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We consider a quasistatic contact problem for an electro-viscoelastic body. The contact is frictional and bilateral with a moving rigid foundation which results in the wear of the contacting surface. The damage of the material caused by elastic deformation is taken into account, its evolution is described by an inclusion of parabolic type. We present a weak formulation for the model and establish existence and uniqueness results. The proofs are based on classical results for elliptic variational...
This paper is devoted to the introduction of a new variant of the extended
finite element method (Xfem) for the approximation of elastostatic fracture
problems. This variant consists in a reduced basis strategy for the definition
of the crack tip enrichment. It is particularly adapted when the asymptotic
crack-tip displacement is complex or even unknown. We give a mathematical result
of quasi-optimal a priori error estimate and some computational tests including
a comparison with some other strategies....
We investigate unilateral contact problems with cohesive forces, leading to
the constrained minimization of a possibly nonconvex functional. We
analyze the mathematical structure of the minimization problem.
The problem is reformulated in terms of a three-field augmented
Lagrangian, and sufficient conditions for the existence of a local
saddle-point are derived. Then, we derive and analyze mixed finite
element approximations to the stationarity conditions of the three-field
augmented Lagrangian....
In this work we consider a solid body constituted by a nonhomogeneous elastoplastic material, submitted to a density of body forces and a density of forces acting on the boundary where the real is the loading parameter. The problem is to determine, in the case of an unbounded convex of elasticity, the Limit load denoted by beyond which there is a break of the structure. The case of a bounded convex of elasticity is done in [El-Fekih and Hadhri, RAIRO: Modél. Math. Anal. Numér. 29 (1995)...
In this work we consider a solid body constituted by a
nonhomogeneous elastoplastic material, submitted to a density of body forces
and a density of forces acting on the boundary where the real is the
loading parameter.
The problem is to determine, in the case of an unbounded convex of elasticity, the Limit
load denoted by beyond which there is a break of the structure. The case of a bounded convex of elasticity is done in [El-Fekih and Hadhri, RAIRO: Modél. Math. Anal. Numér. 29 (1995)...
Per i continui bidimensionali sottili isotropi in c.a., a mezzo del teorema generalizzato del minimo lavoro, si dimostra che il carico relativo alla formazione del completo quadro fessurativo si può ottenere considerando l'assetto finale di apertura delle distorsioni di Volterra, evitando di seguire l'evoluzione del fenomeno definibile da un punto di vista operativo mediante distorsioni localizzate di Somigliana.
Si interpretano i risultati degli esperimenti fatti su mezzi anelastici mediante applicazione di deformazioni crescenti linearmente nel tempo. Si trova che dai risultati di questi esperimenti, si può risalire alla funzione di creep che viene determinata con tre diversi modelli di approssimazione. Si trova inoltre che per decidere sul comportamento a lungo termine dei materiali sono necessari esperimenti a più lungo termine di quelli fatti. Si dimostra poi che le relazioni classiche che rappresentano...
The paper deals with approximations and the numerical realization of a class of hemivariational inequalities used for modeling of delamination and nonmonotone friction problems. Assumptions guaranteeing convergence of discrete models are verified and numerical results of several model examples computed by a nonsmooth variant of Newton method are presented.
The hypothesis that, on the macroscopic level, the accumulated fatigue of an elastoplastic material with kinematic hardening can be identified from the mathematical point of view with the dissipated energy, is used for the construction of a new constitutive elastoplastic fatigue model. Its analytical investigation characterizes conditions for the formation of singularities in a finite time. The corresponding constitutive law is then coupled with the dynamical equation of motion of a one-dimensional...
A molecular dynamics approach to the deformation and stress analysis in structured materials is presented. A new deformation measure for a lumped mass system of points is proposed. In full consistency with the continuum mechanical description, three kinds of stress tensors for the discrete system of atoms are defined. A computer simulation for a set of 10^5 atoms forming a sheet undergoing tension (Case 1) and contraction (Case 2) is given. Characteristic microstress distributions evoked by a crack...
In this paper, we present a numerical approach to evolution of decohesion
in laminated composites based on incremental variational problems. An energy-based framework is adopted, in which we characterize the system by the stored energy and dissipation functionals quantifying reversible and irreversible processes, respectively. The time-discrete evolution then follows from a solution of incremental minimization problems, which are converted to a fully discrete form by employing the conforming finite...
The propagation of fractures in a solid undergoing cyclic loadings
is known as the fatigue phenomenon. In this paper, we present a time continuous
model for fatigue, in the special situation of the debonding of thin layers,
coming from a time discretized version recently proposed by
Jaubert and Marigo [C. R. Mecanique333 (2005) 550–556].
Under very general assumptions on the surface energy density and
on the applied displacement, we discuss the well-posedness of our
problem and we give the main...
The displacement field caused by the classic earthquake mechanism model consisting of a slip along the fault is extended to the case when besides the slip, also an opening occurs caused by tensional forces. The tensor matrix describing the moment tensor does not necessarily have a nil trace. The direct problem is solved finding the radiation pattern for and waves. A method to solve the inverse problem of the determination of the four parameters describing the source is presented and tested on...
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