Comparison of Laplacian based explicit and implicit gradient elasticity with reference to one-dimensional problems in statics and dynamics
Comparison of Laplacian based explicit and implicit gradient elasticity with reference to one-dimensional problems in statics and dynamics
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DOI：
10.1016/j.euromechsol.2021.104270
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
C. Broese;S. Papargyri-Beskou;C. Tsakmakis
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文献类型：
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作者：
C. Broese;S. Papargyri-Beskou;C. Tsakmakis
先前已经表明，基于拉普拉斯的显式和隐式梯度弹性模型可以作为Mindlin的梯度弹性和Mindlin的微结构（或等效的Eringen的微形态）弹性材料的特定情况导出。此外，它们可以被建立为粘弹性固体的对应物，鉴于类似于基于机械元件的线性粘弹性。本文的目的是比较响应预测的三参数粘弹性固体的梯度弹性对应的粘弹性开尔文模型和经典弹性的梯度弹性对应的预测。比较主要是基于静态和动态的一维问题的封闭形式的解决方案。具体而言，分析包括静态加载，轴向振动和拉伸阶跃脉冲加载的杆。
It has been shown previously, that Laplacian based explicit and implicit gradient elasticity models can be derived as particular cases of Mindlin’s gradient elasticity and Mindlin’s micro-structured (or equivalently Eringen’s micromorphic) elastic materials. Also, they can be established as counterparts of viscoelastic solids, in view of an analogy to linear viscoelasticity based on mechanical elements. The present paper aims to compare responses predicted by the gradient elasticity counterpart of the three-parameter viscoelastic solid with those predicted by the gradient elasticity counterpart of the viscoelastic Kelvin model and by the classical elasticity. The comparison is mainly based on closed form solutions of one-dimensional problems in statics and dynamics. Specifically, the analysis includes static loading, axial vibrations and tension step pulse loading of a bar.