Elasto-plastic finite deformation models for anisotropic damage


  • S. Cleja-Tigoiu


tensorial damage variables, elastic, plastic, free energy imbalance, evolution equations


The paper deals with finite deformation elasto-plastic models with anisotropic damage. The models are mathematically coherent and consistent with free energy imbalance principle. One model is based on the existence of deformation-like damage tensor, F d , which characterizes the passage from the undamaged, stress free configuration to the damaged and stress free configuration. The other one involves a symmetric defect density tensor, which is a measure of non-metricity of the so-called plastic connection, there is a gradient-like model. The constitutive and evolution equations are derived to be compatible with the free energy imbalance principle, which has been reformulated to be applicable to the elasto-plastic materials with damaged structure. We assumed that the plastic flow and the development of damage, i.e. the micro voids and micro cracks, are distinct irreversible mechanisms during the deformation process.


BRUNIG, M., ¨ An anisotropic ductile damage model based on irreversible thermodynamics, Int. J. Plast., 19, 10, pp. 1679–1713, 2003.

BRUNIG, M., RICCI, S., ¨ Nonlocal continuum theory of anisotropically damaged metals, Int. J. Plast., 21, 7, pp. 1346–1382, 2005.

CLAYTON, J.D., MCDOWELL, D.L., BAMMANN, D.J., Modeling dislocations and disclinations with finite micropolar elastoplasticity, Int. J. Plast., 22, 2, pp. 210–256, 2006.

CLEJA-T¸ IGOIU, S., SOOS, E., ´ Elastoplastic models with relaxed configurations and internal state variables, Appl. Mech. Rev., 43, 7, pp. 131–151, 1990.

CLEJA-T¸ IGOIU, S., Material forces in finite elasto-plasticity with continuously distributed dislocations, Int. J. Fract., 147, pp. 67 81, 2007.

CLEJA-T¸ IGOIU, S., Elasto-plastic materials with lattice defects modeled by second order deformations with non-zero curvature, Int. J. Fract., 166, pp. 61–75, 2010.

CLEJA-T¸ IGOIU, S., Elasto-plastic model with second order defect density tensor, 14-th ESAFORM Conference on Material Forming, Belfast, G.B., April 27-29, 2011, in: AIP Conference Proceedings, Vol. 1353, ESAFORM 2011, pp. 1505–1510.

CLEJA-T¸ IGOIU, S., Anisotropic damage in elasto-plastic materials with structural defects, chap.6 in : Multiscale Modelling in Sheet Metal Forming (ed. D. Banabic), Springer, 2016, pp. 301–350.

CLEJA-T¸ IGOIU, S., T¸ IGOIU, V., Strain gradient effects in finite elasto-plastic damaged materials, Int. J. Damage Mech., 20, 4, pp. 484–577, 2011.