The aim of this paper is to propose an experimental procedure for determining the characteristic length of a strain gradient model. The identification problem is studied through a virtual pull-out test of a rigid bar along the symmetry axis of a cylindrical strain gradient elastic domain. To allow an accurate parameter identification based on measured data, we investigate the effect of the characteristic length on the mechanical fields for this problem. We see a significant sensitivity of the inflection point of the displacement profile evaluated on the cross section of the cylinder, with respect to the characteristic length. By adjusting the characteristic length of the strain gradient such that the theoretical models match best with experimental measurements of the surface displacement fields, the characteristic length of the strain gradient can be estimated. In order to allow for more efficient analysis and an almost real-time parameter identification, the initial three-dimensional (3D) problem is reduced to a one-dimensional (1D) problem by exploiting the cylindrical symmetry of the problem. As will be shown, an accurate 1D finite element method (FEM) strain gradient solution can be obtained for this simplified problem. Since the cylindrical symmetry is only true in an infinitely long cylinder, specific boundary conditions are constructed on a cylinder of finite length, which is then used for the comparison of the 1D and 3D problems. Results show, however, that the structural response at the inflection point is insensitive to whether the specific boundary conditions are considered or not, which is why the 1D model can be used for parameter identification. Since the proposed approach is methodological, it can be applied to any material. As a prototype problem in this paper, we consider the case of a bar embedded in Portland cement concrete.

本文的目的是提出一种确定应变梯度模型特征长度的实验程序。通过刚性杆沿圆柱应变梯度弹性域对称轴的虚拟拉拔试验来研究辨识问题。为了根据测量数据进行准确的参数识别，我们研究了特征长度对这个问题的机械场的影响。我们发现在圆柱体横截面上评估的位移曲线的拐点相对于特征长度具有显着的敏感性。通过调整应变梯度的特征长度，使得理论模型与表面位移场的实验测量最佳匹配，可以估计应变梯度的特征长度。为了实现更有效的分析和几乎实时的参数识别，通过利用问题的圆柱对称性，将初始的三维 (3D) 问题简化为一维 (1D) 问题。正如将要显示的，对于这个简化的问题可以获得精确的一维有限元法 (FEM) 应变梯度解。由于圆柱对称仅在无限长的圆柱体中成立，因此在有限长度的圆柱体上构造特定的边界条件，然后将其用于一维和三维问题的比较。但结果表明，拐点处的结构响应对是否考虑特定边界条件并不敏感，这就是为什么可以使用一维模型进行参数识别。由于所提出的方法是方法论的，因此它可以应用于任何材料。作为本文的原型问题，我们考虑了嵌入波特兰水泥混凝土中的钢筋的情况。