In this contribution, a mortar-type method for the coupling of non-conforming NURBS (Non-Uniform Rational B-spline) surface patches is proposed. The connection of non-conforming patches with shared degrees of freedom requires mutual refinement, which propagates throughout the whole patch due to the tensor-product structure of NURBS surfaces. Thus, methods to handle non-conforming meshes are essential in NURBSbased isogeometric analysis. The main objective of this work is to provide a simple and efficient way to couple the individual patches of complex geometrical models without altering the variational formulation. The deformations of the interface control points of adjacent patches are interrelated with a master-slave relation. This relation is established numerically using the weak form of the equality of mutual deformations along the interface. With the help of this relation, the interface degrees of freedom of the slave patch can be condensated out of the system. A natural connection of the patches is attained without additional terms in the weak form. The proposed method is also applicable for nonlinear computations without further measures. Linear and geometrical nonlinear examples show the high accuracy and robustness of the new method. A comparison to reference results and to computations with the Lagrange multiplier method is given.The combination of these two issues requires methods to handle non-conforming patches in order to establish an efficient mechanical response analysis framework for the computation of complex NURBS surface models.Domain decomposition methods decompose the domain of a given problem into subdomains, of which the parametrization does not have to match. The situation at hand is an ideal field of application for domain decomposition methods, where each patch can be regarded as one subdomain. A general overview over domain decomposition methods is given in [6]. The Penalty method [7], the Lagrange multiplier method [8], and Nitsche's method [9] were proposed in the 1970s to enforce Dirichlet boundary conditions in a weak manner. In recent engineering literature, these methods are used as a basis for domain decomposition techniques. Mortar methods are the prevailing domain decomposition method in mathematical literature. Basically, two standard types of mortar formulations exist, which are referred to as the non-conforming positive definite problem and the saddle point problem based on unconstrained product spaces in [6]. In all cases, a Lagrange multiplier space is used for the matching conditions along the interface. The mortar method leading to the nonconforming positive definite problem was initially proposed by Bernardi et al. [10]. The function spaces are constrained to fulfill the matching condition at the interface in a weak manner. Basically, this means that the basis functions of one side are related to those of the other side in a way that the matching condition is fulfilled. The discretization of the interface condition with Lagrange multiplier functions yields an equation...

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The extent to which time-dependent fracture criteria affect the dynamic behavior of fracture in a discrete structure is discussed in this work. The simplest case of a semi-infinite isotropic chain of oscillators has been studied. Two history-dependent criteria are compared to the classical one of threshold elongation for linear bonds. The results show that steadystate regimes can be reached in the low subsonic crack speed range where it is impossible according to the classical criterion. Repercussions in terms of load and crack opening versus velocity are explained in detail. A strong qualitative influence of history-dependent criteria is observed at low subsonic crack velocities, especially in relation to achievable steady-state propagation regimes. Keywords

a Communicated by I. SevostianovIn the present paper, an asymptotic model is constructed for the short-time deformation of an articular cartilage layer modeled as transversely isotropic, transversely homogeneous biphasic material. It is assumed that the layer thickness is relatively small compared with the characteristic size of the normal surface load applied to the upper surface of the cartilage layer, while the bottom surface is assumed to be firmly attached to a rigid impermeable substrate. In view of applications to articular contact problems, it is assumed that the interstitial fluid is not allowed to escape through the articular surface.

Migratory birds travel over impressively long distances. Consequently, they have to adopt flight regimes being both efficient - in order to spare their metabolic resources - and robust to perturbations. This paper investigates the relationship between both aspects, i.e. mechanical performance and stability in flapping flight of migratory birds. Relying on a poly-articulated wing morphing model and a tail-like surface, several families of steady flight regime have been identified and analyzed. These families differ by their wing kinematics and tail opening. A systematic parametric search analysis has been carried out, in order to evaluate power consumption and cost of transport. A framework tailored for assessing limit cycles, namely Floquet theory, is used to numerically study flight stability. Our results show that under certain conditions, an inherent passive stability of steady and level flight can be achieved. In particular, we find that progressively opening the tail leads to passively stable flight regimes. Within these passively stable regimes, the tail can produce either upward or downward lift. However, these configurations entail an increase of cost of transport at high velocities penalizing fast forward flight regimes. Our model-based predictions suggest that long range flights require a furled tail configuration, as confirmed by field observations, and consequently need to rely on alternative mechanisms to stabilize the flight.