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Plasticity of Finite Deformation and Anisotropic Materials, and Modeling of Fracture and Friction

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Modeling of Metal Forming and Machining Processes

Part of the book series: Engineering Materials and Processes ((EMP))

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Abstract

In Chapter 3, we developed the Eulerian formulation of metal forming problems. In deriving the constitutive equation of this formulation, it is assumed that the elastic and plastic parts of the rate of deformation tensor are additive. This assumption is usually true for small rotation. Further, the objective stress rate measure used in the constitutive equation, namely the Jaumann stress rate tensor, also remains objective only for small rotation. Therefore, we need to modify this constitutive equation for the case of finite deformation and rotation. In Sections 4.2 and 4.3 of this chapter, we first discuss the kinematics of finite deformation, and then the constitutive equation for the case of finite deformation and rotation. Since, in this case, the elastic and plastic parts of the rate of deformation tensor are not additive, the elastic and plastic parts of the constitutive equation are expressed separately. The elastic constitutive equation is expressed in terms of the stress and logarithmic strain tensors and the plastic constitutive equation in terms of the deviatoric stress and the plastic part of the rate of deformation tensors. Since no stress rates are involved, an objective stress rate measure is not needed in this constitutive equation. Next, we discuss the iterative solution procedure to be adopted while using this constitutive equation.

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(2008). Plasticity of Finite Deformation and Anisotropic Materials, and Modeling of Fracture and Friction. In: Modeling of Metal Forming and Machining Processes. Engineering Materials and Processes. Springer, London. https://doi.org/10.1007/978-1-84800-189-3_4

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  • DOI: https://doi.org/10.1007/978-1-84800-189-3_4

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  • Online ISBN: 978-1-84800-189-3

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