Is metal foams flexible?

The mechanical properties of metal foam strongly depend on the internal structure. When the feature size of the member is on the same order of magnitude as the cell feature size, it exhibits a significant scale effect. In order to reveal the mechanical mechanism of this scale effect, the shear and pure bending tests of metal foams  specimens were studied. On the one hand, the analytical solution is given by the theory of strain gradient elasticity, which contains the key model parameters of the size in the materials. On the other hand, each segment of the cell wall is considered to be a Tiemu Xinke beam, thereby establishing a beam-chain network as a micromechanical model of the metal foam. The relationship between the strain gradient continuum and the elastic parameters of the matrix metal material is established by the strain energy equivalent principle. It was found that the boundary layer constraints have an important influence on the mechanical response of the metal foam. In the bending problem, the strain gradient theory solution can be consistent with the numerical solution of the chain net model only after applying appropriate additional corner constraints to the upper and lower surfaces of the discrete model. This provides an intuitive example of understanding the unconventional boundary conditions in strain gradient theory. Through the data fitting, the relationship between the intrinsic size and the cell feature size is obtained, which is consistent with the literature conclusion.

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