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G. Capriz & P. Podio-Guidugli, Duality and stability questions for the linearized traction problem with live loads in elasticity. Pp. 70–78 of Stability in the Mechanics of Continua, F. H. Schroeder, Ed., Springer-Verlag, 1982.
P. Podio-Guidugli, G. Vergara Caffarelli & E. G. Virga, The role of ellipticity and normality assumptions in formulating live-boundary conditions in elasticity. Quart. Appl. Math. 44, pp. 659–664, 1987.
P. Podio-Guidugli, A variational approach to live loadings in finite elasticity. J. Elasticity 19, pp. 25–36, 1988.
M. J. Sewell, On configuration-dependent loading. Arch. Rational Mech. Anal. 23, pp. 327–351, 1967.
M. J. Sewell, On the calculation of potential functions defined on curved boundaries. Proc. Royal Soc. London Ser. A 286, pp. 402–411, 1966.
R. J. Knops & E. W. Wilkes, Theory of Elastic Stability. Handbuch der Physik VIa/3, C. Truesdell, Ed., Springer-Verlag, 1973.
P. Podio-Guidugli & G. Vergara Caffarelli, On a class of live traction problems in elasticity. Pp. 291–304 of Trends and Applications of Pure Mathematics to Mechanics, P. G. Ciarlet & M. Roseau, Eds., Springer-Verlag, 1984.
P. Podio-Guidugli, G. Vergara Caffarelli & E. G. Virga, Una formula di Green per il problema di carichi vivi dell'elastostatica linearizzata. Pp. 1–10 of Atti VII Congresso AIMETA, Vol. II, 1984.
G. Vergara Caffarelli, Green's formulas for linearized problems with live loads. In Metastability and Incompletely Posed Problems, I.M.A. Vol. Math. Appl. 3 (S. Antman and coeditors), Springer-Verlag, 1987.
S. J. Spector, On uniqueness in finite elasticity with general loading. J. Elasticity 10, pp. 145–161, 1980.
S. J. Spector, On uniqueness for the traction problem in finite elasticity. J. Elasticity 12, pp. 367–383, 1982.
T. Valent, Boundary Value Problems of Finite Elasticity. Springer-Verlag, 1988.
P. Podio-Guidugli & E. G. Virga, Sull'equilibrio di un involucro elastico pieno di gas. Atti Acc. Lincei Rend. Fis. (8) LXXXI. Nota I, pp. 287–292; Nota II, pp. 293–298, 1987.
D. Fisher, Configuration dependent pressure potentials. J. Elasticity 19, pp. 77–84, 1988.
J. L. Ericksen, Nilpotent energies in liquid crystal theory. Arch. Rational Mech. Anal. 10, pp. 189–196, 1962.
D. G. B. Edelen, The null set of the Euler-Lagrange operator. Arch. Rational Mech. Anal. 11, pp. 117–121, 1962.
L. C. Martins & P. Podio-Guidugli, On the local measures of mean rotation in continuum mechanics. Forthcoming.
M. E. Gurtin, An Introduction to Continuum Mechanics. Academic Press, 1981.
D. De Tommasi & S. Marzano, On the local analysis of continuum deformations. To appear in Meccanica.
P. G. Ciarlet, Mathematical Elasticity. Vol. I: Three-Dimensional Elasticity. North-Holland, 1988.
M. E. Gurtin, On the nonlinear theory of elasticity. Pp. 237–253 of Contemporary Developments in Continuum Mechanics and Partial Differential Equations, G. M. de la Penha & L. A. J. Medeiros, Eds., North-Holland, 1978.
B. Dacorogna, Weak Continuity and Weak Lower Semicontinuity of Non-Linear Functionals. Lecture Notes in Mathematics, Vol. 922, Springer-Verlag, Berlin, 1982.
B. Dacorogna, Direct Methods in the Calculus of Variations. In press.
P. L. Olver & J. Sivaloganathan, The structure of null Lagrangians. Nonlinearity, 1, pp. 389–398, 1988.
C. Truesdell, A First Course in Rational Continuum Mechanics. Academic Press, 1977. (Second edition in press.)
M. E. Gurtin & A. I. Murdoch, A continuum theory of elastic material surfaces. Arch. Rational Mech. Anal. 57, pp. 291–323, 1975.
F. Andreussi & M. E. Gurtin, On the wrinkling of a free surface. J. Appl. Phys. 48, pp. 3798–3799, 1977.
M. E. Gurtin & A. I. Murdoch, Surface stress in solids. Int. J. Solids Structures, pp. 431–440, 1978.
J. L. Ericksen, Some simpler cases of the Gibbs problem for thermoelastic solids. J. Thermal Stresses 4, pp. 13–30, 1981.
P. J. Flory, Thermodynamic relations for high elastic materials. Trans. Faraday Soc. 57, pp. 829–838, 1961.
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Dedicated to Bernard D. Coleman on his sixtieth birthday
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Podio-Guidugli, P., Caffarelli, G.V. Surface interaction potentials in elasticity. Arch. Rational Mech. Anal. 109, 343–383 (1990). https://doi.org/10.1007/BF00380381
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DOI: https://doi.org/10.1007/BF00380381