Surface perturbation of an elastodynamic contact problem with friction

International audienceWe consider the dynamical process of an elastic body in unilateral fricitonal contact with a rigid foundation. Friction is modelled with the Coulomb law with a coefficient that depends on the slip velocity. To allow for velocity discontinuities we use the elastodynamic (hyperbolic) framework. Nevertheless, this does not lead to a well-posed problem. To remedy this, we perturb the solution of the elastodynamical problem in a thin layer next to the contact boundary. This is a generalization of an approach previously studied in a one-dimensional case. We establish existence and uniqueness results for the perturbed and regularized problem and provide an interpretation of this perturbation

On the dynamic sliding with friction of a rigid block and of an infinite elastic slab

International audienceWe consider dynamic motions of two elastic systems undergoing frictional slip. The first one is the classical model of the frictional slider loaded through an elastic spring. The second one is an infinite elastic slab bounded by two planes which is in contract with a rigid body and submitted to shearing. Slip weakening and slip rate weakening friction laws are both considered. The two simple systems show very different qualitative behaviors. In the case of the slip dependent friction a slider moves with a single slip event when a critical stress level is reached. Under the same conditions, a series of slip events occur for the infinite slab. This difference between the behavior of the two systems is due to the important part played by inertia in the mass concentrated block slider model. In the case of slip rate weakening, the analysis of the problem for the infinite slab indicates a major difficulty: this problem has no unique solution if the rate of weakening exceeds a limit that is explicitly given. Whatever is the selection rule chosen to discriminate the solution, shocks will occur. The slip history obtained for the slab is very different from the one obtained with a block slider. For the infinite elastic slab the slip velocity exhibits sharp variations (shocks). On the contrary, a block slider does not exhibit this behavior. It is a clear example of the limitation of the use of such a simple analogy to describe the actual properties of the relative motions of two media in contact with friction

Existence et unicité pour le frottement élastodynamique avec perturbation par « inertie de surface »

International audienceWe present an existence and uniqueness result for a regularized problem of unilateral contact and friction in elastodynamic obtained with a perturbation of a dynamic elasticity operator defined on the contact boundary. This perturbation keep the local characteristic of the friction law. This is a step in the analysis of the multi-solutions appearing in this kind of problems when a decreasing friction coefficient is used.On présente un résultat d’existence et d’unicité pour un problème régularisé de contact unilatéral avec frottement en élastodynamique obtenu d’une part en régularisant de façon classique la loi de frottement et la condition de contact unilatéral et, d’autre part, en perturbant le système à l’aide d’un opérateur d’élasticité dynamique défini sur le bord de frottement. Un des intérêts de cette perturbation est de conserver le caractère local de la loi de frottement. C’est une étape dans l’analyse des multi-solutions qui apparaissent lorsque l’on utilise un coefficient de frottement décroissant en vitesse de glissement, et fait suite à des travaux dans le cas monodimensionnel

Detection of quantitative trait loci for carcass composition traits in pigs

A quantitative trait locus (QTL) analysis of carcass composition data from a three-generation experimental cross between Meishan (MS) and Large White (LW) pig breeds is presented. A total of 488 F2 males issued from six F1 boars and 23 F1 sows, the progeny of six LW boars and six MS sows, were slaughtered at approximately 80 kg live weight and were submitted to a standardised cutting of the carcass. Fifteen traits, i.e. dressing percentage, loin, ham, shoulder, belly, backfat, leaf fat, feet and head weights, two backfat thickness and one muscle depth measurements, ham + loin and back + leaf fat percentages and estimated carcass lean content were analysed. Animals were typed for a total of 137 markers covering the entire porcine genome. Analyses were performed using a line-cross (LC) regression method where founder lines were assumed to be fixed for different QTL alleles and a half/full sib (HFS) maximum likelihood method where allele substitution effects were estimated within each half-/full-sib family. Additional analyses were performed to search for multiple linked QTL and imprinting effects. Significant gene effects were evidenced for both leanness and fatness traits in the telomeric regions of SSC 1q and SSC 2p, on SSC 4, SSC 7 and SSC X. Additional significant QTL were identified for ham weight on SSC 5, for head weight on SSC 1 and SSC 7, for feet weight on SSC 7 and for dressing percentage on SSC X. LW alleles were associated with a higher lean content and a lower fat content of the carcass, except for the fatness trait on SSC 7. Suggestive evidence of linked QTL on SSC 7 and of imprinting effects on SSC 6, SSC 7, SSC 9 and SSC 17 were also obtained

Detection of quantitative trait loci for growth and fatness in pigs

A quantitative trait locus (QTL) analysis of growth and fatness data from a three-generation experimental cross between Meishan (MS) and Large White (LW) pig breeds is presented. Six boars and 23 F1 sows, the progeny of six LW boars and six MS sows, produced 530 F2 males and 573 F2 females. Nine growth traits, i.e. body weight at birth and at 3, 10, 13, 17 and 22 weeks of age, average daily gain from birth to 3 weeks, from 3 to 10 weeks and from 10 to 22 weeks of age, as well as backfat thickness at 13, 17 and 22 weeks of age and at 40 and 60 kg live weight were analysed. Animals were typed for a total of 137 markers covering the entire porcine genome. Analyses were performed using two interval mapping methods: a line-cross (LC) regression method where founder lines were assumed to be fixed for different QTL alleles and a half-/full-sib (HFS) maximum likelihood method where allele substitution effects were estimated within each half-/full-sib family. Both methods revealed highly significant gene effects for growth on chromosomes 1, 4 and 7 and for backfat thickness on chromosomes 1, 4, 5, 7 and X, and significant gene effects on chromosome 6 for growth and backfat thickness. Suggestive QTLs were also revealed by both methods on chromosomes 2 and 3 for growth and 2 for backfat thickness. Significant gene effects were detected for growth on chromosomes 11, 13, 14, 16 and 18 and for backfat thickness on chromosome 8, 10, 13 and 14. LW alleles were associated with high growth rate and low backfat thickness, except for those of chromosome 7 and to a lesser extent early-growth alleles on chromosomes 1 and 2 and backfat thickness alleles on chromosome 6