An explicit integration scheme for rate-dependent crystal plasticity （CP） was developed. Additive decomposition of the velocity gradient tensor into lattice and plastic parts is adopted for describing the kinematics...An explicit integration scheme for rate-dependent crystal plasticity （CP） was developed. 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 roiling processes were simulated. The results show good accuracy and reliability of the integration scheme. The results were compared with 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.展开更多
In this paper,we establish a family of symplectic integrators for a class of high order Schrodinger equations with trapped terms.First,we find its symplectic structure and reduce it to a finite dimensional Hamilton sy...In this paper,we establish a family of symplectic integrators for a class of high order Schrodinger equations with trapped terms.First,we find its symplectic structure and reduce it to a finite dimensional Hamilton system via spatial discretization.Then we apply the symplectic Euler method to the Hamiltonian system.It is demonstrated that the scheme not only preserves symplectic geometry structure of the original system,but also does not require to resolve coupled nonlinear algebraic equations which is different with the general implicit symplectic schemes.The linear stability of the symplectic Euler scheme and the errors of the numerical solutions are investigated.It shows that the semi-explicit scheme is conditionally stable,first order accurate in time and 2l th order accuracy in space.Numerical tests suggest that the symplectic integrators are more effective than non-symplectic ones,such as backward Euler integrators.展开更多
文摘An explicit integration scheme for rate-dependent crystal plasticity （CP） was developed. 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 roiling processes were simulated. The results show good accuracy and reliability of the integration scheme. The results were compared with 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.
基金supported by the Provincial Natural Science Foundation of Jiangxi(No.2008GQS0054)the Foundation of Department of Education Jiangxi province(No.GJJ09147)+1 种基金the Foundation of Jiangxi Normal University(Nos.2057 and 2390)State Key Laboratory of Scientific and Engineering Computing,CAS.This work is partially supported by the Provincial Natural Science Foundation of Anhui(No.090416227).
文摘In this paper,we establish a family of symplectic integrators for a class of high order Schrodinger equations with trapped terms.First,we find its symplectic structure and reduce it to a finite dimensional Hamilton system via spatial discretization.Then we apply the symplectic Euler method to the Hamiltonian system.It is demonstrated that the scheme not only preserves symplectic geometry structure of the original system,but also does not require to resolve coupled nonlinear algebraic equations which is different with the general implicit symplectic schemes.The linear stability of the symplectic Euler scheme and the errors of the numerical solutions are investigated.It shows that the semi-explicit scheme is conditionally stable,first order accurate in time and 2l th order accuracy in space.Numerical tests suggest that the symplectic integrators are more effective than non-symplectic ones,such as backward Euler integrators.
