The equilibrium equations and constitutive equations of the growing deformable body in the framework of continuum theory

International Journal of Non-Linear Mechanics

Volumn 39, Issue 6, 2004, Pages 951-962

  Huang, Zaixing ^a  

^a NANJING UNIVERSITY OF AERONAUTICS AND ASTRONAUTICS   (China)

Author keywords

Accretive boundary condition; Constitutive equation; Coupling function of growth; Equilibrium equation; Growing deformable body

Indexed keywords

BOUNDARY CONDITIONS; CONTINUUM MECHANICS; ENTROPY; EQUATIONS OF MOTION; GROWTH (MATERIALS); NONLINEAR EQUATIONS; THERMODYNAMICS;

CONSTITUTIVE EQUATIONS; EQUILIBRIUM EQUATIONS; GROWING DEFORMABLE BODY; MOMENTUM;

DEFORMATION;

EID: 0345306155     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(03)00077-5     Document Type: Article

References (18)

1. Naumov V.E. Mechanics of growing deformable solids. a review J. Eng. Mech. 120(2):1994;207-220.
2. Taber L.A. Biomechanics of growth, remodeling, and morphogenesis. Appl. Mech. Rev. 48(8):1995;487-545.
3. Cowin C.S., Hegedus H.D. Bone remodeling I. theory of adaptive elasticity J. Elasticity. 6(3):1976;313-325.
4. Rodriguez E.K., Hoger A., McCulloch A.D. Stress-dependent finite growth in soft elastic tissues. J. Biomech. 27(4):1994;455-467.
5. M. Epstein, G.A. Maugin, Elements of a theory of growth, in: E. Inan, K.Z. Markov (Eds.), Continuum Models and Discrete Systems Proceedings of the Ninth International Symposium, Istanbul, Turkey, 1998, pp. 555-561.
6. Epstein M., Maugin G.A. Thermomechanics of volumetric growth in uniform bodies. Int. J. Plasticity. 16(7-8):2000;951-978.
7. C.B. Brown , L.E. Goodman, Gravitational stresses in accreted bodies, Proc. R. Soc. London, Ser. A 276 (1367) 571-576.
8. R. Skalak, Growth as a finite displacement field, in: D.E. Carlson, R.T. Shield (Eds.), Proceedings of IUTAM Symposium on Finite Elasticity, Matinus Nijhoff Publishers, The Hague, 1982, pp. 347-355.
9. R. Segev, G. Rodnay, Continuum kinematics of volumetric growth, in: E. Inan, K.Z. Markov (Eds.), Continuum Models and Discrete Systems Proceedings of the Ninth International Symposium, Istanbul, Turkey, 1998, pp. 321-328.
10. Arutyunyan N.K., Naumov V.E., Radaev Y.N. A mathematical model of a dynamically accreted deformable body, part 1. kinematics and measure of deformation of the growing body Mech. Solids. 25(6):1990;86-99.
11. Arutyunyan N.K., Naumov V.E., Radaev Y.N. Mathematical model of a dynamically accreted deformable body, part 2. evolution boundary-value problem of the theory of the growing bodies Mech. Solids. 26(1):1991;67-80.
12. Roman P. Some Modern Mathematics for Physicists and Other Outsiders. 1975;Pergamon Press, London.
13. D.G.B. Edelen, Nonlocal field theories, in: A.C. Eringen (Ed.), Continuum Physics, Vol. IV, Academic Press, New York, 1976, pp. 75-204.
14. Deshibqueres M.C., Spanjaard D. Concept in Surface Physics. 1996;Springer, Berlin.
15. Kreuzer H.J. Nonequilibrium Thermodynamics and Its Statistical Foundations. 1981;Clarendon Press, Oxford.
16. G.E. Murch, Diffusion in crystalline solids in: P. Haasen (Ed.), Phase Transformations in Materials, VCH Verlagsgesellschaft, Weinheim, 1991.
17. C. Truesdell, R.A. Noll, The Classical Field Theories, Handbuch der Physik, Vol. III/1, Springer, Berlin, 1960.
18. Eringen A.C. Mechanics of Continua. 2nd Edition: 1980;R.E. Krieger Publishing Company, Melbourne.