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.

先前已经证明，基于Laplacian的显式和隐式梯度弹性模型可以作为Mindlin梯度弹性和Mindlin的微结构化弹性材料（或等效地为Eringen的微形态）弹性材料的特殊情况导出。而且，鉴于类似于基于机械元件的线性粘弹性，它们可以被确定为粘弹性固体的对应物。本文旨在比较三参数粘弹性固体的梯度弹性对应物与粘弹性开尔文模型的梯度弹性对应物和经典弹性所预测的响应。比较主要基于一维静态和动态问题的闭式解。具体来说，分析包括静态负载，