Numerical identification procedure between a micro-Cauchy model and a macro-second gradient model for planar pantographic structures
Numerical identification procedure between a micro-Cauchy model and a macro-second gradient model for planar pantographic structures
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平面缩放结构微柯西模型与宏观秒梯度模型的数值辨识过程
DOI：
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
I. Giorgio
中科院分区：
文献类型：
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作者：
I. Giorgio
为了设计在延伸方面表现出高韧性（与肌肉共享的特性）的超材料微观结构，最近有人提出考虑缩放结构（Dell’Isola 等人，Z Angew Math Phys 66(6):3473–3498, 2015）。可以使用标准柯西第一梯度理论在适当小的长度尺度上对此类结构进行建模（详细解析互连枢轴/圆柱体）。然而，这种建模选择的计算成本不允许研究更复杂的机械系统，包括例如许多缩放子结构。这里考虑的微观模型是二次各向同性圣维南第一梯度连续体，包括几何非线性并由两个拉梅参数表征。所引入的受电弓宏观二维模型的特征在于第一和第二放置梯度中的变形能量二次方。然而，正如 Dell’Isola 等人所强调的那样。 (Proc R Soc Lond A 472(2185):20150790, 2016)，如果必须描述大变形和大位移配置，则需要第二梯度刚度取决于第一放置梯度。本文提出的数值识别过程包括使用微观模型进行的多次数值模拟来拟合宏观本构参数。在少数变形问题中通过最佳拟合识别获得的参数也非常适合许多其他问题，这表明所提出的简化模型适合以相对较低的计算量获得有效模型。所提供的数值证据表明严格的数学同质化结果很可能成立。
In order to design the microstructure of metamaterials showing high toughness in extension (property to be shared with muscles), it has been recently proposed (Dell’Isola et al. in Z Angew Math Phys 66(6):3473–3498, 2015) to consider pantographic structures. It is possible to model such structures at a suitably small length scale (resolving in detail the interconnecting pivots/cylinders) using a standard Cauchy first gradient theory. However, the computational costs for such modelling choice are not allowing for the study of more complex mechanical systems including for instance many pantographic substructures. The microscopic model considered here is a quadratic isotropic Saint-Venant first gradient continuum including geometric nonlinearities and characterized by two Lamé parameters. The introduced macroscopic two-dimensional model for pantographic sheets is characterized by a deformation energy quadratic both in the first and second gradient of placement. However, as underlined in Dell’Isola et al. (Proc R Soc Lond A 472(2185):20150790, 2016), it is needed that the second gradient stiffness depends on the first gradient of placement if large deformations and large displacements configurations must be described. The numerical identification procedure presented in this paper consists in fitting the macro-constitutive parameters using several numerical simulations performed with the micro-model. The parameters obtained by the best fit identification in few deformation problems fit very well also in many others, showing that the reduced proposed model is suitable to get an effective model at relevantly lower computational effort. The presented numerical evidences suggest that a rigorous mathematical homogenization result most likely holds.
不同载荷下泡沫孔的塌陷准则
DOI：
10.1002/pamm.201110174
发表时间：
2011
期刊：
PAMM
影响因子：
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作者：
Ievdokymov M;H.Altenbach;V. Eremeyev
通讯作者：
V. Eremeyev