Comparison of gradient elasticity models for the bending of micromaterials
Comparison of gradient elasticity models for the bending of micromaterials
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DOI：
10.1016/j.commatsci.2015.10.031
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发表时间：
2016-04
影响因子：
3.3
通讯作者：
C. Liebold;W. Müller
中科院分区：
文献类型：
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作者：
C. Liebold;W. Müller
在各向同性材料和小变形静弹性理论的背景下，考虑了两种高阶连续介质力学理论。从广义连续体的角度出发，提出了应变梯度和微极理论的一种修正/简化方法。利用欧拉-伯努利梁假设，导出了每个扩展理论的解析解策略。在一个开源的有限元环境中，利用有限元实现了由平衡公式导出的四阶微分方程的数值解。在由环氧树脂和聚合物SU-8制成的微梁的AFM实验中，记录了力和挠度数据。结果，微光束的正尺寸效应取决于厚度被观察和量化。采用最小二乘法拟合了材料长度尺度参数和弹性模量，并与文献值进行了比较。
In the context of static elasticity theory for isotropic materials and small deformations, two continuum mechanical theories of higher order are considered. Thinking of generalized continua, a modification/simplification of the strain gradient- and the micropolar theory is shown. An analytical solution strategy is derived for each extended theory using the Euler–Bernoulli beam assumptions. A numerical solution of the resultant differential equations of fourth order, derived from the equilibrium formulation, is realized using a finite element implementation in an open source FE environment. In AFM experiments with microbeams, made of epoxy and of the polymer SU-8, force and deflection data is recorded. As a result, positive size effects depending on thickness are observed and quantified for the microbeams. The material length scale parameters and the elastic moduli are fitted with a least square approach and compared to literature values.