THEORETICAL AND NUMERICAL ANALYSES OF SIZE EFFECTS IN ELASTIC DEFORMATIONS OF METAL FOAMS

The mechanical properties of the metal foam is strongly dependent on its internal structure. When the characteristic size of the specimen and the cell size d of the internal structure are of the same order of magnitude, there exist obvious size effects. In order to reveal the mechanical mechanism behind such size effects, simple shear and bending tests of metal foam specimens were performed. On one hand, the problems were solved analytically by using the strain gradient elasticity theory, which contains the key parameter l_c, i.e., the material characteristic length scale. On the other hand, the beam lattice was established as the micromechanics model of metal foams by taking each cell wall as a Timoshenko beam. The relationship between the parameters of the generalized continuum and foam's matrix material was established according to the strain energy equivalence principle. It is found that boundary layer constraint conditions have an important impact on the mechanical response of metal foams. For the bending problem, the analytical solution based on strain gradient theory matches the result obtained by the lattice model only when the proper extra constraints are applied on the upper and lower surfaces of the lattice model. This provides an intuitive example for understanding non-classical boundary conditions in the strain gradient theory. By fitting the theoretical and numerical results, the relationship between the material length scale parameter l_c and the cell size d is obtained, which agrees well with the conclusion from literature.