186 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
Homogenization of the one-dimensional wave equation
We present a method for two-scale model derivation of the periodic
homogenization of the one-dimensional wave equation in a bounded domain. It
allows for analyzing the oscillations occurring on both microscopic and
macroscopic scales. The novelty reported here is on the asymptotic behavior of
high frequency waves and especially on the boundary conditions of the
homogenized equation. Numerical simulations are reported
A second order minimality condition for the Mumford-Shah functional
A new necessary minimality condition for the Mumford-Shah functional is
derived by means of second order variations. It is expressed in terms of a sign
condition for a nonlocal quadratic form on , being a
submanifold of the regular part of the discontinuity set of the critical point.
Two equivalent formulations are provided: one in terms of the first eigenvalue
of a suitable compact operator, the other involving a sort of nonlocal capacity
of . A sufficient condition for minimality is also deduced. Finally, an
explicit example is discussed, where a complete characterization of the domains
where the second variation is nonnegative can be given.Comment: 30 page
Quasistatic crack growth based on viscous approximation: a model with branching and kinking.
Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions of cracks in brittle materials in the setting of antiplane shear. The crack path is not prescribed a priori and is chosen in an admissible class of piecewise regular sets that allows for branching and kinking
Quasistatic delamination of sandwich-like Kirchhoff-Love plates
A quasistatic rate-independent adhesive delamination problem of laminated plates with a finite thickness is considered. By letting the thickness of the plates go to zero, a rate-independent delamination model for a laminated Kirchhoff-Love plate is obtained as limit of these quasistatic processes. The same dimension reduction procedure is eventually applied to processes which are sensitive to delamination modes, namely opening vs. shearing is distinguishe
Phase-field models for brittle and cohesive fracture
In this paper we first recapitulate some basic notions of brittle and cohesive fracture models, as well as the phase-field approximation to fracture. Next, a critical assessment is made of the sensitivity of the phase-field approach to brittle fracture, in particular the degradation function, and the use of monolithic versus partitioned solution schemes. The last part of the paper makes extensions to a recently developed phase-field model for cohesive fracture, in particular for propagating cracks. Using some simple examples the current state of the cohesive phase-field model is shown
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
A comparison of delamination models: Modeling, properties, and applications
This contribution presents recent results in the modeling and the analysis of delamination problems. It addresses adhesive contact, brittle, and cohesive zone models both in a quasistatic and a viscous, dynamic setting for the bulk part. Also different evolution laws for the delaminating surface are discussed
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
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
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