Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Thermomechanics


Author: Hans Ziegler
Journal: Quart. Appl. Math. 30 (1972), 91-107
DOI: https://doi.org/10.1090/qam/99737
MathSciNet review: QAM99737
Full-text PDF Free Access

References | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] D. C. Drucker, H. J. Greenberg and W. Prager, The safety factor of an elastic-plastic body in plane stress, J. Appl. Mech. 18, 371 (1951) MR 0051119
  • [2] D. C. Drucker, W. Prager and H. J. Greenberg, Extended limit design theorems for continuous media, Quart. Appl. Math. 9, 381 (1952) MR 0045573
  • [3] R. v. Mises, Mechanik der plastischen Formänderung von Kristallen, Z. angew. Math. Mech. 8, 161 (1928)
  • [4] W. Prager, Probleme der Plastizitatstheorie, Birkhäuser, Basel 1954; see also Introduction to plasticity, Addison-Wesley, Reading, 1959. MR 0105910
  • [5] W. T. Koiter, Stress-strain relations, uniqueness and variational theorems for elastic-plastic materials with a singular yield surface, Quart. Appl. Math. 11, 350 (1953) MR 0059769
  • [6] D. C. Drucker and H. G. Hopkins, Combined concentrated and distributed load on ideally-plastic circular plates, in Proc. 2nd U. S. Nat. Congr. Applied Mech., Ann Arbor 1954, New York 1955, p. 517
  • [7] D. C. Drucker, Limit analysis of cylindrical shells under axially-symmetric loading, in Proc. 1st Midwestern Conf. Solid Mech., Urbana, 1953, p. 158
  • [8] R. M. Haythornthwaite and R. T. Shield, A note on the deformable region in a rigid-plastic structure, J. Mech. Phys. Solids 6, 127 (1958) MR 0092466
  • [9] P. G. Hodge, Jr., The rigid-plastic analysis of symmetrically loaded cylindrical shells, J. Appl. Mech. 21, 336 (1954) MR 0069015
  • [10] H. G. Hopkins and W. Prager, The load-carrying capacity of circular plates, J. Mech. Phys. Solids 2, 1 (1953) MR 0057735
  • [11] H. G. Hopkins and A. J. Wang, Load-carrying capacities for circular plates of perfectly plastic material with arbitrary yield condition, J. Mech. Phys. Solids 3, 117 (1954) MR 0066912
  • [12] H. G. Hopkins, On the plastic theory of plates, Proc. Roy. Soc (A) 241, 153 (1957) MR 0087363
  • [13] H. G. Hopkins and W. Prager, On the dynamics of plastic circular plates, Z. angew Math. Phys. 5, 317 (1954) MR 0066910
  • [14] E. H. Lee and P. S. Symonds, Large plastic deformation of beams under transverse impact, J. Appl. Mech. 19, 308 (1952)
  • [15] E. T. Onat, and W. Prager, Limit analysis of arches, J. Mech. Phys. Solids 1, 73 (1953) MR 0052967
  • [16] E. T. Onat and W. Prager, The influence of axial forces on the collapse load of frames, in Proc. 1st Midwestern Conf. Solid Mechanics, Urbana, 1953, p. 40
  • [17] E. T. Onat, The plastic collapse of cylindrical shells under axially symmetrical loading, Quart. Appl. Math. 13, 63 (1955) MR 0069016
  • [18] E. T. Onat and W. Prager, Limit analysis of shells of revolution, Koninkl. Nederl. Akad. Wet., Proc. (B) 57, 534 (1954) MR 0066913
  • [19] W. H. Pell and W. Prager, Limit design of plates, in Proc. 1st U. S. Nat. Congr. Appl. Mech., Chicago 1951, New York 1952, p. 547 MR 0054505
  • [20] W. Schumann, On limit analysis of plates, Quart. Appl. Math. 16, 61 (1958) MR 0102256
  • [21] A. J. Wang and H. G. Hopkins, On the plastic deformation of built-in circular plates under impulsive load, J. Mech. Phys. Solids 3, 22 (1954) MR 0066911
  • [22] A. J. Wang, The permanent deflection of a plastic plate under blast loading, J. Appl. Mech. 22, 357 (1955)
  • [23] H. Ziegler, On the theory of the plastic potential, Quart. Appl. Math. 19, 39 (1961) MR 0122161
  • [24] D. C. Drucker, A more fundamental approach to plastic stress-strain relations, in Proc. 1st U. S. Congr. Appl. Mech., Chicago, 1951, New York 1952, p. 487 MR 0054502
  • [25] G. I. Taylor, A connection between the criterion of yield and the strain-ratio relationship in plastic solids, Proc. Roy. Soc. (A) 191, 441 (1947) MR 0022519
  • [26] R. Hill, A variational principle of maximum plastic work in classical plasticity, Quart. J. Mech. Appl. Math. 1, 18 (1948) MR 0025384
