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References
D.N. Arnold and R.S. Falk, Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials. Arch. Rational Mech. Anal. 98 (1987) 143–165.
E. Benvenuto, La Scienza delle Costruzioni e il suo Sviluppo Storico. Sansoni, Firenze (1981).
E. Benvenuto, An Introduction to the History of Structural Mechanics. Part I: Statics and Resistance of Solids. Part II: Vaulted Structures and Elastic Systems. Springer, Berlin (1991).
P. Bisegna and P. Podio-Guidugli, Mohr's arbelos. Meccanica 30 (1995) 417–424.
A. Campanella, P. Podio-Guidugli, and E.G. Virga, Restrizioni costitutive per materiali elastici lineari trasversalmente isotropi. In: Atti VIII Congr. AIMETA, Torino, Vol. II (1986) 465–470.
P.G. Ciarlet, Mathematical Elasticity, Vol. I: Three-Dimensional Elasticity. North-Holland, Amsterdam (1988). Vol. II: Plates. North-Holland, Amsterdam (1997).
G. Fichera, Existence theorems in elasticity. In: Handbuch der Physik VIa/2. Springer, Berlin (1972).
G. Fichera, Existence theorems in linear and semi-linear elasticity. Z. Angew. Math. Phys. 54 (1974) T24-T36.
S. Forte and M. Vianello, Symmetry classes for elasticity tensors. J. Elasticity 43 (1996) 81–108.
M. François, G. Geymonat, and Y. Berthaud, Determination of the symmetries of an experimentally determined stiffness tensor: application to acoustic measurements. Int. J. Solids Structures 35 (1998) 4091–4106.
M.E. Gurtin, The linear theory of elasticity. In: Handbuch der Physik VIa/2, Springer, Berlin (1972).
M.E. Gurtin, An Introduction to Continuum Mechanics. Academic Press, New York (1981).
P.R. Halmos, Finite-Dimensional Vector Spaces. Van Nostrand (1958).
M.J. Horta Dantas, On the boundary value problems of linear elasticity with constraints. J. Elasticity 54 (1999) 93–111.
O.D. Kellogg, Foundations of Potential Theory. Springer, Berlin (1929), reprinted by Dover (1953).
R.J. Knops and L.E. Payne, Uniqueness Theorems in Linear Elasticity, B.D. Coleman (ed.), Springer Tracts in Natural Philosophy, Vol. 19. Springer, Berlin (1971).
M.R. Lancia, P. Podio-Guidugli, and G. Vergara Caffarelli, Null Lagrangians in linear elasticity. Math. Models Methods Appl. Sci. 5 (1995) 415–427.
J.L. Lions and E. Magenes, Problèmes aux Limites non Homogènes et Applications. Dunod, Paris (1968).
L.C. Martins and P. Podio-Guidugli, A new proof of the representation theorem for isotropic, linear constitutive relations. J. Elasticity 8 (1978) 319–322.
L.C. Martins and P. Podio-Guidugli, A variational approach to the polar decomposition theorem. Rend. Accad. Naz. Lincei Classe Sci. Fis. Mat. Nat. 66 (6) (1979) 487–493.
S.G. Mikhlin, Mathematical Physics, an Advanced Course. North-Holland, Amsterdam (1970).
W. Noll, A general framework for problems in the statics of finite elasticity. In: G.M. de la Penha and L.A. Medeiros (eds), Contemporary Developments in Continuum Mechanics and Partial Differential Equations. North-Holland, Amsterdam (1978).
A.C. Pipkin, Constraints in linearly elastic materials. J. Elasticity 6 (1976), 179–193.
P. Podio-Guidugli, Inertia and invariance. Annali Mat. Pura Appl. (IV) CLXXII (1997) 103–124.
P. Podio-Guidugli, The compatibility constraint in linear elasticity. J. Elasticity 59 (2000) in press.
P. Podio-Guidugli and G. Vergara Caffarelli, Surface interaction potentials in elasticity. Arch. Rational Mech. Anal. 109 (1990) 343–383.
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Podio-Guidugli, P. A Primer in Elasticity. Journal of Elasticity 58, 1–104 (2000). https://doi.org/10.1023/A:1007672721487
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DOI: https://doi.org/10.1023/A:1007672721487