Distribution based model for the grain boundaries in polycrystalline plasticity

This contribution focuses on the development of constitutive models for the grain boundary region between two crystals, relying on the dislocation based polycrystalline model documented in (Evers, L.P., Parks, D.M., Brekelmans, W.A.M., Geers, M.G.D., 2002. Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation. J. Mech. Phys. Solids 50, 2403–2424; Evers, L.P., Brekelmans, W.A.M., Geers, M.G.D., 2004a. Non-local crystal plasticity model with intrinsic SSD and GND effects. J. Mech. Phys. Solids 52, 2379–2401; Evers, L.P., Brekelmans, W.A.M., Geers, M.G.D., 2004b. Scale dependent crystal plasticity framework with dislocation density and grain boundary effects. Int. J. Solids Struct. 41, 5209–5230). The grain boundary is first viewed as a geometrical surface endowed with its own fields, which are treated here as distributions from a mathematical point of view. Regular and singular dislocation tensors are introduced, defining the grain equilibrium, both in the grain core and at the boundary of both grains. Balance equations for the grain core and grain boundary are derived, that involve the dislocation density distribution tensor, in both its regular and singular contributions. The driving force for the motion of the geometrically necessary dislocations is identified from the pull-back to the lattice configuration of the quasi-static balance of momentum, that reveals the duality between the stress and the curl of the elastic gradient. Criteria that govern the flow of mobile geometrically necessary dislocations (GNDs) through the grain boundary are next elaborated on these bases. Specifically, the sign of the projection of a lattice microtraction on the glide velocity defines a necessary condition for the transmission of incoming GNDs, thereby rendering the set of active slip systems for the glide of outgoing dislocations. Viewing the grain boundary as adjacent bands in each grain with a constant GND density in each, the driving force for the grain boundary slip is further expressed in terms of the GND densities and the differently oriented slip systems in each grain. A semi-analytical solution is developed in the case of symmetrical slip in a bicrystal under plane strain conditions. It is shown that the transmission of plastic slip occurs when the angle made by the slip direction relative to the grain boundary normal is less than a critical value, depending on the ratio of the GND densities and the orientation of the transmitted dislocations

A 3D modelling of the protrusion and retraction of a single cell during the motiliy and the rolling

The rolling is an important kind of cell adhesion, especially in the case of the immune mechanism, due to the leukocyte action, which is strongly influenced by molecular affinity [1]. Our purpose, in this paper, is the presentation of a 3D theorical model which describes the behaviour of the contact interface cell-wall during the rolling and the cell deformation. The first point concerns the modelling of the contact interface, which is assimilated to a circular plate, linked to the wall (e.g vein) by elastic springs. The second point concerns the modelling of the active deformation due to the change of the cytoskeleton structure during the cell motility

Influence of the mechanical damping on the rolling of a single biological cell: A stochastic approach

The rolling is an important kind of cell adhesion, especially in the case of the immune mechanism, due to the leukocyte action, which is strongly influenced by molecular affinity [1].
Our purpose, in this paper, is the presentation of a 2D model which describes the behaviour of the contact interface cell-wall during the rolling. The cell membrane and the wall are assimilated to two rectilinear elastic beams, linked by elastic springs in the case of undamped connections [2] or viscoelastic element in the case of a dissipative behavior. As a first step, the motion of the interface is analyzed, under the external actions of the dynamical fluid pressure, the Van der Waals (attractive forces) and electrostatic effects (repulsive). The second point corresponds to the combination of the vibration of the contact zone and the rupture of the existing connections under a pulling effort. The last step concerns the description of the kinetic of junction between the free ligands and receptors, which constitutes the new connections.
The numerical simulations show the rolling phenomenon, the influence of the mechanical damping on the behavior of the contact interface and the kinetics of junctions between the adhesion free molecules

Asymptotic behaviour of micropolar adhesives

This work describes the asymptotic mechanical behaviour of two elastic adherends adhesively bonded by a thin elastic micropolar adhesive when the thinness of the adhesive layer goes to 0. This asymptotic analysis is performed using first the asymptotic expansion method through the mixed Hellinger-Reissner variational formulation. Then we use an epi-convergence argument, through the definition of an energy functional associated to the problem. Finally the case of two elastic micropolar adherends adhesively joined by a thin micropolar adhesive is studied

Dynamical analysis of homogenized second gradient anisotropic media for textile composite structures and analysis of size effects

International audienceIn order to predict the dispersion relation of 3D composite structures in the low frequency range, we construct effective first and second order grade continuum models. The effective properties of textile composites are obtained computationally by an equivalent strain energy method based on the response of the representative volume unit cell (RUC) under prescribed boundary conditions as described in Goda and Ganghoffer (2016). The expressions of the phase velocities for the three modes of wave propagation in a 3D context (longitudinal, horizontal shear and vertical shear) reveal that the second order continuum is dispersive, due to the presence of the second order elasticity constants. The shape change of the phase velocity when increasing the wave number shows the dispersive behavior of the second gradient medium, whereas Cauchy medium is non dispersive. Plots of the iso-frequency contour for the two investigated composites in the case of second gradient and Cauchy effective medium show that the second gradient contributions does not modify the anisotropic behavior of the considered composites. Important size effects on the dynamical behavior are shown, especially reflected by the dispersive behavior and the anisotropic dynamic responses, due to the significant overall increase of the second order rigidity matrix when increasing the RUC size

Martensitic transformation plasticity simulations by finite elements

The mechanical behaviour associated to the martensitic transformation has been modelled using a 2D FE description. The martensite variants are constituted of different elements of the mesh and four different variants are allowed to transform in the grain. The transformation progress is prescribed using a thermodynamical criterion based on the maximal work associated to the variant formation. Transformation plasticity deformation and plates orientation patterns are obtained for three stress levels. These results are discussed in regard to the model used and the physical parameters introduced in the model

MECHANICAL AND THERMODYNAMICAL STUDY OF A MACROSCOPICALLY COHERENT PHASE TRANSITION. CASE OF THE MARTENSITIC TRANSFORMATION

In the general framework of a macroscopically coherent phase transition, the mechanical and thermodynamical behaviour of a two-phase volume element under structural evolution will be investigated and discussed. The identification of internal entropy production will then allow to formulate a general evolution condition for such a system and the internal stress state will appear to influence strongly the transformation behaviour, via the interface. The case of a martensitic transformation is considered. From that rigourous mechanical approach, we obtain the thermodynamical balance equation used for martensitic transformation

MICROMECHANICAL SIMULATION OF A MARTENSITIC TRANSFORMATION BY FINITE ELEMENTS

A micromechanical model describing the martensitic transformation on the grain scale has been developed, using Finite Elements. First results gained from the simulation illustrate how the morphological evolution within the grain is directly controlled by the internal stress state. The reversible and irreversible part of transformation "plasticity" strain and their evolution with the transformation can then be obtained from these calculations