| In this paper,the large deformation isotropic and anisotropic constitutive models on the intermediate configuration based on deformation gradient multiplication decomposition are discussed systematically.The relationship between the models and the superposed rigid body rotation on the intermediate configuration and its spin is studied,including the corresponding strategy to determine the spin,and the effective realization of constitutive integral is studied.As for the constitutive model with initial isotropy,the isotropic elastoplastic model is established by using the law of thermodynamics.By using the tensor function representation theory,it is proved that the inelastic spin on the intermediate configuration must be zero tensor under the condition that isotropic hardening or kinematic hardening with the back stress on the intermediate configuration is symmetric,and the model is independent of superposition rigid body rotation on the intermediate configuration.The model is pushed to the current configuration,which is represented by stress Jaumman elastic rate,deformation rate and elasto-plastic tangent model.In the process of establishing the model.Some special properties of isotropic functions are established by using the tensor function representation theory,and a simple relation of the tensor valued function from the intermediate configuration to the current configuration is derived.Based on these special properties and relations,the mathematical expressions of the model on different configurations are established,including rate-form constitutive equation and continuous tangential stiffness.In order to improve the integration efficiency of the above constitutive model,different from the existing algorithm using the main space,in the basis tensor space in the cylindrical coordinate system updated with the state,a concise and compact closed form of the equation is established,and the corresponding effective algorithm of constitutive integration is established.For multi-yield surface plasticity,the basis tensor is used to express the first and second derivatives of each yield surface and potential function,and a strategy is proposed to predict the regression by taking the middle direction of two plastic flow directions as the boundary of the critical region.For isotropic-kinematic hardening plasticity,the relative stress is used to replace the stress,and the corresponding return mapping algorithm is given.The above algorithms are implemented in a number of finite element examples and compared with the algorithm based on spectral decomposition.The results show that the compatibility and effectiveness of the constitutive integration algorithm are improved remarkably.As for the constitutive model with initial anisotropy,which is rate independence or rate dependence,the anisotropic elastic-plastic model and anisotropic viscoelastic model are respectively established by using the thermodynamic law.The energy function uses the structure tensor on the intermediate configuration,instead of the usual structure tensor on the initial configuration,thus the energy function is the isotropic function of the strain measure and the structure tensor,and the model is independent of the superposition constant rigid body rotation on the intermediate configuration.The effect of different spin on the model is discussed,and the equivalent spin are obtained by using the formula of spin rates independent of coordinates,which can guarantee the invariance of elastic rotation tensor,and the strategy of determining suitable spin for actual materials is given.A constitutive model considering different spin is implemented in finite element software,and the differences between them are discussed.The results show that the spin hypothesis should be carefully selected in the finite element simulation. |
