1,720,979 research outputs found
Damage in domains and interfaces: a coupled predictive theory
No full textIn this study, we propose a model coupling damage of domains and damage of interfaces. A predictive
theory of continuum damage mechanics is developed within the framework of the principle of virtual
power. Because damage results from microscopic motions, the power of these microscopic motions is
included in the power of the internal forces. The power of the internal forces we choose depends on
the damage velocity and on its gradient to take into account local interactions. An interaction between
the domain damage and the damage along the interface is introduced. To overcome the insensitivity of
the local interface model to elongation, nonlocal elongation has been considered as a source of damage.
Representative numerical examples confirm that our proposed model can be used to describe various
damage phenomena in agreement with experiments
Collisions and fracture : a l-D theory : how to tear off a chandelier from the ceiling
No full textWhen a plate falls on the ground, it breaks. We study this phenomenon at the macroscopic level. We restrict ourselves to 1-D problems and illustrate the theory with a chandelier to which a falling stone is tied. The collisions are assumed instantaneous. Percussions are introduced at the unknown fracture points. Equations of motion and constitutive laws give a set of differential equations, whose corresponding variational problem may be solved in SBV (special functions of bounded variation). The example shows how the theory applies and gives realistic results
Well-posedness of a phase transition model with the possibility of voids
No full textThe paper deals with a phase transition model applied to a two-phase system. There is a wide literature on the study of phase transition processes in case that no voids nor overlapping can occur between the two phases. The main novelty of our approach is the possibility of having voids during the phase change. This aspect is described in the model by the mass balance equation whose effects are included by means of the pressure of the system in the dynamical relations. The state variables axe the absolute temperature (whose evolution is ruled by the entropy balance equation), the strain tensor (satisfying a quasi-static macroscopic equation of motion), and the volume fractions of the two phases (whose evolutions are described by a vectorial equation coming from the principle of virtual power and related to the microscopic motions). Well-posedness of the initial-boundary value problem associated to the PDEs system resulting from this model is proved
Damage of materials: damaging effects of macroscopic vanishing motions
No full textWe investigate a mechanical model describing the evolution of damage in elastic and viscoelastic materials. The state variables are macroscopic deformations and the volume fraction of sound material. The equilibrium equations are recovered by refining the principle of virtual power including also microscopic forces. After proving an existence and uniqueness result for a regularized problem, we investigate the behaviour of solutions, in the case when a vanishing sequence of external forces is applied. By use of a rigorous asymptotics analysis, we show that macroscopic deformations can disappear at the limit, but their damaging effect remains in the equation describing the evolution of damage at a microscopic level. Moreover, it is proved that the balance of the energy is satisfied at the limit
Incompressibility and Large Deformations
No full textWe present a new point of view on the motion of an incompressible solid with large deformations. The escription of the shape changes of the solid involves the stretch matrix of the classical polar decomposition. The incompressibility condition is , accounting for possible cavitation or phase change. The reaction to the incompressibility condition is a pressure which is positive. There is cavitation or phase change when the pressure is null. The motion of a three-dimensional solid is investigated between time 0 and a final time . It is possible to prove that the model is coherent in terms of mechanics and mathematics. Let us note that the pressure is a measure allowing possible internal collisions due to cavitation
A phase transition model with the entropy balance
No full textThis paper deals with a phase transition model in which the energy balance is equivalently rewritten in terms of the entropy balance. The thermodynamical consistence of the model is proved and also under physically meaningful assumptions on the data, existence of a solution is stated for the corresponding initial boundary values problem by a maximum principle. Hence, L1-arguments yield the uniqueness of the solution and show that it evolves in accordance with thermodynamics and everyday practical properties
Collisions and fractures: A model in SBD
No full textWe investigate collisions (assumed to be instantaneous) and fractures of three-dimensional solids. Equations of motion and constitutive laws provide a set of partial differential equations, whose corresponding variational problem may be solved in the space of special functions with bounded deformations (SBD), exploiting the direct method of calculus of variations
Damage theory: microscopic effects of vanishing macroscopic motions
No full textThis paper deals with a mechanical model describing the evolution of damage in elastic and viscoelastic materials. The state variables are macroscopic deformations and a microscopic phase parameter, which is related to the quantity of damaged material. The equilibrium equations are recovered by refining the principle of virtual powers including also microscopic forces. After proving an existence and uniqueness result for a regularized problem, we investigate the behavior of solutions, in the case when a vanishing sequence of external forces is applied. By use of a rigorous asymptotics analysis, we show that macroscopic deformations can disappear at the limit, but their damaging effect remains in the equation describing the evolution of damage at a microscopic level. Moreover, it is proved that the balance of the energy is satisfied at the limit
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