On spatial and material settings of thermo-hyperelastodynamics for open systems

Acta Mechanica

Volumn 160, Issue 3-4, 2003, Pages 179-217

  Kuhl, E ^a   Steinmann, P ^a  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BIOMECHANICS; ELASTICITY; ENTROPY; KINETIC ENERGY; MIXTURES; THERMODYNAMICS;

CLASSICAL THERMODYNAMICS; MATERIAL MOTION PROBLEM; THEORY OF MIXTURES; THERMOHYPERELASTODYNAMICS;

CONTINUUM MECHANICS;

EID: 0037301832     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00707-002-0974-1     Document Type: Article

References (51)

1. Beaupré, G. S., Orr, T. E., Carter, D. R.: An approach for time dependent bone modelling and remodelling. J. Orth. Res. 8, 651-670 (1990).
2. de Boer, R.: Theory of porous media - Highlights in the historical development and current state. Berlin Heidelberg New York: Springer 2000.
3. Bowen, R. M.: Theory of mixtures. In: Continuum physics (Eringen, A. C., ed.), pp. 1-127, vol. III: Mixtures and EM field theories. San Francisco London New York: Academic Press 1976.
4. Carter, D. R., Beaupré, G. S.: Skeletal function and form mechanobiology of skeletal development, aging and regeneration. Cambridge University Press 2001.
5. Chadwick, P.: Applications of an energy momentum tensor in nonlinear elastostatics. J. Elast. 5, 249-258 (1975).
6. Cowin, S. C., Hegedus, D. H.: Bone remodelling I: Theory of adaptive elasticity. J. Elast. 6, 313-326 (1976).
7. Diebels, S.: Mikropolare Zweiphasenmodelle: Formulierung auf der Basis der Theorie poröser Medien. Stuttgart: Habilitationsschrift, Bericht aus dem Institut für Mechanik (Bauwesen) Nr. II-4, Universität Stuttgart 2000.
8. Ehlers, W.: Grundlegende Konzepte in der Theorie poröser Medien. Technische Mechanik 16, 63-76 (1996).
9. Epstein, M., Maugin, G. A.: The energy momentum tensor and material uniformity in finite elasticity. Acta Mech. 83, 127-133 (1990).
10. Epstein, M., Maugin, G. A.: Thermomechanics of volumetric growth in uniform bodies. Int. J. Plast. 16, 951-978 (2002).
11. Eshelby, J. D.: The force on an elastic singularity. Phil. Trans. Royal Soc. London 244, 87-112 (1951).
12. Eshelby, J. D.: The elastic energy momentum tensor. J. Elast. 5, 321-335 (1975).
13. Goldstein, H.: Classical mechanics. Reading, Mass.: Addison Wesley 1950.
14. Green, A. E., Nagdi, P. M.: A re-examination of the basic postulates of thermomechanics. Proc. Royal Soc. London A 432, 171-194 (1991).
15. Green, A. E., Nagdi, P. M.: A unified procedure for construction of theories of deformable media. I. Classical continuum physics. Proc. Royal Soc. London A 448, 335-356 (1995).
16. Gurtin, M. E.: On the nature of configurational forces. Arch. Rat. Mech. Anal. 131, 67-100 (1995).
17. Gurtin, M. E.: Configurational forces as basic concepts of continuum physics. New York Berlin Heidelberg: Springer 2000.
18. Harrigan, T. P., Hamilton, J. J.: Optimality condition for finite element simulation of adaptive bone remodeling. Int. J. Solids Struct. 29, 2897-2906 (1992).
19. Harrigan, T. P., Hamilton, J. J.: Finite element simulation of adaptive bone remodelling: A stability criterion and a time stepping method. Int. J. Num. Meth. Eng. 36, 837-854 (1993).
20. Haupt, P.: Continuum mechanics and theory of materials. Berlin Heidelberg New York: Springer 1999.
21. Hegedus, D. H., Cowin, S. C.: Bone remodeling II: Small strain adaptive elasticity. J. Elast. 6, 337-352 (1976).
22. Humphrey, J. D.: Cardiovascular solid mechanics. Berlin Heidelberg New York: Springer 2002.
23. Humphrey, J. D., Rajagopal, K. R. Rajagopal: A constrained mixture model for growth and remodeling of soft tissues. Mathematical and methods in applied sciences (accepted for publication 2002).
