296 research outputs found
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
Infinite-contrast periodic composites with strongly nonlinear behavior: Effective-medium theory versus full-field simulations
This paper presents a combined numerical-theoretical study of the macroscopic
behavior and local field distributions in a special class of two-dimensional
periodic composites with viscoplastic phases. The emphasis is on strongly
nonlinear materials containing pores or rigid inclusions. Full-field numerical
simulations are carried out using a Fast-Fourier Transform algorithm [H.
Moulinec, P. Suquet, C. R. Acad. Sci. Paris II 318, 1417 (1994)]
Moulinec, P. Suquet, C. R. Acad. Sci. Paris II 318, 1417 (1994), while the
theoretical results are obtained by means of the `second-order' nonlinear
homogenization method [P. Ponte Castaneda, J. Mech. Phys. Solids 50, 737
(2002)]. The effect of nonlinearity and inclusion concentration is investigated
in the context of power-law (with strain-rate sensitivity m) behavior for the
matrix phase under in-plane shear loadings. Overall, the `second-order'
estimates are found to be in good agreement with the numerical simulations,
with the best agreement for the rigidly reinforced materials. For the porous
systems, as the nonlinearity increases (m decreases), the strain field is found
to localize along shear bands passing through the voids (the strain
fluctuations becoming unbounded) and the effective stress exhibits a singular
behavior in the dilute limit. More specifically, for small porosities and fixed
nonlinearity m>0, the effective stress decreases linearly with increasing
porosity. However, for ideally plastic behavior (m = 0), the dependence on
porosity becomes non-analytic. On the other hand, for rigidly-reinforced
composites, the strain field adopts a tile pattern with bounded strain
fluctuations, and no singular behavior is observed (to leading order) in the
dilute limit.Comment: 28 pages, 28 B&W figures, 2 tables of color maps, to be published in
International Journal of Solids and Structures (in press
Nonsmooth analysis of doubly nonlinear evolution equations
In this paper we analyze a broad class of abstract doubly nonlinear evolution
equations in Banach spaces, driven by nonsmooth and nonconvex energies. We
provide some general sufficient conditions, on the dissipation potential and
the energy functional,for existence of solutions to the related Cauchy problem.
We prove our main existence result by passing to the limit in a
time-discretization scheme with variational techniques. Finally, we discuss an
application to a material model in finite-strain elasticity.Comment: 45 page
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
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
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
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
A framework for polyconvex large strain phase-field methods to fracture
Variationally consistent phase-field methods have been shown to be able to predict complex three-dimensional crack patterns. However, current computational methodologies in the context of large deformations lack the necessary numerical stability to ensure robustness in different loading scenarios. In this work, we present a novel formulation for finite strain polyconvex elasticity by introducing a new anisotropic split based on the principal invariants of the right Cauchy-Green tensor, which always ensures polyconvexity of the resulting strain energy function. The presented phase-field approach is embedded in a sophisticated isogeometrical framework with hierarchical refinement for three-dimensional problems using a fourth order Cahn-Hilliard crack density functional with higher-order convergence rates for fracture problems. Additionally, we introduce for the first time a Hu-Washizu mixed variational formulation in the context of phase-field problems, which permits the novel introduction of a variationally consistent stress-driven split. The new polyconvex phase-field fracture formulation guarantees numerical stability for the full range of deformations and for arbitrary hyperelastic materials
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