Gradient Elasticity Based on Laplacians of Stress and Strain
Gradient Elasticity Based on Laplacians of Stress and Strain
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DOI：
10.1007/s10659-017-9644-3
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发表时间：
2018-03-01
影响因子：
2
通讯作者：
Beskos, D.
中科院分区：
文献类型：
--
作者：
Broese, C.;Tsakmakis, C.;Beskos, D.
利用Mindlin的一般微结构弹性理论，我们导出了基于应力和应变的拉普拉斯函数的梯度弹性模型。我们证明了这种基于拉普拉斯的梯度弹性模型也可以在热力学上一致的梯度弹性的基础上得到。这一证明依赖于一个非常规热力学框架。结果表明，基于弹簧单元和阻尼器单元的线性粘弹性固体与特定的梯度弹性模型之间可以建立一个普遍的类比。在此基础上建立了梯度弹性模型的运动控制方程。通过采用与能量有关的自变量，导出了材料参数的条件，并为两种方法指定了适当的伴随边界条件。最后，参考一维色散关系对所考虑的模型进行了比较。
Using Mindlin's general microstructural elasticity theory we derive models pertaining to a gradient elasticity based on both Laplacians of stress and strain. We prove that such Laplacian-based gradient elasticity models can also be derived on the basis of a thermodynamically consistent gradient elasticity. The proof relies upon a non-conventional thermodynamic framework. It is shown that a general analogy between linear viscoelastic solids based on spring and dashpot elements and specific gradient elasticity models can be established. The governing differential equations of motion of resulting gradient elasticity models are then formulated. By employing energy related arguments, conditions on the material parameters are derived and the appropriate concomitant boundary conditions are specified for both approaches. Finally, the considered models are compared to each other with reference to one-dimensional dispersion relations.