Multiscale Analysis Of Mechanical Properties Of Metal Foams

Cellular materials such as metal foam have excellent mechanical properties,and its special mesostructure characteristics have important influence on the mechanical properties at different scales.In this paper,in order to investigate the mechanical behavior of metal foam,the beam lattice model is used as the micromechanics model of metal foam,and meanwhile the analytical solutions are provided based on the strain gradient elasticity theory,the relationship between the macroscopic response of the metal foam and the meso-structural parameters is given.Finally,the influences of the matrix material's visco/hyper elasticity and the cell arrangement on the mechanical response of the material are studied.The specific studies include:(1)The beam lattice model was used to model the mesostructure of metal foam.For example,the periodic lattice is considered as the equivalence of periodic triangle,square or hexagon-cell foam;While the Voronoi lattice are built for foams with random cell shapes;And three dimensional lattice model for foams with a cell arrangement of six party closest packing was also studied.The relationship between parameters of the generalized continuum such as the strain gradient elasticity and matrix material and cell structure of foams was established according to the strain energy equivalence principle.(2)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 on the same order of magnitude,there exist obvious size effects.In order to reveal the mechanical mechanism behind such size effects,we studied the simple shear and bending tests of metal foam specimens.On one hand,we solved the problems analytically by using the strain gradient elasticity theory,which contains the key parameter lc,i.e.the material characteristic length scale.On the other hand,the bending and shear tests on periodic hexagonal cell foams were simulated by the beam lattice model,and the uniaxial compression test was simulated by using the three dimensional beam lattice model.It is found that the material length scale parameter is strongly related to the cell size d,and the macroscopic mechanical response changes with the relative ratio of the sample's characteristic size to the cell size d.The smaller the ratio of sample size to cell size,the stronger the size dependence.In addition,the boundary layer constraint conditions have an important impact on the mechanical response of metal foams.In the bending test,the analytical solution based on strain gradient theory matches the result obtained by the lattice model only when applying the proper extra constraints 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,we obtained the relationship between the material length scale parameter lc and the cell size d,which agreed well with the conclusion from literature.The comparison between the simulation and experimental results of uniaxial compression shows that the young's modulus of the metal foam material exhibits obvious size dependence such as decrease along with the decrease of sample size.However,the compressive strength independent of the sample size.(3)The effects of viscoelasticity and hyperelasticity on the macroscopic mechanical response of foam materials were studied.In addition,several types of nonlocal lattices were discussed,that is,the interaction is not only between the 1st-nearest neighbor nodes,but also between the 2ndnearest neighbors and even the 3rd-nearest neighbor nodes.This nonlocal lattice is very similar to the peridynamics model in nature.The simulation results showed that the material has higher elastic modulus and specific stiffness than the ordinary honeycomb material,and can achieve more excellent composite properties.