An elastic micropolar mixture theory for predicting elastic properties of cellular materials

Abstract

An efficient modeling approach is established to predict the elastic response of cellular materials with distributions of cell geometries. The approach does not require complex and timeconsuming computational techniques usually associated with modeling such materials. Unlike most current analytical techniques, the modeling approach directly accounts for the cellular material microstructure. The approach combines micropolar elasticity theory and elastic mixture theory to predict elastic response of cellular materials to a wide range of loading conditions. The modeling approach is applied to the two-dimensional balsa wood material. Predicted properties are in good agreement with experimentally-determined properties, which emphasizes the model's potential to predict the elastic response of other cellular solids, such as open cell and closed cell foams.

A problem with viscoelastic mixtures: numerical analysis and computational experiments

“…Remark 2 We note that, from their definition, coefficients b 1 and b 2 equal a 3 and a 4 , respectively. Moreover, after tedious algebraic manipulations, from the conditions of Theorem 2.1, for each dimension considered, we can derive conditions ( 16)- (18). However, even if we are able to simplify conditions ( 13)-( 15), using the conditions of Theorem 2.1, we could not conclude them from there.…”

“…During the last fifty years the literature concerning binary mixtures has increased drastically because their applications can be found in different fields. For instance, they can be used to model the well-known composites (see, e.g., [17]), used in the automotive or nautical industries, or even some type of cells in biology (see [18]).…”

On the time decay of solutions in micropolar viscoelasticity

“…We can find applications of the micropolar elasticity, for instance, in the works of Elangovan et al [6] about elastic properties of cellular materials, Fatemi et al [9] about stress analysis in bone, Kordolemis and Giannakopoulos [14] about smart cables and textiles and Nikogosyan and Sargsyan [25] about thin shells. This list could be enlarged with more contributions, but we think that the cited papers are sufficiently representative.…”

Representation theorems and fundamental solutions for micropolar solid–fluid mixtures under steady state vibrations

“…This theory can be successfully applied to the study of engineering materials, as well as soils, rocks, granular materials, sand and underground water mixtures. Consolidation problems in the building industry, earthquake problems, oil exploration problems and cellular solids can be studied with the help of the mixture theories (de Boer, 2005;Elangovan et al, 2008).…”