A polyconvex hyperelastic model for fiber-reinforced materials in application to soft tissues
Source abstract
Abstract
In this paper a generalized anisotropic hyperelastic constitutive model for fiber-reinforced materials is proposed. Collagen fiber alignment in biological tissues is taken into account by means of structural tensors, where orthotropic and transversely isotropic material symmetries appear as special cases. The model is capable to describe the anisotropic stress response of soft tissues at large strains and is applied for example to different types of arteries. The proposed strain energy function is polyconvex and coercive. This guarantees the existence of a global minimizer of the total elastic energy, which is important in the context of a boundary value problem.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Elasticity and Material Modeling · Elasticity and Wave Propagation · Composite Material Mechanics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (39)
Show source-provided references
1. Humphrey JD (2002) Cardiovascular Solid mechanics: cells, tissues, and organs. Springer, New York10.1007/978-0-387-21576-1 ↗
2. Fung YC (1993) Biomechanics mechanical properties of living tissues, 2nd ed. Springer, New York
3. Sacks MS (2000) J Elasticity 61:19910.1023/A:1010917028671 ↗
4. Holzapfel GA, Gasser TC, Ogden RW (2000) J Elasticity 61:110.1023/A:1010835316564 ↗
5. Schmid H, Nash MP, Young AA, Hunter PJ (2006) ASME J Biomech Eng 128:74210.1115/1.2244576 ↗
6. Arruda EM, Boyce MC (1993) J Mech Phys Solids 41:38910.1016/0022-5096(93)90013-6 ↗
7. Bischoff JE, Arruda EA, Grosh K (2002) J Appl Mech 69:57010.1115/1.1485754 ↗
8. Kuhl E, Garikipati K, Arruda EM, Grosh K (2005) Mech Phys Solids 53:155210.1016/j.jmps.2005.03.002 ↗
9. Lanir Y (1978) Biophys J 24:54110.1016/S0006-3495(78)85400-9 ↗
10. Kastelic J, Palley I, Baer E (1980) J Biomech 13:88710.1016/0021-9290(80)90177-3 ↗
11. Freed AD, Doehring TC (2005) ASME J Biomech Eng 127:58710.1115/1.1934145 ↗
12. Gasser TC, Ogden RW, Holzapfel GA (2006) J R Soc Interface 3:1510.1098/rsif.2005.0073 ↗
13. Holzapfel GA, Gasser TC, Ogden RW (2004) ASME J Biomech Eng 126:26410.1115/1.1695572 ↗
14. Merodio J, Ogden RW (2002) Arch Mech 54:525
15. Merodio J, Ogden RW (2003) Int J Solids Struct 40:470710.1016/S0020-7683(03)00309-3 ↗
16. Wilber JP, Walton JR (2002) Math Mech Solids 7:21710.1177/108128602027726 ↗
17. Chuong CJ, Fung YC (1983) ASME J Biomech Eng 105:26810.1115/1.3138417 ↗
18. Ball JM (1977) Arch Rat Mech Anal 63:33710.1007/BF00279992 ↗
19. Schröder J, Neff P (2003) Int J Solids Struct 40:40110.1016/S0020-7683(02)00458-4 ↗
20. Ball JM (2002) Geometry, mechanics, and dynamics. Springer, New York, p 310.1007/0-387-21791-6_1 ↗
21. Steigmann DJ (2003) Math Mech Solids 8:49710.1177/10812865030085004 ↗
22. Itskov M, Aksel N (2004) Int J Solids Struct 41:383310.1016/j.ijsolstr.2004.02.027 ↗
23. Itskov M, Ehret AE, Mavrilas D (2006) Biomech Model Mechanobiol 5:1710.1007/s10237-005-0006-x ↗
24. Balzani D, Neff P, Schröder J, Holzapfel GA (2006) Int J Solids Struct 43:605210.1016/j.ijsolstr.2005.07.048 ↗
25. Itskov M (2007) Tensor algebra and tensor analysis for engineers with application to continuum mechanics. Springer, Berlin
26. Itskov M (2002) ZAMM 82:53510.1002/1521-4001(200208)82:8<535::AID-ZAMM535>3.0.CO;2-U ↗
27. Truesdell C, Noll W (1965) Handbuch der Physik, vol III/3. Springer, Berlin
28. Ogden RW (1984) Non-linear elastic deformations. Ellis Horwood, Chichester
29. Zhang JM, Rychlewski J (1990) Arch Mech 42:267
30. Spencer AJM (1984) Continuum theory of the mechanics of fibre-reinforced composites. Springer Wien, p 110.1007/978-3-7091-4336-0 ↗
31. Boehler JP (1977) ZAMM 57:32310.1002/zamm.19770570608 ↗
32. Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, Cambridge10.1017/CBO9780511804441 ↗
33. Hill R (1968) J Mech Phys Solids 16:22910.1016/0022-5096(68)90031-8 ↗
34. Müller S, Qi T, Yan BS (1994) Ann Inst Henri Poincaré Analyse non linéaire 11:21710.1016/S0294-1449(16)30193-7 ↗
35. Ball JM (1996) Bull Amer Math Soc 33:26910.1090/S0273-0979-96-00648-9 ↗
36. Holzapfel GA, Sommer G, Gasser CT, Regitnig P (2005) Am J Physiol Heart Circ Physiol 289:204810.1152/ajpheart.00934.2004 ↗
37. Vande Geest JP, Sacks MS, Vorp DA (2004) ASME J Biomech Eng 126:81510.1115/1.1824121 ↗
38. Treloar LRG (1975) The physics of rubber elasticity, 3rd ed. Oxford University Press
39. Gent A (2004) Rubber Chem Technol 96:59