Uchida Makoto, Kaneko Yoshihisa
Graduate School of Engineering, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka-city, 558-8585 Japan.
Heliyon. 2018 Apr 2;4(4):e00578. doi: 10.1016/j.heliyon.2018.e00578. eCollection 2018 Apr.
The objective of the present study is to establish the experimental modeling process of the nonuniform deformation behavior of heterogeneous materials. For this purpose, the constant stress moment, which is the work conjugate quantity of the constant strain gradient for the finite volume evaluation region, is introduced. The proposed stress moment can be evaluated from the stress field. The extended constitutive equation that relates the strain, stress, strain gradient, and stress moment is then formulated to predict the nonuniform deformation behavior of heterogeneous materials. In order to confirm that the proposed method is appropriate to represent the nonuniform deformation, finite element method (FEM) simulations of bending of macroscopically and microscopically heterogeneous materials were performed. The proposed method could predict the bending deformation of macroscopically heterogeneous material as precisely as the homogeneous case because the distribution of the heterogeneity is introduced in the extended constitutive equation. A bending simulation of a laminated cantilever was then performed using the extended constitutive equation for the microscopically heterogeneous material. The proposed method was capable of representing the analytically verified size-dependent bending deformation of the laminated cantilever.
本研究的目的是建立非均匀材料非均匀变形行为的实验建模过程。为此，引入了常应力矩，它是有限体积评估区域常应变梯度的功共轭量。所提出的应力矩可从应力场进行评估。然后建立了将应变、应力、应变梯度和应力矩联系起来的扩展本构方程，以预测非均匀材料的非均匀变形行为。为了确认所提出的方法适用于表示非均匀变形，对宏观和微观非均匀材料的弯曲进行了有限元法（FEM）模拟。所提出的方法能够像均匀材料情况一样精确地预测宏观非均匀材料的弯曲变形，因为在扩展本构方程中引入了非均匀性分布。然后使用扩展本构方程对微观非均匀材料的层合悬臂梁进行弯曲模拟。所提出的方法能够表示经分析验证的层合悬臂梁尺寸相关的弯曲变形。
