Kinematics and Deformations of a Continuum Material
Abstract
Continuum mechanics is an applied science with the wide applications in material, mechanical and chemical engineering. Kinematics is a science study of material deformations (from external forces) and movements. Those deformations are comprised of linear and angular deformations while movements come from translations and rotations. This article presents the procedures of determining the material deformation at current time from the undeformed shape at initial time . This technique is commonly used in rigid bodies, elastic solids, hyperelastic materials, including viscoelastic materials. The deformation gradient tensor can be decomposed to right stretch tensor (or left stretch tensor ) and rotation tensor . The rate of deformation has the more profound effects in liquids than in solids.Keywords : continuum mechanics, kinematics, deformation gradient, rate of deformationReferences
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ASTM D412-98a. (2003). Standard Test Methods for Vulcanized Rubber and Thermoplastic Elastomers-Tension. West Conshohocken, PA, United States: ASTM International.
Bird, R.B., R.C. Armstrong, O. Hassager (1977). Dynamics of Polymeric Liquids: Volume 1 Fluid Mechanics.
(1st ed.). New York, USA: John Wiley and Sons.
Bird, R.B., R.C. Armstrong, O. Hassager (1987). Dynamics of Polymeric Liquids: Volume 1 Fluid Mechanics.
(2nd ed.). New York, USA: John Wiley and Sons.
Cengel, Y. A. and J. M. Cimbala (2006). Fluid Mechanics, Fundamentals and Applications. (International Edition). New York, USA: McGraw Hill.
Irgens, Fridtjov (2008). Continuum Mechanics. Berlin Heidelberg: Springer-Verlag. ISBN: 978-3-540-74297-5.
Itskov, Mikhail (2014). Tensor Algebra and Tensor Analysis for Engineers with Applications to Continuum Mechanics. (4th ed.). New York, USA:Springer.
Jog, C. S. (2015), Continuum Mechanics: Foundations and Applications of Mechanics, Volume I. (Third edition). Cambridge University Press.
Lai, W. Michael, David Rubin and Erhard Krempl (2010), Introduction to Continuum Mechanics. (4th ed.).
New York, USA: Butterworth-Heinemann.
Morozov, Alexander and Spagnolie, Saverio E. (2015), Introduction to Complex Fluids, Complex Fluids in Biological Systems, Experiment, Theory, and Computation. Edited by Spagnolie, Saverio E. New York, USA: Springer. ISBN 978-1-4939-2064-8.
Morrison, F. A. (2001), Understanding Rheology, New York, USA: Oxford University Press.
Munson, B. R., D. F. Young, and T. H. Okiishi (2002). Fundamentals of Fluid Mechanics. (4th ed.). New York,
USA: John Wiley and Sons.
NPTEL (2016). Mechanical Engineering – Continuum Mechanics, Lecture-21: The Rate of Deformation and Spin, Module-3: Kinematics. Ad hoc document. Joint initiative of IITs and IISc – Funded by MHRD. Government of India. Retrieved July 7, 2019, from https://nptel.ac.in/courses/112103167/21.
Rudnicki, J.W. (2015). Fundamentals of Continuum Mechanics. West Sussex, UK: John Wiley & Sons, Ltd.
Wangchai, Sathaphon (2005). Finite Element Analysis of Heat Generation in Particle Filled Natural Rubber Valcanizates During Cyclic Deformation, Master Thesis. Department of Mechanical Engineering, King Mongkut’s Institute of Technology North Bangkok, Thailand. (in Thai).
White, F.M. (2010). Fluid Mechanics. (7th ed.). New York, USA: McGraw Hill.
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2020-01-17
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