An anisotropic elastic formulation for configurational forces in stress space
Source abstract
Abstract
A new variational principle for an anisotropic elastic formulation in stress space is constructed, the Euler–Lagrange equations of which are the equations of compatibility (in terms of stress), the equilibrium equations and the traction boundary condition. Such a principle can be used to extend recently obtained configurational balance laws in stress space to the case of anisotropy.
Source: expertdata · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Elasticity and Material Modeling · Composite Material Mechanics · Numerical methods in engineering
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (18)
Show source-provided references
1. Eshelby JD (1975). The elastic energy-momentum tensor. J Elasticity 5: 321–33510.1007/BF00126994 ↗
2. Eshelby JD (1956). The continuum theory of lattice defects. In: Seitz, F and Turnbull, D (eds) Solid state physics, pp 79–144. Academic Press, New York
3. Gelfand IM, Fomin SV (2000) Calculus of variations, Dover
4. Georgievskii DV, Pobedrya BYe (2004) The number of independent compatibility equations in the mechanics of deformable solids. Prikl Mat Mekh 68(6):1043–1048 (trans: J Appl Math Mech 68:941–946 (2004))10.1016/j.jappmathmech.2004.11.015 ↗
5. Gupta A, Markenscoff X (2007) Configurational forces as dissipative mechanisms: a revisit, Comptes Rendus Mecanique (In press)10.1016/j.crme.2007.11.004 ↗
6. Kröner E (1981) Continuum theory of defects. In: Balian R et al (eds) Les Houches, Session 35, 1980 – Physique des defauts. North-Holland, New York, pp 215–315
7. Kucher V, Markenscoff X and Paukshto M (2004). Some properties of the boundary value problem of linear elasticity in terms of stresses. J Elasticity 74(2): 135–14510.1023/B:ELAS.0000033858.20307.d8 ↗
8. Li S, Gupta A and Markenscoff X (2005). Conservation laws of linear elasticity in stress formulations. Proc Roy Soc Lon A 461: 99–11610.1098/rspa.2004.1347 ↗
9. Markenscoff X (1976). Independent 4th-order elastic coefficients for quartz. Appl Phys Lett 29(12): 768–77010.1063/1.88942 ↗
10. Markenscoff X and Gupta A (2007). Configurational balance laws for incompatibility in stress space. Proc R Soc Lond A 463: 1379–139210.1098/rspa.2007.1828 ↗
11. Maugin GA (1993). Material inhomogeneities in elasticity. Chapman & Hall, London10.1007/978-1-4899-4481-8 ↗
12. Noether E (1918) Invariante variationsprobleme, Göttinger Nachrichten, (Mathematisch-physikalische Klasse) 2:235–257 (trans: Transport Theory and Statistical Physics 1:186–207 (1971))10.1080/00411457108231446 ↗
13. Pobedrja BE (1980). A new formulation of the problem in mechanics of a deformable solid body under stress. Soviet Math Doklady 22(1): 88–91
14. Pobedria BE, Holmatov T (1982) On the existence and uniqueness of solutions in the elasticity theory problem with stresses, Vestnik Moskovskogo Universiteta, Seriya 1 (Matematika Mekhanika), 1, pp 50–51
15. Pobedrya BYe (1994) The problem in terms of a stress tensor for an anisotropic medium. Prikl Mat Mekh 58(1):77–85. (trans: J Appl Math Mech 58(1):81–89 (1994))10.1016/0021-8928(94)90032-9 ↗
16. Smith GF and Rivlin RS (1957). The anisotropic tensors. Quart Appl Math 15(3): 308–31410.1090/qam/101883 ↗
17. Smith GF (1970). The crystallographic property tensors of orders 1 to 8. Ann N Y Acad Sci 172(5): 57–10610.1111/j.1749-6632.1970.tb34968.x ↗
18. Weyl H (1946). The classical groups, their invariants and representations. Princeton Univ Press, Princeton, NJ