The analysis of damage and plastic deformation in metals is very important towards the full understanding of the various damage mechanisms in these materials. A coupled theory of damage mechanics and finite strain plasticity is proposed. The theory is based on a sound mathematical and mechanical background and is thermodynamically consistent. It is formulated using spatial coordinates utilizing a von Mises type yield criterion with both isotropic and kinematic hardening. The derivation is based on the concept of effective stress that was originally proposed by Kachanov  for the case of uniaxial tension. The plasticity model is first formulated in a fictitious undamaged configuration of the body. Then certain transformation equations are derived to transform this model into a damage-plasticity model in the damaged configuration of the body. Certain assumptions are made in order to make this transformation possible. These assumptions include small elastic strains and the hypothesis of elastic energy equivalence of Ref 17. The corotational stress rate equations are also discussed since they are used extensively in the constitutive relations. Therefore, the use of spin tensors is also discussed since they play a major role in the definition of the corotational rates. In addition, a modified spin tensor is proposed to be used in the coupled model. Furthermore, the nature of the fourth-rank damage effect tensor is discussed for a general state of deformation and damage. Also, the explicit matrix representation of this tensor is rigorously derived and can be used in future applications to solve plane stress and plane strain problems involving damage. Finally, the problem of finite simple shear is investigated using the proposed model. The resulting equations are solved using a Runge-Kutta-Verner fifth order and sixth order method. The stress-strain curves are obtained for a certain expression of the modified spin tensor and are compared with other spin tensors. Also, the evolution of the backstress and damage variables is presented. The results obtained compare favorably with previous results.
Finite Strain Plasticity and Damage in Constitutive Modeling of Metals With Spin Tensors
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Voyiadjis, G. Z., and Kattan, P. I. (March 1, 1992). "Finite Strain Plasticity and Damage in Constitutive Modeling of Metals With Spin Tensors." ASME. Appl. Mech. Rev. March 1992; 45(3S): S95–S109. https://doi.org/10.1115/1.3121396
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