Material forces in finite elasto-plasticity with continuously distributed dislocations
In this paper we propose a thermodynamically consistent model for elasto-plastic material with structural inhomogeneities such as dislocations, subjected to large deformations, in isothermal processes. The plastic measure of deformation is represented by a pair of plastic distortion, and plastic connection with non-zero torsion (in order to have the non-zero Burgers vector). The developments are focused on the balance equations (for material forces and for physical force system), derived from an appropriate principle of the virtual power formulated within the constitutive framework of finite elasto-plasticity and on constitutive restrictions imposed by the free energy imbalance. The presence of the material forces (microforce and microstress momentum) is a key point in the exposure, and viscoplastic (generally rate dependent) constitutive representation are derived.
KeywordsFinite deformation Plastic distortion Configuration with torsion Plastic connection Stress momentum Material forces Free energy imbalance Principle of virtual power Dislocations
AMS Subject Classifications (2000)74C99 74A20
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- 2.Bilby BA (1960). Continuous distribution of dislocations. In: Sneddon, IN and Hill, R (eds) Progress in solid mechanics, pp 329–398. North-Holland, Amsterdam Google Scholar
- 3.Beju I, Soós E, Teodorescu PP (1983) Spinor and non-Euclidean tensor calculus with applications. Ed. Tehnica, Bucureşti Romania, Abacus Press, Tunbridge Wells, Kent, England (romanian version 1979)Google Scholar
- 5.Cleja-Ţigoiu S (1990) Large elasto-plastic deformations of materials with relaxed configurations – I. Constitutive assumptions, II. Role of the complementary plastic factor. Int J Eng Sci 28:171–180, 273–284Google Scholar
- 6.Cleja-Ţigoiu S (2001). A model of crystalline materials with dislocations. In: Cleja-Ţigoiu, S and Ţigoiu, V (eds) Proceedings of 5th international Seminar geometry continua and microstructures, pp 25–36. Sinaia, Romania Google Scholar
- 10.Cleja-Ţigoiu S and Soós E (1990). Elastoplastic models with relaxed configurations and internal state variables. Appl Mech Rev 43: 131–151 Google Scholar
- 15.Gupta A, Steigmann D, Stölken JS (2006) On the evolution of plasticity and incompatibility. Math Mech Solids. online: doi: 10.1177/1081286506064721
- 21.Hirth J and Lothe JP (1982). Theory of dislocations. Krieger Publishing, Malabar, Florida Google Scholar
- 22.Kondo K, Yuki M (1958) On the current viewpoints of non-Riemannian plasticity theory. In: RAAG memoirs of the unifying study of basic problems in engng and physical sciences by means of geometry II (D), Tokyo, pp 202–226Google Scholar
- 29.Maugin GA (1999) The thermomechanics of nonlinear irreversible behaviors. World ScientificGoogle Scholar
- 34.Steinmann P (1997) Continuum theory of dislocations: impact to single cristal plasticity. In: Owen DRJ, Onãte E, Hinton E Computational plasticity, fundamental and applications. CIME, Barcelona.Google Scholar
- 37.Teodosiu C (1970) A dynamic theory of dislocations and its applications to the theory of the elastic-plastic continuum. In: Simmons JA, de Witt R, Bullough R (eds) Fundamental aspects of dislocation theory, Nat Bur Stand (U.S.), Spec. Publ. 317, II, pp 837–876Google Scholar