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考虑非关联流动法则以及各向同性硬化条件,采用广义中点法(Generalized Midpoint Method,GMM)进行Drucker-Prager(DP)弹塑性本构关系数值积分,给出调整后最终应力的解析解。GMM属于隐式算法,具有良好的计算精度与数值稳定性;最近点投影法(Closest Point Project Method,CPPM)是其特例,具有一阶精度并且无条件稳定。DP塑性势函数的特殊性质导致上述GMM解由初始应力状态与应变增量显式确定,无需迭代求解,因此计算效率大幅提高,同时避免了迭代过程的收敛性问题。数值算例证明:当加载偏离角度较大时,GMM(ξ=1/2)的计算精度高于CPPM,可适应更大的加载步长;而对于比例加载,任意GMM等同于精确解,采用CPPM可获得最高的计算效率。推导了满足DP屈服准则厚壁圆筒的弹塑性理论解,对比验证算法精度。采用非关联流动各向同性线性硬化DP材料模拟厚壁圆筒变形局部化效应。
Considering the non-associated flow laws and the isotropic hardening conditions, the numerical integration of Drucker-Prager (DP) elasto-plastic constitutive equation is given by Generalized Midpoint Method (GMM), and the analytical solution of the final stress after adjustment is given. GMM is an implicit algorithm with good computational accuracy and numerical stability. Closest Point Project Method (CPPM) is a special case of it. It has first-order accuracy and is unconditionally stable. The special properties of DP plastic potential function cause the above GMM solution to be explicitly determined by the initial stress state and strain increment without iterative solution. Therefore, the computational efficiency is greatly improved, and the convergence of the iterative process is avoided. The numerical examples show that the GMM (ξ = 1/2) is more accurate than CPPM when the loading deviation angle is larger, and it can accommodate larger loading steps. For proportional loading, any GMM is equivalent to the exact solution. CPPM achieves the highest computational efficiency. The elastic-plastic theoretical solution of the thick-walled cylinder satisfying the DP yield criterion is derived, and the accuracy of the algorithm is verified. Simulation of Thickness Cylindrical Deformation Localization Using Uncoordinated Flow Isotropic Linearly Hardened DP Material.