24. Kalpakides, V. K., Dascalu, C.: On the configurational force balance in thermomechanics. Proc. Royal Soc. London A (submitted for publication 2002).
25. Kienzler, R., Herrmann, G.: Mechanics in material space with applications in defect and fracture mechanics. Berlin Heidelberg New York: Springer 2000.
26. Krstin, N., Nackenhorst, U., Lammering, R.: Zur konstitutiven Beschreibung des anisotropen beanspruchungsadaptiven Knochenumbaus. Technische Mechanik 20, 31-40 (2000).
27. Kühn, W., Hauger, W.: A theory of adaptive growth of biological materials. Arch. Appl. Mech. 70, 183-192 (2000).
28. Kuhl, E., Steinmann, P.: Mass- and volume specific views on thermodynamics for open systems. Kaiserslautern: Internal Report No. J02-03, LTM, University of Kaiserslautern 2002.
29. Kuhl, E., Steinmann, P.: Theory and numerics of geometrically nonlinear open system mechanics. Kaiserslautern: Internal Report No. J02-05, LTM, University of Kaiserslautern 2002.
30. Kuhl, E., Steinmann, P.: Material forces in open system mechanics. Kaiserslautern: Internal Report No. J02-07, LTM, University of Kaiserslautern 2002.
31. Liu, I.-S.: Method of Lagrange multipliers for exploitation of the entropy principle. Arch. Rat. Mech. Anal. 46, 131-148 (1972).
32. Liu, I.-S.: Continuum mechanics. Berlin Heidelberg New York: Springer 2002.
33. Malvern, L. E., Introduction to the mechanics of a continuous medium. Englewood Cliffs, NJ: Prentice Hall 1969.
34. Maugin, G. A.: Material inhomogenities in elasticity. London: Chapman & Hall 1993.
35. Maugin, G. A.: Material forces: Concepts and applications. Appl. Mech. Rev. 48, 213-245 (1995).
36. Maugin, G. A.: The thermomechanics of nonlinear irreversible behaviors. Singapore New Jersey London Hong Kong: World Scientific Publishing 1999.
37. Maugin, G. A., Trimarco, C.: Pseudomomentum and material forces in nonlinear elasticity: Variational formulations and application to brittle fracture. Acta Mech. 94, 1-28 (1992).
38. Müller, I.: Thermodynamik: Die Grundlagen der Materialtheorie. Düsseldorf: Bertelsmann Universitätsverlag 1973.
39. Müller, I.: Grundzüge der Thermodynamik. Berlin Heidelberg New York: Springer 1994.
40. Rogula, D.: Forces in material space. Arch. Mech. 29, 705-713 (1977).
41. Schrödinger, E.: What is life? Reprinted by Cambridge University Press 1944.
42. Shield, R. T.: Inverse deformation results in finite elasticity. ZAMP 18, 490-500 (1967).
43. Silhavý, M.: The mechanics and thermodynamics of continuous media. New York Berlin Heidelberg: Springer 1997.
44. Steinmann, P.: Application of material forces to hyperelastostatic fracture mechanics. I. Continuum mechanical setting. Int. J. Solids Struct. 37, 7371-7391 (2000).
45. Steinmann, P.: On spatial and material settings of hyperelastodynamics. Acta Mech. 156, 193-218 (2002).
46. Steinmann, P.: On spatial and material settings of hyperelastostatic crystal defects. J. Mech. Phys. Solids (in press).
47. Steinmann, P.: On spatial and material settings of thermo hyperelastodynamics. J. Elast. (in press).
48. Steinmann, P., Ackermann, D., Barth, F. J.: Application of material forces to hyperelastostatic fracture mechanics. II. Computational setting. Int. J. Solids Struct. 38, 5509-5526 (2001).
49. Taber, L. A.: Biomechanics of growth, remodeling, and morphogenesis. ASME Appl. Mech. Rev. 48, 487-545 (1995).
50. Truesdell, C., Toupin, R.: The classical field theories. In: Handbuch der Physik (Flügge, S., ed.), vol. III/1. Berlin: Springer 1960.
51. Weinans, H., Huiskes, R., Grootenboer, H. J.: The behavior of adaptive bone remodeling simulation models. J. Biomech. 25, 1425-1441 (1992).