A Generalized Continuum Theory and Its Relation to Micromorphic Theory
Publication: Journal of Engineering Mechanics
Volume 135, Issue 3
Abstract
Classic continuum mechanics views a crystal as a homogeneous and continuous medium, in which the basic structural unit of the crystal is taken without structure and is idealized as point mass. Micromorphic theory views a material as a continuous collection of deformable point particles; each particle has finite size and additional nine internal degrees of freedom describing the stretches and rotations of the particle. This paper presents a multiscale field theory that views a crystalline material as a continuous collection of lattice points, while embedded within each point is a group of discrete atoms. The atomistic formulation of the field theory is briefly introduced. Its relation with the well-known micromorphic theory is derived. The applicability of the classical continuum theory, micromorphic theory, and the generalized continuum field theory is discussed.
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Acknowledgments
The support of this work by the National Science Foundation under Award No. NSFCMMI-0646674 is gratefully acknowledged.
References
Chen, Y. (2006). “Local stress and heat flux in atomistic systems involving three-body forces.” J. Chem. Phys., 124, 054113–1-6.
Chen, Y., and Lee, J. D. (2003a). “Connecting molecular dynamics to micromorphic theory. Part I: Instantaneous mechanical variables.” Physica A, 322, 359–376.
Chen, Y., and Lee, J. D. (2003b). “Connecting molecular dynamics to micromorphic theory. Part II: Balance laws.” Physica A, 322, 377–392.
Chen, Y., and Lee, J. D. (2005). “Atomistic formulation of a multiscale theory for nano/micro physics.” Philos. Mag., 85(33–35), 4095–4126.
Chen, Y., and Lee, J. D. (2006). “Conservation laws at nano/micro scales.” J. Mech. Mater. Struct., 1, 681–704.
Chen, Y., Lee, J. D., Lei, Y., and Xiong, L. (2006a). “A multiscale field theory: Nano/micro materials.” Multiscaling in molecular and continuum mechanics, G. C. Sih ed., Springer, New York, 23–65.
Chen, Y., Lee, J. D., and Xiong, L. (2006b). “Stresses and strains at nano/micro scales.” J. Mech. Mater. Struct., 1(4), 705–723.
Cosserat, E. and F. (1909). Theorie des corps deformable, Hermann, Paris.
Eringen, A. C. (1965). “Theory of micropolar continua.” Developments in mechanics, Vol. 3, T. C. Huang and M. W. Johnson Jr., eds., Wiley, New York.
Eringen, A. C. (1999). Microcontinuum field theories. I: Foundations and solids, Springer, New York.
Eringen, A. C., and Suhubi, E. S. (1964). “Nonlinear theory of simple micro-elastic solids—I.” Int. J. Eng. Sci., 2, 189–203.
Hardy, R. J.(1982). “Formulas for determining local properties in molecular-dynamics simulations: Shock waves.” J. Chem. Phys., 76(1), 622–628.
Irvine, J. H., and Kirkwood, J. G. (1950). “The statistical theory of transport processes. IV: The equations of hydrodynamics.” J. Chem. Phys., 18, 817–822.
Mindlin, R. D. (1964). “Microstructure in linear elasticity.” Arch. Ration. Mech. Anal., 16, 51–78.
Mindlin, R. D., and Eshel, N. N. (1968). “On first strain gradient theories in linear elasticity.” Int. J. Solids Struct., 4, 109–124.
Mindlin, R. D., and Tiersten, H. F. (1962). “Effects of couple stresses in linear elasticity.” Arch. Ration. Mech. Anal., 11, 415–448.
Toupin, R. A. (1962). “Elastic materials with couple-stresses.” Arch. Ration. Mech. Anal., 11, 385–414.
Xiong, L., Chen, Y., and Lee, J. D. (2007). “Atomistic simulation of mechanical properties of diamond and silicon carbide by a field theory.” Modell. Simul. Mater. Sci. Eng., 15, 535–551.
Xiong, L., Chen, Y., and Lee, J. D. (2008). “Simulation of dislocation nucleation and motion in single crystal magnesium oxide by a field theory.” Comput. Mater. Sci., 42, 168–177.
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© 2009 ASCE.
History
Received: Sep 7, 2007
Accepted: Aug 25, 2008
Published online: Mar 1, 2009
Published in print: Mar 2009
Notes
Note. Associate Editor: George Z. Voyiadjis
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