Nonclassical continua, pseudobalance, and the law of action and reaction

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A new class of fit regions

EnA new set of regularity assumptions is proposed for the regions of space which can be occupied by the continuous bodies of continuum mechanics. The new assumptions are more restrictive than those made in the preceding proposals [3,4,8]. This has the favorable effect of excluding some pathological regions which were present in all classes of fit regions proposed earlier

A new class of fit regions

EnA new set of regularity assumptions is proposed for the regions of space which can be occupied by the continuous bodies of continuum mechanics. The new assumptions are more restrictive than those made in the preceding proposals [3,4,8]. This has the favorable effect of excluding some pathological regions which were present in all classes of fit regions proposed earlier

The variational structure of classical plasticity

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On the visco-elastic properties of open-cell polyurethane foams

International audienceThis communication is a summary of our previous work [12] on the elastic properties of open-cell polyurethane foams, and an anticipation of some results of a work in progress [2] on the rate-dependent properties of the same material. The elastic properties are described by a two-phase model obtained assuming a non-convex double-well strain energy density. The model captures some peculiar aspects of the stress-strain response of the material, such as strain localization and hysteresis. But it does not capture some typical inelastic effects, such as stress softening in a cyclic test, rate dependence, and memory effects. On the basis of some specific compression tests, we come to the conclusion that these effects can be described within the theory of linear viscoelasticity. This leads us to complete the previous elastic model by adding a visco-elastic element with fractional damping

A unified model for adhesive interfaces with damage, viscosity and friction

International audienceA general framework for models describing adhesive contact between rigid bodies is proposed. The intensity of adhesion is supposed to decrease under the action of prescribed tangential and normal relative displacements. The reduction is attributed to progressive damage, and comes with energy dissipation. Additional dissipation due to viscosity and friction is also taken into account. The response of the interface is described by a single state variable. It is determined by general laws expressing a mechanical version of the first two laws of thermodynamics, combined with a set of phenomenological assumptions

On the rate-dependent properties of open-cell polyurethane foams

International audienceExperiments on blocks of open-cell polyurethane foam in uniaxial compression show a progressive strain localization. In a preceding paper, localization is described by a model involving a two-phase nonlinear elastic material. The model is in a good qualitative agreement with experiments, but it was unable to capture some finer aspects of the experimental response, such as stress softening, rate-dependence, and some memory effects. In the context of filler-reinforced rubbers, the inelastic aspects of the response have been studied by several authors. Several models have been proposed, in which a specimen is generally represented as a chain of rheological elements, each consisting of a linear elastic spring set in parallel with one or more dissipative elements. Here we anticipate some results of a research still in progress, in which a good description of the response of open-cell foams is obtained from the existing models for filler-reinforced rubbers by taking visco-elastic dissipative elements obeying a fractional exponential law, and by replacing the convex elastic strain energy of the springs with a non-convex energy of the double-well type

Adhesive Contact : a Survey and a Unified Formulation

International audienceA brief survey of the most widely used Cohesive Zone Models is first presented and discussed. Then, a general framework for these laws is given under the form of a unified formulation recently proposed by Del Piero and Raous (Del Piero, Raous [1]). This unified formulation is based on : – general laws, typically, energy conservation and dissipation principles, that is, mechanical versions of the first two laws of thermodynamics, – a set of state variables, that is, an array of independent variables which fully determine the response to all possible deformation processes, – a set of elastic potential and dissipation potentials, which are functions of state in terms of which the general laws take specific forms, – a set of constitutive assumptions. The behavior of the interface is first characterized by two given loading curves f n (u n) and f t (u t) , which are supposed to be star-shaped with respect to the origin, where u n and u t are the normal and tangential components of the relative displacement on the interface and R n and R t are respectively the components of the contact force. A state variable α is introduced to measure the current intensity of damage. The variables {u n , u t , α} have to satisfy a set of inequalities which defines the state space. To exemplify this, for the special case where there is no viscosity, the loading curve R n =f n (u n) and the state space are given for the normal components in Fig.1 (a) and (b). The response due to a deformation process of loading-unloading starting from the origin is represented by the dashed line in the force-displacement plane (a) and in the state space (b). As described in [1], the strain energy is then given by : Ψ(u n , u t , α) = 1 2 g n (α)

Strain localization in polyurethane foams. Experiments and theoretical model.

International audienceStrain localization has been observed in polyurethane foams subjected to confined compression up to 70% of deformation. This phenomenon is described by a one-dimensional model, in which the foam is represented as a chain of non-linear elastic springs with non-convex strain energy density, and localization is attributed to progressive phase transition

Strain localization in open-cell polyurethane foams: experiments and theoretical model

International audienceConfined compression tests performed by the authors on open-cell polyurethane foams reveal the presence of strain localization. After a brief description of the experiments, a theoretical model is proposed. In the model, the foam is represented as a chain of elastic springs with a two-phase strain energy density, and the strain localization is due to a progressive collapse of the springs. The collapse is a sort of continuum instability, which can be attributed to phase transition. An appropriate choice of the material constants leads to a close reproduction of the experimental force-elongation response curves