Meso-mechanics Analysis For Double Elastic Modulus Of Foam Materials And Stability Of The Beam With Double Modulus

With the development of modern aircraft design technology, more and more materials with light weight and impact resistance are applied in the structures of aircraft. Among them, the foam solid is one of the materials being used most extensively. The foam solid manifests complicated mechanical behaviors due to its abundant meso-structures. Many scientists have paid much attention on this domain and more and more results are reported now.In this paper, the equivalent elastic constants of foam solid and their effects on the stability of structure (e.g., beam) are studied. Emphasis is focused on the double modulus effect of foam solid. Firstly, the double modulus effect of foam solid is verified by experiments and finite element modeling. Then, a new model of meso-mechanics for the foam solid is established, on which the formula to estimate the equivalent tensile and compressive elastic modulus are derived, respectively. In addition, a criterion (called the trace stress criterion) to judge the tensile and compressive state within material is proposed. On the basis of the trace stress criterion, the constitutive equation and consistent equation characterizing the material with the double modulus effect are advanced.–This is a new result, which satisfies the constitutive axioms of rational mechanics compared with the existing results (e.g., the constitutive equation based on the principal stress criterion). Meanwhile, we give the buckling load of a simple-supported Euler beam with the double modulus by numerical calculation, and analyze the influences of the double modulus to the stability of beam. At last, some problems needing to be further explored are pointed out.