Computational Homogenization of Architectured Materials

Architectured materials involve geometrically engineered distributions of microstructural phases at a scale comparable to the scale of the component, thus calling for new models in order to determine the effective properties of materials. The present chapter aims at providing such models, in the case of mechanical properties. As a matter of fact, one engineering challenge is to predict the effective properties of such materials; computational homogenization using finite element analysis is a powerful tool to do so. Homogenized behavior of architectured materials can thus be used in large structural computations, hence enabling the dissemination of architectured materials in the industry. Furthermore, computational homogenization is the basis for computational topology optimization which will give rise to the next generation of architectured materials. This chapter covers the computational homogenization of periodic architectured materials in elasticity and plasticity, as well as the homogenization and representativity of random architectured materials

Lithiation of ramsdellite-pyrolusite MnO \u3c inf\u3e 2 ; NMR, XRD, TEM and electrochemical investigation of the discharge mechanism

Electrolytic manganese dioxide (EMD) is made in aqueous sulfuric acid and neutralized or ion exchanged with aqueous lithium hydroxide before use in Li batteries. Solid state Li NMR studies show that Li is present on surface and vacancy sites and migrates into Mn (III) related sites after heat treatment to remove water. During heat treatment the MnO2 rearranges from ramsdellite/pyrolusite intergrowth EMD to a defect pyrolusite heat-treated manganese dioxide (HEMD). EMD exhaustively treated with lithium hydroxide solution has 40-50% of the protons in EMD exchanged for Li ions to produce a structurally unchanged γ-MnO2. Li magic angle spinning (MAS) NMR reveals that this lithiated material contains lithium in cation vacancy and Mn (III) related sites in the MnO2 lattice in addition to ionic Li on the surface. During heat treatment, the vacancy lithium content prevents the ramsdellite to pyrolusite rearrangement in HEMD formation. Instead, an ordered ramsdellite/pyrolusite intergrowth of lithiated manganese dioxide (LiMD) is formed with an approximate composition of 50% ramsdellite and 50% pyrolusite. Li MAS NMR of LiMD shows Li resonances near 280 and 560 ppm, consistent with Li transition from surface and cation vacancy sites into the ramsdellite lattice. LiMD discharged against lithium shows two processes, one near 3.1 V, the other about 2.8 V. Li MAS NMR studies show the initial reduction results a lithium resonance near 560 ppm associated with Li near a mixed valence Mn (III/IV) environment followed by appearance of a resonance near 100 ppm consistent with a Li environment near Mn (III). TEM studies of the reduced material show initial expansion of the ramsdellite lattice accompanied by a loss in crystallinity in the 3.1 V discharge process followed by disappearance of the pyrolusite content via conversion to ramsdellite in the second discharge process. © 2005 Elsevier B.V. All rights reserved