About the solution of a paradox related to axial pull out of a bar from a concrete cylindrical elastic domain in standard first gradient 3D Isotropic

This presentation aims at resolving a paradox occurring in standard first gradient theories and related to the axial pull out of a bar from a concrete cylindrical elastic domain. In the limit of the inner cylinder radius going to zero, we have the following paradox within standard first gradient elasticity in three dimensions: the total elastic energy goes to zero for every value of the axial displacement prescribed to the bar. In the presentation, we propose to solve such a paradox by means of strain-gradient elasticity. The number of constitutive coefficients (7 in total), following Piola’s ansatz and granular micromechanics, is reduced to Young modulus, Poisson ratio, and a characteristic length L. Results of numerical simulations show that this approach leads to non-zero energy for the limit of the inner cylinder radius going to zero. The energy, in such a case, is proportional to the characteristic length L. Besides, the application of the strain-gradient theory does not require the application of any double force at the boundary. This implies the possibility to confirm these results by experiments and the fact that the axial pull out of a bar from a concrete cylindrical domain could serve as a methodology for the determination of constitutive coefficients of 3D isotropic second gradient elasticity.