15,200 research outputs found
Variational Multisymplectic Formulations of Nonsmooth Continuum Mechanics
This paper develops the foundations of the multisymplectic
formulation of nonsmooth continuum mechanics. It may be regarded as a PDE generalization of previous techniques that developed a variational approach to collision problems. These methods have already proved of value in
computational mechanics, particularly in the development of asynchronous integrators and efficient collision methods. The present formulation also includes solid-fluid interactions and material interfaces and, in addition, lays
the groundwork for a treatment of shocks
Variational problems in fracture mechanics
We present some recent existence results for the variational model of crack
growth in brittle materials proposed by Francfort and Marigo in 1998. These
results, obtained in collaboration with Francfort and Toader, cover the case of
arbitrary space dimension with a general quasiconvex bulk energy and with
prescribed boundary deformations and applied loads.Comment: 9 page
Strain injection techniques in dynamic fracture modeling
A computationally affordable modeling of dynamic fracture phenomena is performed in this study by using strain injection techniques and Finite Elements with Embedded strong discontinuities (E-FEM). In the present research, classical strain localization and strong discontinuity approaches are considered by injecting discontinuous strain and displacement modes in the finite element formulation without an increase of the total number of degrees of freedom. Following the Continuum Strong Discontinuity Approach (CSDA), stress–strain constitutive laws can be employed in the context of fracture phenomena and, therefore, the methodology remains applicable to a wide number of continuum mechanics models. The position and orientation of the displacement discontinuity is obtained through the solution of a crack propagation problem, i.e. the crack path field, based on the distribution of localized strains. The combination of the above mentioned approaches is envisaged to avoid stress-locking and directional mesh bias phenomena. Dynamic simulations are performed increasing the loading rate up to the appearance of crack branching, and the variation in terms of failure modes is investigated as well as the influence of the strain injection together with the crack path field algorithm. Objectivity of the presented methodology with respect to the spatial and temporal discretization is analyzed in terms of the dissipated energy during the fracture process. The dissipation at the onset of branching is studied for different loading rate conditions and is linked to the experimental maximum velocity observed before branching takes place.Fil: Lloberas Valls, Oriol. Universidad Politecnica de Catalunya; España. Centre Internacional de Metodes Numerics en Enginyeria; EspañaFil: Huespe, Alfredo Edmundo. Centre Internacional de Metodes Numerics en Enginyeria; España. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; ArgentinaFil: Oliver, J.. Centre Internacional de Metodes Numerics en Enginyeria; España. Universidad Politecnica de Catalunya; EspañaFil: Dias, I.F.. Laboratório Nacional de Engenharia Civil; Portuga
The -limit for singularly perturbed functionals of Perona-Malik type in arbitrary dimension
In this paper we generalize to arbitrary dimensions a one-dimensional
equicoerciveness and -convergence result for a second derivative
perturbation of Perona-Malik type functionals. Our proof relies on a new
density result in the space of special functions of bounded variation with
vanishing diffuse gradient part. This provides a direction of investigation to
derive approximation for functionals with discontinuities penalized with a
"cohesive" energy, that is, whose cost depends on the actual opening of the
discontinuity
Function spaces for liquid crystals
We consider the relationship between three continuum liquid crystal theories:
Oseen-Frank, Ericksen and Landau-de Gennes. It is known that the function space
is an important part of the mathematical model and by considering various
function space choices for the order parameters , , and ,
we establish connections between the variational formulations of these
theories. We use these results to derive a version of the Oseen-Frank theory
using special functions of bounded variation. This proposed model can describe
both orientable and non-orientable defects. Finally we study a number of
frustrated nematic and cholesteric liquid crystal systems and show that the
model predicts the existence of point and surface discontinuities in the
director
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