A procedure for the experimental identification of the strain Gradient characteristic length

For the experimental identification of the characteristic length in strain-gradient models, an experimental procedure is proposed. A virtual pull-out test in a strain gradient elastic domain is utilized. 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. 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. The real pullout test induces damage in concrete, requiring a concise exploration of the damaged elastic-plastic formulation for a single spring.