A primal formulation for imposing periodic boundary conditions on conforming and nonconforming meshes
A primal formulation for imposing periodic boundary conditions on conforming and nonconforming meshes
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DOI：
10.1016/j.cma.2019.112663
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发表时间：
2020-02
影响因子：
7.2
通讯作者：
S. Aduloju;T. Truster
中科院分区：
文献类型：
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作者：
S. Aduloju;T. Truster
发展了一种变分多尺度非连续Galerkin（VMDG）方法，用于包含协调网格和非协调网格的区域的微尺度模拟。基本上，所施加的体积平均应变（或宏观应变）和域直径的乘积充当VMDG项内的强加位移跳跃。因此，该方法是适合于模拟块和真正的（自我）周期性的代表性体积元（RVE）的变形。原始位移场和宏观应变是唯一的未知量，因为该方法消除了运动约束的拉格朗日乘子（LM）强制。严格推导的方法提供了一个框架，以适应无论是宏观应力或宏观应变的驱动程序的微尺度边值问题。该方法首先是有限变形，然后专门为小变形运动学。数学修改的方法也研究了其对切线对称性和收敛速度的影响。对各向同性和各向异性材料的数值研究结果表明，该方法对于模拟复杂的协调和非协调RVE具有鲁棒性、精确性、稳定性和变分一致性。
A variational multiscale Discontinuous Galerkin (VMDG) method is developed for microscale modeling of domains containing conforming and non-conforming meshes. Essentially, the product of the applied volume-average strain (or macro-strain) and the domain diameter acts as an imposed displacement jump within the VMDG terms. Hence, the method is suitable for modeling deformation of both block and truly (self) periodic representative volume elements (RVEs). The primal displacement field and macro-strain are the only unknowns because the method eliminates the Lagrange multiplier (LM) enforcement of the kinematic constraint. Rigorous derivation of the method provides a framework to accommodate either the macro-stress or macro-strain as the driver of the microscale boundary value problem. The method is developed first for finite deformations and then specialized to small deformation kinematics. Algorithmic modifications to the method are also studied for their effects on tangent symmetry and convergence rate. The results from numerical studies for isotropic and anisotropic materials show that the proposed method is robust, accurate, stable and variationally consistent for modeling complicated conforming and nonconforming RVEs.