  • [27] J. F. W. Bishop and R. Hill, A theory of plastic distortion of a polycristalline aggregate under combined stresses, Phil. Mag. (7) 42, 414 (1951). MR 0041691
  • [28] J. Kestin and J. R. Rice, Paradoxes in the application of thermodynamics to strained solids, in A critical review of thermodynamics, Mono Book, Baltimore, 1970
  • [29] J. R. Rice, Inelastic constitutive relations for solids: an internal variable theory and its application to metal plasticity, Brown University Report N00014-67-A-0191-0003/12, Providence.
  • [30] L. Onsager, Reciprocal relations in irreversible processes, Phys. Rev. 37 (II), 405 (1931) and 38 (II), 2265 (1931)
  • [31] M. A. Biot, Theory of stress-strain relations in anisotropic viscoelasticity and relaxation, J. Appl. Phys. 25, 1385 (1954)
  • [32] M. A. Biot, Variational principles in irreversible thermodynamics with application to viscoelasticity, Phys. Rev. 97, 1463 (1955) MR 0070514
  • [33] M. A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys. 27, 240 (1956) MR 0077441
  • [34] T. Alfrey, Non-homogeneous stresses in visco-elastic media, Quart. Appl. Math. 2, 113 (1944) MR 0010499
  • [35] N. J. Hoff, Approximate analysis of structures in the presence of moderately large creep deformations, Quart. Appl. Math. 12, 49 (1954) MR 0061004
  • [36] H. Ziegler, A possible generalization of Onsager's theory, in H. Parkus and L. I. Sedov, editors, IUTAM symp. on irreversible aspects of continuum mechanics, Vienna, Springer, Vienna, 1968, p. 411
  • [37] H. Ziegler, An attempt to generalize Onsager's principle, and its significance for rheological problems, Z. angew. Math. Phys. 9b, 748 (1958) MR 0094943
  • [38] H. Ziegler, Proof of an orthogonality principle in irreversible thermodynamics, Z. angew. Math. Phys. 21, 853 (1970)
  • [39] J. W. Gibbs, Elementary principles in statistical mechanics, in The collected works, Yale Univ. Press, New Haven, 1948, vol. II
  • [40] H. Ziegler and L. K. Yu, Incompressible Reiner-Rivlin fluids obeying the orthogonality condition, Ing. Arch. 41 (1972), at press
  • [41] L. K. Yu, Further applications of the orthogonality principle to incompressible Reiner-Rivlin fluids, Ing. Arch. 41 (1971), at press
  • [42] H. Ziegler, Systems with internal parameters obeying the othogonality condition, Z. angew. Math. Phys. 23 (1972), at press
  • [43] S. R. DeGroot, Thermodynamics of irreversible processes, North-Holland, Amsterdam 1952, p. 196
  • [44] H. Ziegler, Zwei Extremalprinzipien der irreversiblen Thermodynamik, Ing. Arch. 30, 410 (1961) MR 0134717
  • [45] H. Ziegler, Die statistischen Grundlagen der irreversiblen Thermodynamik, Ing. Arch. 31, 317 (1962) MR 0153414
  • [46] H. Ziegler, Some extremum principles in irreverible thermodynamics, with application to continuum mechanics, in I. N. Sneddon and R. Hill, editors, Progr. Solid Mech. 4, 91 (1963) MR 0163470
  • [47] H. Ziegler, Thermodynamic considerations in continuum mechanics, The 1964 Minta Martin Lecture, MIT and AIAA (1964)
  • [48] H. Ziegler, Thermodynamik der Deformationen, in Proc. 11th Congr. Appl. Mech. Munich 1964, Springer, Berlin 1966, p. 99
  • [49] W. Traupel, Die Grundlagen der Thermodynamik, Braun, Karlsruhe 1971, p. 9
  • [50] W. Noll, On the continuity of the solid and fluid states, J. Rational Mech. Anal. 4, 13 (1955) MR 0067670
  • [51] M. Reiner, A mathematical theory of dilantancy, Amer. J. Math. 67, 350 (1945) MR 0012594
  • [52] R. S. Rivlin, The hydrodynamics of non-Newtonian fluids, Proc. Roy. Soc. A 193, 260 (1948) MR 0025847
  • [53] K. Weissenberg, A continuum theory of rheological phenomena, Nature 159, 310 (1947)
  • [54] R. S. Rivlin, Steady flow of non-Newtonian fluids through tubes, Quart. Appl. Math. 14, 299 (1956) MR 0090335
  • [55] A. Sommerfeld, Vorlesungen über Theoretische Physik, vol. 5, Thermodynamik und Statistik, bearbeitet und ergänzt von F. Bopp und J. Meixner, Akad. Verlagsgesellschaft, Leipzig 1965, pp. 293 and 309 MR 0062030
  • [56] R. H. Fowler, Statistical mechanics, Cambridge University Press, Cambridge, 1929 MR 643100


Additional Information

DOI: https://doi.org/10.1090/qam/99737
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society