Multi-slip and non-local evolution equations in finite elasto-plastic materials with dislocations
Keywords:dislocations, non-Schmid flow rule, crystalline materials, non-local evolution equations, finite elasto-plasticity
The paper deals with elasto-plastic models which describe the behaviour at large strain of materials with crystalline structure, which contain continuously distributed dislocations. The non-local evolution equations for dislocation densities are derived to be compatible with the the principle of free energy imbalance, when a nonSchmid flow rule describes the evolution of the plastic distortion within the crystalographic systems. We analyze the constitutive restrictions that follow from the principle of the free energy imbalance for the case when the free energy density is dependent on the scalar dislocation densities and their gradients, and for a more general case when the influence of the tensorial measure of dislocations is considered too.
ASARO, R.J., NEEDLEMAN, A., Texture development and strain hardening in rate dependent polycrystals, Acta Metallurgica, 33, pp. 923-953, 1985.
BILBY, B.A., Continuous distribution of dislocations, in: ”Progress in Solid Mechanics” (eds. Sneddon, I.N., Hill, R.), North-Holland: Amsterdam, pp. 329-398, 1960.
BORTOLONI, L., CERMELLI, P., Dislocation Patterns and Work-Hardening in Crystalline Plasticity, J. Elasticity, 76, pp. 113-138, 2004.
CERMELLI, P., GURTIN, M.E., Geometrically necessary dislocations in viscoplastic single crystals and bicrystals undergoing small deformations, International Journal of Solids and Structures, 39, pp. 6281-6309, 2002.
CLAYTON, J.D., MCDOWELL, D.L., BAMMANN, D.J., Modeling dislocations and disclinations with finite micropolar elastoplasticity, Int. J. Plast., 16, pp. 210-256, 2006.
CLEJA-T¸ IGOIU, S., SOOS, E., ´ Elastoplastic models with relaxed configurations and internal state variables, Applied Mechanics Reviews, 43, pp. 131-151, 1990.
CLEJA-T¸ IGOIU, S., Large elasto-plastic deformations of materials with relaxed configurations- I. Constitutive assumptions, II. Role of the complementary plastic factor, Int. J. Engng. Sci. 28, pp. 171-180, 273-284, 1990.
CLEJA-T¸ IGOIU, S., Couple stress and non-Riemannian plastic connection in finite elastoplasticity, ZAMP, 53, pp. 996-1013, 2002.
CLEJA-T¸ IGOIU, S., Material Forces in Finite Elastoplasticity with Continuously Distributed Dislocations, Int. J. Fracture, 147, pp. 67-81, 2007.
CLEJA-T¸ IGOIU, S., FORTUNE, D., VALL ´ EE, C., ´ Torsion equation in anisotropic elasto-plastic materiials with continuously distributed dislocations, Math. Mech. Solids, 13, pp. 667-689, 2008.
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