Abstract
I have been puzzled for a long time by the unnatural divide between the theory of bulk growth—strikingly underdeveloped—and that for surface growth—much better developed, along apparently independent lines. Recent advances in growth mechanics (DiCarlo and Quiligotti, 2002) make it now possible to subsume growth phenomena of both kinds under one and the same format, where surface growth is obtained as an infinitely intense bulk growth confined in a layer of vanishingly small thickness. This has allowed me to recover the results collected in Gurtin, 2000 from the standpoint of DiCarlo and Quiligotti, 2002. In particular, I am able to construe Gurtin’s technique of referential control volumes that evolve in time as a special application of the principle of virtual power.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Notes: References
Cahn, John W. (1980). “Surface stress and the chemical equilibrium of small crystals. 1. The case of the isotropic surface,” Act. Metall. 28, 1333–1338.
Casey, James. (1987). “Invariance considerations in large strain elasto-plasticity,” ASME J. Appl. Mech. 54, 247.
Casey, James, and Paul M. Naghdi. (1980). “A remark on the use of the decomposition F = Fe Fp in plasticity,” ASME J. Appl. Mech. 47, 672–675.
Casey, James, and Paul M. Naghdi. (1981). “A correct definition of elastic and plastic deformation and its computational significance,” ASME J. Appl. Mech. 48, 683–984.
Cermelli, Paolo, and Morton E. Gurtin. (1994). “The dynamics of solid-solid phase transitions. 2. Incoherent interfaces,” Arch. Rational Mech. Anal. 127, 41–99.
DiCarlo, Antonio (in preparation). Material Remodelling.
DiCarlo, Antonio, Paola Nardinocchi, and Luciano Teresi (forthcoming). “Creep as passive growth.”
DiCarlo, Antonio, and Sara Quiligotti. (2002). “Growth and balance,” Mech. Res. Comm. 29, 449–456.
Epstein, Marcelo. (1999). “On material evolution laws,” in Geometry, Continua & Microstructure (G.A. Maugin ed.). Paris: Hermann, 1–9.
Epstein, Marcelo, and Gerard A. Maugin. (2000). “Thermomechanics of volumetric growth in uniform bodies,” Int. J. Plast. 16, 951–978.
Green, Albert E. and Paul M. Naghdi. (1971). “Some remarks on elastic-plastic deformation at finite strain,” Int. J. Engng. Sci. 9, 1219–1229.
Gurtin, Morton E. (2000). Configuration Forces as Basic Concepts of Continuum Physics. Berlin: Springer-Verlag.
Kröner, Ekkehart. (1960). “Allgemeine Kontinuumstheorie der Verset-zungen und Eigenspannungen,” Arch. Rational Mech. Anal. 4, 273–334.
Lee, Erastus H. (1969). “Elastic-plastic deformations at finite strains,” J. Appl. Mechanics 36, 1–6.
Quiligotti, Sara. (2002). “On bulk growth mechanics of solid-fluid mixtures: kinematics and invariance requirements,” Theor. Appl. Mech. 28/29, 277–288.
Rodriguez, Edward K., Anne Hoger, and Andrew D. McCulloch. (1994). “Stress-dependent finite growth in soft elastic tissues,” J. Biomechanics 27, 455–467.
Taber, Larry A. (1995). “Biomechanics of growth, remodeling, and morphogenesis,” Appl. Mech. Rev. 48, 487–545.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this paper
Cite this paper
DiCarlo, A. (2005). Surface and Bulk Growth Unified. In: Steinmann, P., Maugin, G.A. (eds) Mechanics of Material Forces. Advances in Mechanics and Mathematics, vol 11. Springer, Boston, MA. https://doi.org/10.1007/0-387-26261-X_6
Download citation
DOI: https://doi.org/10.1007/0-387-26261-X_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-26260-4
Online ISBN: 978-0-387-26261-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)