应变空间中一般加载规律的弹塑性本构关系

Elasto-plastic constitutive relation under general loading law in strain space

为了建立多维应力、应变空间的弹塑性本构关系,将一般加载规律一维全量理论的简单弹塑性模型推广到一般加载规律的多维增量理论,并且给出应力空间的加载函数和应变空间的加载函数以及它们之间的正确的变换关系.在此基础上,在应变空间中建立了推导一般加载规律的多维增量理论的本构关系的一种途径.应用这种途径,从应变空间的加载函数出发,推导了等向强化材料的一般加载规律的弹塑性本构关系.理论和实例表明,这种途径对等向强化材料、随动强化材料、理想弹塑性材料和热弹塑性问题都适用.

To establish the non -linear elasto-plastic incremental constitutive relations of multi-dimensional stress and strain space, the simple non-linear elasto-plastic model under general loading law is generalized from one-dimensional stress and strain space into multi-dimensional stress and strain space. The translation relation of the loading function in stress space and the loading function in strain space is given. An approach to get the derivation of non-linear elasto-plastic constitutive relation in strain space is established under general loading law. By using this approach, the expressions for the non - linear elasto-plastic incremental constitutive relation and the heat-elasto-plastic incremental constitutive relation are derived in strain space for isotropic hardening material. Theory and practice show that this approach is applicable to perfect elasto - plastic material, isotropic hardening material and kinematic hardening material.