Deformation gradient based kinematic hardening model |
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| Institution: | 1. School of Computing and Mathematics, Keele University, Staffordshire ST5 5BG, UK;2. Department of Mechanics, Tianjin University, Tianjin 300072, China;3. Department of Civil and Environmental Engineering, Tufts University, MA, USA;1. National Institute for Health Research (NIHR) Biomedical Research Centre at Moorfields Eye Hospital NHS Foundation Trust and UCL Institute of Ophthalmology, London, UK;2. UCL Department of Mechanical Engineering, London, UK;3. UCL School of Pharmacy, London, UK;1. CETIM - Centre Technique des Industries Mécaniques, 5 avenue Félix Louat - BP 80067, F-60304 Senlis Cedex, France;2. Mines Douai, Polymers and Composites Technology & Mechanical Engineering Department, 941 rue Charles Bourseul - CS 10838, F-59508 Douai Cedex, France;3. ENSTA Bretagne, FRE CNRS 3744, IRDL, F-29200 Brest, France;1. CNRS, 3SR Lab, F-38000 Grenoble, France;2. Université de Grenoble/CNRS, TIMC-IMAG UMR 5525, Grenoble, France;3. Univ. Grenoble Alpes, 3SR Lab, F-38000 Grenoble, France |
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| Abstract: | A kinematic hardening model applicable to finite strains is presented. The kinematic hardening concept is based on the residual stresses that evolve due to different obstacles that are present in a polycrystalline material, such as grain boundaries, cross slips, etc. Since these residual stresses are a manifestation of the distortion of the crystal lattice a corresponding deformation gradient is introduced to represent this distortion. The residual stresses are interpreted in terms of the form of a back-stress tensor, i.e. the kinematic hardening model is based on a deformation gradient which determines the back-stress tensor. A set of evolution equations is used to describe the evolution of the deformation gradient. Non-dissipative quantities are allowed in the model and the implications of these are discussed. Von Mises plasticity for which the uniaxial stress–strain relation can be obtained in closed form serves as a model problem. For uniaxial loading, this model yields a kinematic hardening identical to the hardening produced by isotropic exponential hardening. The numerical implementation of the model is discussed. Finite element simulations showing the capabilities of the model are presented. |
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