基于微态方法的耦合韧性损伤的弹塑性本构模型

基于广义连续介质力学提出了一个热力学一致性的耦合微态韧性损伤的弹塑性本构模型。该模型遵循Forest的微态方法，在有限变形中提出引入额外的微态损伤因子及其一阶梯度以考虑材料的内部特征尺度。通过广义虚功原理得到了微态损伤的补充控制方程，对亥姆霍兹自由能进行扩展，得到了新的包含微态损伤变量的损伤能量释放率，在微态损伤的正则化作用下，采用隐式迭代更新局部损伤和应力等状态变量。基于Galerkin加权余量法，推导了以传统位移和微态损伤为基本未知量的有限元列式。利用该数值模型，对DP1000材料的单向拉伸实验和十字形零件的冲压实验进行了应变局部化与材料断裂的有限元分析。结果表明，该微态弹塑性损伤模型可以得到一致的有限元模拟响应曲线并收敛到实验曲线，从而避免发生网格依赖性问题。

The elastoplastic constitutive model coupled with ductile damage based on micromorphic approach

A thermodynamically-consistent micromorphic constitutive model fully coupled with ductile damage is formulated based on the generalized continuum mechanics.This model following the micromorphic approach proposed by Forest,introduces the new micromorphic damage and its first gradient to extend the local continuum damage model incorporating with the material characteristic length scale.Using the generalized principle of virtual work leads to the additional balance equations associated with micromorphic damage.The new damage energy release rate is derived from the extended Helmholtz free energy and regularized by the micromorphic damage.The micromorphic damage model as well as the classical displacements are implemented in finite element method.The numerical study of strain-softening and cracking in uniaxial tensile test and the cross-section drawing process of the DP1000 is performed.It is pointed out that the problem of mesh-dependency is avoided and the converged system responses are obtained and found to be consistent with experimental curves.