Computational modelling of isotropic multiplicative growth

CMES - Computer Modeling in Engineering and Sciences

Volumn 8, Issue 2, 2005, Pages 119-134

  Himpel, G ^b   Kuhl, E ^b   Menzel, A ^b   Steinmann, P ^a  

^a France   (Germany)

^b NONE

Author keywords

Biomaterials; Growth; Multiplicative decomposition; Remodelling

Indexed keywords

ALGORITHMS; DECOMPOSITION; DEFORMATION; FREE ENERGY; FUNCTIONS; KINEMATICS; MATHEMATICAL MODELS; STRESSES;

GROWTH; ISOTROPIC MULTIPLICATIVE GROWTH; MULTUPLICATIVE DECOMPOSITION; REMODELING;

BIOMATERIALS;

EID: 20444439539     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (34)

1. Ambrosi, D.; Mollica, F. (2002): On the mechanics of a growing tumor. International Journal of Engineering Science, vol. 40, pp. 1297-1316.
2. Beaupré, G. S.; Orr, T. E.; Carter, D. R. (1990): An approach for time-dependent bone modeling and remodeling - Theoretical development. Journal of Orthopaedic Research, vol. 8, pp. 651-661.
3. Chen, Y.-C.; Hoger, A. (2000): Constitutive functions of elastic materials in finite growth and deformation. Journal of Elasticity, vol. 59, pp. 175-193.
4. Cowin, S. C.; Hegedus, D. H. (1976): Bone remodeling i: Theory of adaptive elasticity. Journal of Elasticity, vol. 6, no. 3, pp. 313-326.
5. Epstein, M.; Maugin, G. A. (2000): Thermomechanics of volumetric growth in uniform bodies. International Journal of Plasticity, vol. 16, pp. 951-978.
6. Garikipati, K.; Narayanan, H.; Arruda, E. M.; Grosh, K.; Calve, S. (2004): Material forces in the context of biotissue remodelling. In Steinmann, P.; Maugin, G. A.(Eds): Mechanics of Material Forces, pp. 77-84. Euromech Colloquium 445. preprint.
7. Harrigan, T. P.; Hamilton, J. J. (1992): Optimality conditions for finite element simulation of adaptive bone remodeling. International Journal of Solids and Structures, vol. 29, no. 23, pp. 2897-2906.
8. Harrigan, T. P.; Hamilton, J. J. (1993): Finite element simulation of adaptive bone remodeling: A stability criterion and time stepping method. International Journal for Numerical Methods in Engineering, vol. 36, pp. 837-854.
9. Himpel, G. (2003): On the modeling of material growth in anisotropic solids. Internal variable approach and numerical implementation. Technical report, Institut für Mechanik (Bauwesen), Lehrstuhl I, Universität Stuttgart, Diplomarbeit, 2003. Report/Preprint No. 03-I-08.
10. Holzapfel, G. A. (2000): Nonlinear solid mechanics, a continuum approach for engineering. Wiley.
11. Holzapfel, G. A.; Gasser, T. C.; Ogden, R. W. (2000): A new constitutive framework for arterial wall mechanics and a comparative study of material models. Journal of Elasticity, vol. 61, pp. 1-48.
12. Holzapfel, G. A.; Ogden, R. W.(Eds): Biomechanics of soft tissue in cardiovascular systems. No. 441 in CISM Courses and Lectures. Springer.
13. Humphrey, J. D. (2002): Cardiovascular solid mechanics. Cells, tissues, and organs. Springer.
14. Humphrey, J. D.; Delange, S. L. (2004): An introduction to biomechanics. Springer.
15. Humphrey, J. D.; Rajagopal, K. R. (2002): A constrained mixture model for growth and remodeling of soft tissues. Mathematical Models and Methods in Applied Sciences, vol. 12, pp. 407-430.
16. Imatani, S.; Maugin, G. A. (2002): A constitutive model for material growth and its application to three-dimensional finite element analysis. Mechanics Research Communications, vol. 29, pp. 477-483.
17. Klisch, S. M.; van Dyke, T. J.; Hoger, A. (2001): A theory of volumetric growth for compressible elastic biological materials. Mathematics and Mechanics of Solids, vol. 6, pp. 551-575.
18. Kuhl, E.; Garikipati, K.; Arruda, E.; Grosh, K. (2004): Remodeling of biological tissue: Mechanically induced reorientation of a transversely isotropic chain network. http://arxiv.org/abs/q-bio.QM/0411037. submitted for publication.
19. Kuhl, E.; Menzel, A.; Garikipati, K. (2004a): On the convexity of transversely isotropic chain network models. Philosophical Magazine. accepted for publication.
20. Kuhl, E.; Menzel, A.; Steinmann, P. (2003): Computational modeling of growth - A critical review, a classification of concepts and two new consistent approaches. Computational Mechanics, vol. 32, no. 1-2, pp. 71-88.
21. Kuhl, E.; Steinmann, P. (2003): Theory and numerics of geometrically nonlinear open system mechanics. International Journal for Numerical Methods in Engineering, vol. 58, pp. 1593-1615.
22. Kuhl, E.; Steinmann, P. (2003a): Mass- and volume specific views on thermodynamics for open systems. Proceedings of the Royal Society of London A, vol. 459, pp. 2547-2568.
23. Kuhl, E.; Steinmann, P. (2004): Computational modeling of healing: An application of the material force method. Biomechanics and Modeling in Mechanobiology, vol. 2, pp. 187-203.
24. Lee, E. H. (1969): Elastic-plastic deformation at finite strains. Journal of Applied Mechanics, vol. 36, pp. 1-6.
25. Lubarda, V. A. (2004): Constitutive theories based on the multiplicative decomposition of deformation gradient: Thermoelasticity, elastoplasticity, and biomechanics. Applied Mechanics Reviews, vol. 57, no. 2, pp. 95-108.
26. Lubarda, V. A.; Hoger, A. (2002): On the mechanics of solids with a growing mass. International Journal of Solids and Structures, vol. 39, pp. 4627-4664.
27. Menzel, A. (2005): Modelling of anisotropic growth in biological tissues - A new approach and computational aspects. Biomechanics and Modeling in Mechanobiology, vol. 3, no. 3, pp. 147-171.
28. Menzel, A. (2005a): Anisotropic remodelling of biological tissues. In Holzapfel, G. A.; Ogden, R. W.(Eds): IUTAM Symposium on Mechanics of Biological Tissue. Springer. accepted for publication.
29. Ogden, R. W. (1997): Non-linear elastic deformations. Dover.
30. Rao, I. J.; Humphrey, J. D.; Rajagopal, K. R. (2003): Biological growth and remodeling: A uniaxial example with possible application to tendons and ligaments. CMES: Computer Methods in Engineering and Sciences, vol. 4, no. 3 & 4, pp. 439-455.
31. Rodriguez, E. K.; Hoger, A.; McCulloch, A. D. (1994): Stress-dependent finite growth in soft elastic tissues. Journal of Biomechanics, vol. 27, no. 4, pp. 455-467.
32. Taber, L. A. (1995): Biomechanics of growth, remodeling, and morphogenesis. ASME Applied Mechanics Reviews, vol. 48, no. 8, pp. 487-545.
33. Taber, L. A.; Perucchio, R. (2000): Modeling heart development. Journal of Elasticity, vol. 61, pp. 165-197.
34. van Rietbergen, B.; Huiskes, R.; Eckstein, F.; Rüegsegger, P. (2003): Trabecular bone tissue strains in the healthy and osteoporotic human femur. Journal of Bone and Mineral Research, vol. 18, no. 10, pp. 1781-1788.