Generalization of a uniaxial elasto‐plastic material model based on the Prandtl‐Reuss theory. Issue 8 (8th May 2018)

• Record Type: Journal Article
• Authors: Gelke, S.; Ihlemann, J.
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 98:Issue 8(2018)
• Page Start: 1420
• Page End: 1435
• Publication Date: 2018-05-08
• Subjects: distortional hardening -- hypo‐elasticity -- metal plasticity -- Prandtl‐Reuss equations -- yield surface evolution; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201700200
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: The present paper introduces a material model following the Prandtl‐Reuss theory of time‐independent elasto‐plasticity. Applying a hypo‐elastic relation a material model for uniaxial tension/compression is derived which is completely based on scalar kinematics. Combined isotropic and kinematic hardening is provided in terms of nonlinear formulations showing saturation. The proof of thermodynamic consistency is supplied. Further, the model is generalized by the concept of representative directions and implemented for finite element application, so that arbitrary spatial deformation processes can be simulated. Especially, the elastic response of the model is investigated. Comparative simulations give evidence that spurious phenomena such as shear oscillation and numerically induced ratcheting are absent for the presented generalized material model. Distinct distortional hardening is obtained after generalization describing metal plasticity adequately. Finally the model is extended to show tension/compression anisotropy. Abstract : The present paper introduces a material model following the Prandtl‐Reuss theory of time‐independent elasto‐plasticity. Applying a hypo‐elastic relation a material model for uniaxial tension/compression is derived which is completely based on scalar kinematics. Combined isotropic and kinematic hardening is provided in terms of nonlinear formulations showing saturation. The proof of thermodynamic consistency is supplied. Further, the model is generalized by the concept of representative directions and implemented for finite element application, so that arbitrary spatial deformation processes can be simulated. Especially, the elastic response of the model is investigated. Comparative simulations give evidence that spurious phenomena such as shear oscillation and numerically induced ratcheting are absent for the presented generalized material model. Distinct distortional hardening is obtained after generalization describing metal plasticity adequately. Finally the model is extended to show tension/compression anisotropy.