Computational homogenization of cellular materials
Computational homogenization of cellular materials
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DOI：
10.1016/j.ijsolstr.2014.02.029
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发表时间：
2014-06
影响因子：
3.6
通讯作者：
V. Nguyen;L. Noels
中科院分区：
文献类型：
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作者：
V. Nguyen;L. Noels
在这项工作中，我们建议使用二阶多尺度计算均匀化方法研究细胞材料的行为。在宏观加载过程中，薄型构件（如胞壁或胞杆）会发生微屈曲。即使构成微观结构的材料的行为仍然是椭圆的，均匀化的行为也会失去其椭圆性。在这种情况下，形成一个局部化带，并在宏观尺度上传播。当局部化发生时，标准方法中的局部作用假设不再适用，即材料点上的应力状态仅取决于该点的应变状态，这促使采用二阶多尺度计算均匀化格式。在该方案的宏观尺度上，采用不连续伽辽金法求解Mindlin应变梯度连续体。在微观尺度上，考虑了典型体积单元的经典有限元分辨率。由于由元胞材料生成的网格在边界上显示空洞，并且通常不一致，因此重新制定了周期边界条件，并通过多项式插值方法强制执行。在两个尺度都存在不稳定现象的情况下，采用弧长路径跟踪技术同时解决宏观和微观问题。
In this work we propose to study the behavior of cellular materials using a second-order multi-scale computational homogenization approach. During the macroscopic loading, micro-buckling of thin components, such as cell walls or cell struts, can occur. Even if the behavior of the materials of which the micro-structure is made remains elliptic, the homogenized behavior can lose its ellipticity. In that case, a localization band is formed and propagates at the macro-scale. When the localization occurs, the assumption of local action in the standard approach, for which the stress state on a material point depends only on the strain state at that point, is no-longer suitable, which motivates the use of the second-order multi-scale computational homogenization scheme. At the macro-scale of this scheme, the discontinuous Galerkin method is chosen to solve the Mindlin strain gradient continuum. At the microscopic scale, the classical finite element resolutions of representative volume elements are considered. Since the meshes generated from cellular materials exhibit voids on the boundaries and are not conforming in general, the periodic boundary conditions are reformulated and are enforced by a polynomial interpolation method. With the presence of instability phenomena at both scales, the arc-length path following technique is adopted to solve both macroscopic and microscopic problems.