, isothermal chemical vapour infiltration (CVI) of pyrolytic carbon is proposed. A continuous scalar phase-field parameter is introduced to label explicitly the solid and the gas phases within the system. Following the conceptual line of Ginzburg-Landau theory, we formulate the initial boundary value problem of CVI. In variance with the traditional formulations, we account for the different intensities of homogeneous and heterogeneous chemical reactions during CVI by introducing a scalar-valued intensity parameter that depends only on the phase-field. The various homogeneous and heterogeneous reaction processes during CVI are described in terms of a reduced chemical reaction scheme. Finally, we discuss the application of the developed methodology for numerical simulation of a simplified two-dimensional model problem. Using a finite element method, we obtain numerical approximations for the concentration profiles along the direction of infiltration.
{"title":"Phase-field model for deposition of pyrolytic carbon","authors":"Alexander Ekhlakov, S. Dimitrov, T. Langhoff, E. Schnack","doi":"10.1002/CNM.1082","DOIUrl":"https://doi.org/10.1002/CNM.1082","url":null,"abstract":"A diffuse interface model for the determination of the evolution of the deposited substrate surface during isobaric, isothermal chemical vapour infiltration (CVI) of pyrolytic carbon is proposed. A continuous scalar phase-field parameter is introduced to label explicitly the solid and the gas phases within the system. Following the conceptual line of Ginzburg-Landau theory, we formulate the initial boundary value problem of CVI. In variance with the traditional formulations, we account for the different intensities of homogeneous and heterogeneous chemical reactions during CVI by introducing a scalar-valued intensity parameter that depends only on the phase-field. The various homogeneous and heterogeneous reaction processes during CVI are described in terms of a reduced chemical reaction scheme. Finally, we discuss the application of the developed methodology for numerical simulation of a simplified two-dimensional model problem. Using a finite element method, we obtain numerical approximations for the concentration profiles along the direction of infiltration.","PeriodicalId":51245,"journal":{"name":"Communications in Numerical Methods in Engineering","volume":"24 1","pages":"2139-2154"},"PeriodicalIF":0.0,"publicationDate":"2008-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/CNM.1082","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51533864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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