1 An explicit integration scheme for hypo-elastic viscoplastic crystal plasticity K. ZHANG 1  , B. HOLMEDAL 1 , S. DUMOULIN 2 , O.S. HOPPERSTAD 3,4 1 Department of Materials Science and Engineering, Norwegian University of Science and Technology, NO- 7491 Trondheim, Norway 2 SINTEF Materials and Chemistry, NO-7465 Trondheim, Norway 3 Department of Structural Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway 4 Structural Impact Laboratory (SIMLab), Center for Research-based Innovation, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway Abstract: An explicit integration scheme for rate-dependent crystal plasticity (CP) has been developed in this work. Additive decomposition of the velocity gradient tensor into lattice and plastic parts is adopted for describing the kinematics; the Cauchy stress is calculated by using a hypo-elastic formulation, applying the Jaumann stress rate. This CP scheme has been implemented into a commercial finite element code (CPFEM). Uniaxial compression and rolling processes were simulated. The results show good accuracy and reliability of the integration scheme. The results were compared to simulations using one hyper-elastic CPFEM implementation which involves multiplicative decomposition of the deformation gradient tensor. It is found that the hypo-elastic implementation is only slightly faster and has a similar accuracy as the hyper-elastic formulation. Keywords: crystal plasticity; hypo-elasticity; hyper-elasticity; forward Euler integration 1. Introduction Crystal plasticity (CP) models originate from the physical aspect of plastic deformation, i.e. slip dominated plastic deformation [1]. Constitutive laws of single crystals together with homogenization methods across polycrystalline aggregates define the polycrystal plasticity model [2, 3]. Mechanical properties, texture evolution and other material phenomena can be simulated using CP models [2-5]. The main inputs into CP models are initial texture and material parameters. One key component of a crystal plasticity model at single grain level is the determination of shear strains or shear strain rates on slip systems, which can generally be solved using two different approaches, either rate-independent or rate-dependent. For the rate-independent method, the shear strain is determined to accommodate the prescribed plastic deformation using a minimum dissipation energy assumption [1]. Only the slip systems for which the resolved shear stress equals the critical resolved shear stress are considered to be active. It can be implemented numerically by solving linear equations or using e.g. the Simplex method with high computational efficiency [6]. Corresponding author: K. ZHANG, Tel.: +47-73594004. E-mail: kai.zhang@ntnu.no