摘要
提出了一个非光滑多重屈服面的CAP弹塑性Cosserat连续体模型。考虑到Cosserat连续体理论的特点,将其应力和应变速率向量的偏量和球量部分分离,针对各分屈服面分别被激活及某两个屈服面同时被激活的情况,发展了非线性本构速率方程积分的一致性算法,且率本构方程积分的返回映射算法和一致性弹塑性切线模量矩阵均为显式表示,避免了计算切线本构模量矩阵时的矩阵求逆。利用所发展的模型和一致性算法,数值模拟了平面应变条件下由应变软化及非关联塑性引起的边坡渐进破坏问题和隧道开挖问题。数值结果表明,所发展的模型和一致性算法在保持应变局部化问题的适定性、保证数值求解过程的收敛性和计算效率等方面具有良好的性能。
An elastoplastic Cosserat continuum model for CAP constitutive model with non-smooth multiplicative yield surfaces is presented. Splitting the scalar product of the stress rate and the strain rate into the deviatoric and the spherical parts, the consistent algorithm of the CAP elastoplastic model is derived according to one or two yielding surfaces being activated in the framework of Cosserat continuum theory, i.e. the return mapping algorithm for the integration of the rate constitutive equation and the closed form of the consistent elastoplastic tangent modulus matrix. The matrix inverse operation usually required in the calculation of elastoplastic tangent constitutive modulus matrix is avoided. The strain localization and progressive failure phenomena of the slope due to strain softening and the failure of the tunnel due to the excavation are numerically simulated using the developed model with corresponding finite element method. Numerical results of the plane strain examples illustrate the capability and good performance of the present model in keeping the well-posedness of the boundary value problems with strain softening behaviors and non-associated plasticity incorporation and ensuring the second order convergence rate and the computational efficiency of the model in numerical solution procedure.
出处
《岩石力学与工程学报》
EI
CAS
CSCD
北大核心
2008年第5期960-970,共11页
Chinese Journal of Rock Mechanics and Engineering
基金
国家自然科学基金重大研究计划项目(90715011)
国家自然科学基金资助项目(10672033)
大连理工大学青年教师培养基金项目
