On the commutability of homogenization and linearization in finite elasticity

We study non-convex elastic energy functionals associated to (spatially) periodic, frame indifferent energy densities with a single non-degenerate energy well at SO(n). Under the assumption that the energy density admits a quadratic Taylor expansion at identity, we prove that the Gamma-limits associated to homogenization and linearization commute. Moreover, we show that the homogenized energy density, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the quadratic term associated to the linearization of the initial energy density

Landscapes of Urbanization and De-Urbanization: A Large-Scale Approach to Investigating the Indus Civilization's Settlement Distributions in Northwest India.

Survey data play a fundamental role in studies of social complexity. Integrating the results from multiple projects into large-scale analyses encourages the reconsideration of existing interpretations. This approach is essential to understanding changes in the Indus Civilization's settlement distributions (ca. 2600-1600 b.c.), which shift from numerous small-scale settlements and a small number of larger urban centers to a de-nucleated pattern of settlement. This paper examines the interpretation that northwest India's settlement density increased as Indus cities declined by developing an integrated site location database and using this pilot database to conduct large-scale geographical information systems (GIS) analyses. It finds that settlement density in northwestern India may have increased in particular areas after ca. 1900 b.c., and that the resulting landscape of de-urbanization may have emerged at the expense of other processes. Investigating the Indus Civilization's landscapes has the potential to reveal broader dynamics of social complexity across extensive and varied environments.ER

Largest ancient fortress of South-West Asia and the western world?:Recent fieldwork at Sasanian Qaleh Iraj at Pishva, Iran

The article presents recent works at Qale Iraj, near Varamin, Iran. My short contribution is on the Middle Persian ostraka found at the site

Liquid crystals and their defects

These lecture notes discuss classical models of liquid crystals, and the different ways in which defects are described according to the different models.Comment: CIME lecture course, Cetraro, 201

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro- and micro-scale kinematics are defined and linked in a physically meaningful way; (2) duality, through which the natures of the force- and stress-like quantities are uniquely identified as the duals (power-conjugates) of the adopted kinematical variables; and (3) the Principle of Multiscale Virtual Power, a generalization of the well-known Hill-Mandel Principle of Macrohomogeneity, from which equilibrium equations and homogenization relations for the force- and stress-like quantities are unequivocally obtained by straightforward variational arguments. The proposed theory provides a clear, logically-structured framework within which existing formulations can be rationally justified and new, more general multiscale models can be rigorously derived in well-defined steps. Its generality allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities, fluid mechanics and coupled multi-physics. This is illustrated in a number of examples where a range of models is systematically derived by following the same steps. Due to the variational basis of the theory, the format in which derived models are presented is naturally well suited for discretization by finite element-based or related methods of numerical approximation. Numerical examples illustrate the use of resulting models, including a non-conventional failure-oriented model with discontinuous kinematics, in practical computations

Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46162/1/205_2004_Article_BF00380256.pd

Takht-i Sangin: on the Pre-Hellenistic Finds

International audienc

L'art gréco-bactrien

International audienc