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Displaying 21 –
40 of
207
We consider a mathematical model which describes a static contact between a nonlinear elastic body and an obstacle. The contact is modelled with Signorini's conditions, associated with a slip-dependent version of Coulomb's nonlocal friction law. We derive a variational formulation and prove its unique weak solvability. We also study the finite element approximation of the problem and obtain an optimal error estimate under extra regularity for the solution. Finally, we establish the convergence of...
Rate-independent evolution for material models with nonconvex elastic energies is studied without any spatial regularization of the inner variable; due to lack of convexity, the model is developed in the framework of Young measures. An existence result for the quasistatic evolution is obtained in terms of compatible systems of Young measures. We also show as this result can be equivalently reformulated with probabilistic language and leads to the description of the quasistatic evolution in terms...
Rate-independent evolution for material models with nonconvex
elastic energies is studied without any spatial regularization of
the inner variable; due to lack of convexity, the model is developed
in the framework of Young measures. An existence result for the
quasistatic evolution is obtained in terms of compatible systems of
Young measures. We also show as this result can be equivalently
reformulated with probabilistic language and leads to the
description of the quasistatic evolution in terms...
We propose and study semidiscrete and fully discrete finite element schemes based on appropriate relaxation models for systems of Hyperbolic Conservation Laws. These schemes are using piecewise polynomials of arbitrary degree and their consistency error is of high order. The methods are combined with an adaptive strategy that yields fine mesh in shock regions and coarser mesh in the smooth parts of the solution. The computational performance of these methods is demonstrated by considering scalar...
We propose and study semidiscrete and fully discrete
finite element schemes based on appropriate relaxation models for
systems of Hyperbolic Conservation Laws.
These schemes are using piecewise polynomials of arbitrary degree and
their consistency error is of high order.
The methods are combined with an adaptive strategy that yields
fine mesh in shock regions and coarser mesh in the smooth parts of the
solution.
The computational performance of these methods is demonstrated by considering
scalar...
We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in by the sequence of linear strains of mapping bounded in Sobolev space . We apply this result to establish equalities for semiconvex envelopes for functions defined on linear strains via a construction of quasiconvex functions with linear growth.
We establish an approximation theorem for a sequence of
linear elastic strains approaching a compact set in L1 by the
sequence of linear strains of mapping bounded in Sobolev space W1,p
. We apply this result to establish equalities for
semiconvex envelopes for functions defined on linear strains via a
construction of quasiconvex functions with linear growth.
An optimal control problem is considered where the state of the system is described by a variational inequality for the operator w → εΔ²w - φ(‖∇w‖²)Δw. A set of nonnegative functions φ is used as a control region. The problem is shown to have a solution for every fixed ε > 0. Moreover, the solvability of the limit optimal control problem corresponding to ε = 0 is proved. A compactness property of the solutions of the optimal control problems for ε > 0 and their relation with the limit problem...
In this note we give sharp lower bounds for a non-convex functional when minimised over the space of functions that are piecewise affine on a triangular grid and satisfy an affine boundary condition in the second lamination convex hull of the wells of the functional.
In this note we give sharp lower bounds for a non-convex functional when
minimised over the space of functions that are piecewise affine
on a triangular grid and satisfy
an affine boundary condition in the second lamination convex
hull of the wells of the functional.
We consider the problem of frictional contact between an elastic body and an obstacle. The elastic constitutive law is assumed to be nonlinear. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We present two alternative yet equivalent weak formulations of the problem, and establish existence and uniqueness results for both formulations using arguments of elliptic variational inequalities and fixed point theory. Moreover, we show the continuous...
This paper deals with a nonlinear problem modelling the contact between an elastic body and a rigid foundation. The elastic constitutive law is assumed to be nonlinear and the contact is modelled by the well-known Signorini conditions. Two weak formulations of the model are presented and existence and uniqueness results are established using classical arguments of elliptic variational inequalities. Some equivalence results are presented and a strong convergence result involving a penalized problem...
The thermoelastic stresses created in a solid phase domain in the course of solidification of a molten ingot are investigated. A nonlinear behaviour of the solid phase is admitted, too. This problem, obtained from a real situation by many simplifications, contains a moving boundary between the solid and the liquid phase domains. To make the usage of standard numerical packages possible, we propose here a fixed-domain approximation by means of including the liquid phase domain into the problem (in...
It is proved that, as in three-dimensional elasticity, Betti's theorem represents a criterion for the existence of a stored-energy function for a Cosserat elastic shell.
Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15The popular elastic law of Fung that describes the non-linear stress-
strain behavior of soft biological tissues is extended into a viscoelastic material
model that incorporates fractional derivatives in the sense of Caputo. This one-dimensional material model is then transformed into a
three-dimensional constitutive model that is suitable for general analysis.
The model is derived in a configuration that differs from the current, or
spatial,...
Currently displaying 21 –
40 of
207