Della LongaLLonderoA. Thin walled beams with residual stress. J Elasticity2009; 96: 27–41.
3.
HogerA. On the residual stress possible in an elastic body with material symmetry. Arch Rat Mech Anal1985; 88: 271–290.
4.
HogerA. On the determination of residual stress in an elastic body. J Elasticity1986; 16: 303–324.
5.
ManC-SLuWY. Towards an acoustoelastic theory for measurement of residual stress. J Elasticity1987; 17: 159–182.
6.
McMahonJGorielyATaborM. Nonlinear morphoelastic plates I: Genesis of residual stress. Math Mech Solids2011; 8: 812–832.
7.
ParoniR. Theory of linearly elastic residually stressed plates. Math Mech Solids2006; 11: 137–159.
8.
ParoniR. The equations of motion of a plate with residual stress. Meccanica2006; 41: 1–21.
9.
ParoniRTomassettiG. A variational justification of linear elasticity with residual stress, J Elasticity2009; 97: 189–206.
10.
ParoniRTomassettiG. From non-linear elasticity to linear elasticity with initial stress via Γ-convergence. Contin Mech Thermodyn2011; 23: 347–361.
11.
SteigmannDJ. Linear theory for the bending and extension of a thin, residually stressed, fiber-reinforced lamina. Int J Eng Sci2009; 47: 1367–1378.
12.
SteigmannDJ. Elastic waves interacting with a thin, prestressed, fiber-reinforced surface film. Int J Eng Sci2010; 48: 1604–1609.
13.
SteigmannDJOgdenRW. A note on residual stress, lattice orientation and dislocation density in crystalline solids. J Elasticity2012; DOI: 10.1007/s10659-012-9378-1.
14.
AnzellottiGBaldoSPercivaleD. Dimension reduction in variational problems, asymptotic development in Γ-convergence and thin structures in elasticity. Asymptot Anal1994; 9: 61–100.
15.
FreddiLLonderoAParoniR. A simple variational derivation of slender rods theory. Appl Indust Math Italy II Ser Math Appl Sci2007; 75: 363–374.
16.
FreddiLMorassiAParoniR. Thin-walled beams: the case of the rectangular cross-section. J Elasticity2005; 76: 45–66.
17.
FreddiLMorassiAParoniR. Thin-walled beams: a derivation of Vlassov theory via Γ-convergence. J Elasticity2007; 86: 263–296.
FreddiLMuratFParoniR. Saint-Venant's theory for beams with multi-connected cross-section: justification and error estimate. Asymptot Anal2010; 70: 177–198.
20.
PercivaleD. Thin elastic beams: the variational approach to St. Venant’s problem. Asymptot Anal1999; 20: 39–59.
21.
CiarletPGDestuynderP. A justification of the two-dimensional linear plate model. J Mécanique1979; 18: 315–344.
22.
AdamsRA. Sobolev Spaces (Pure and Applied Mathematics, Vol. 65). New York: Academic Press, 1975.
23.
GurtinM. An Introduction to Continuum Mechanics (Mathematics in Science and Engineering, Vol. 158). New York: Academic Press, 1981.
24.
GiraultVRaviartPA. Finite Element Methods for Navier–Stokes Equations. Berlin: Springer-Verlag, 1986.
25.
OleinikOAShamaevASYosifianGA. Mathematical Problems in Elasticity and Homogenization. Amsterdam: North-Holland, 1992.
26.
Le DretH. Problemes Variationnels dans les Multi-domaines. Modélisation des Jonctions et Applications. Paris: Masson, 1991.
27.
Dal MasoG. An Introduction to Γ-Convergence. Boston, MA: Birkhäuser, 1993.
28.
ScardiaL. Asymptotic models for curved rods derived from nonlinear elasticity by Γ-convergence. Proc R Soc Edinburgh Sect A2009; 139: 1037–1070.
29.
TruesdellC. The Elements of Continuum Mechanics. New York: Springer-Verlag, 1966.
30.
FreddiLParoniR. The energy density of martensitic thin films via dimension reduction. Interfaces Free Bound2004; 6: 439–459.