Non-monotonicity of the frictional bimaterial effect

Sliding along frictional interfaces separating dissimilar elastic materials is qualitatively different from sliding along interfaces separating identical materials due to the existence of an elastodynamic coupling between interfacial slip and normal stress perturbations in the former case. This bimaterial coupling has important implications for the dynamics of frictional interfaces, including their stability and rupture propagation along them. We show that while this bimaterial coupling is a monotonically increasing function of the bimaterial contrast, when it is coupled to interfacial shear stress perturbations through a friction law, various physical quantities exhibit a non-monotonic dependence on the bimaterial contrast. In particular, we show that for a regularized Coulomb friction, the maximal growth rate of unstable interfacial perturbations of homogeneous sliding is a non-monotonic function of the bimaterial contrast, and provide analytic insight into the origin of this non-monotonicity. We further show that for velocity-strengthening rate-and-state friction, the maximal growth rate of unstable interfacial perturbations of homogeneous sliding is also a non-monotonic function of the bimaterial contrast. Results from simulations of dynamic rupture along a bimaterial interface with slip-weakening friction provide evidence that the theoretically predicted non-monotonicity persists in non-steady, transient frictional dynamics.Comment: 14 pages, 5 figure

eXtended hybridizable discontinuous Galerkin for incompressible flow problems with unfitted meshes and interfaces

The eXtended hybridizable discontinuous Galerkin (X-HDG) method is developed for the solution of Stokes problems with void or material interfaces. X-HDG is a novel method that combines the hybridizable discontinuous Galerkin (HDG) method with an eXtended finite element strategy, resulting in a high-order, unfitted, superconvergent method, with an explicit definition of the interface geometry by means of a level-set function. For elements not cut by the interface, the standard HDG formulation is applied, whereas a modified weak form for the local problem is proposed for cut elements. Heaviside enrichment is considered on cut faces and in cut elements in the case of bimaterial problems. Two-dimensional numerical examples demonstrate that the applicability, accuracy, and superconvergence properties of HDG are inherited in X-HDG, with the freedom of computational meshes that do not fit the interfacesPeer ReviewedPostprint (author's final draft

Materials selection and design of microelectrothermal bimaterial actuators

A common form of MEMS actuator is a thermally actuated bimaterial, which is easy to fabricate by surface micromachining and permits out of plane actuation, which is otherwise difficult to achieve. This paper presents an analytical framework for the design of such microelectrothermal bimaterial actuators. Mechanics relationships for a cantilever bimaterial strip subjected to a uniform temperature were applied to obtain expressions for performance metrics for the actuator, i.e., maximum work/volume, blocked (force) moment, and free-end (displacement) slope. Results from finite-element analysis and closed form relations agree well to within 1%. The optimal performance for a given pair of materials and the corresponding thickness ratio were determined. Contours of equal performance corresponding to commonly used substrates (e.g., Si, SiO2) were plotted in the domain of governing material properties (thermal expansion coefficient and Young's modulus) to identify candidate materials for further development. These results and the accompanying methodology provide a rational basis for comparing the suitability of "standard" materials for microelectrothermal actuators, as well as identifying materials that might be suitable for further research

A modified Brazilian test for the generalized-fracturetoughness determination in multimaterial corners. Numerical and experimental results

IX CONGRESO NACIONAL DE MATERIALES COMPUESTOS. Celebrado en Girona, 5, 6, 7 y 8 de julio de 2011In the present work, a general procedure for the experimental evaluation of the generalized fracture toughness in multimaterial corners is defined. The proposed method is suitable for closed corners (all material wedges being bonded) having two singular terms in the asymptotic stress representation at the corner tip. For a particular corner configuration, the method finds the load configuration at which one of the singular terms vanishes, thus the main stress contribution being controlled by the other non-vanishing singular term. The experimental test, until failure, using the previously defined load configuration allows the generalized fracture toughness associated to each singular term to be evaluated. The whole procedure has been applied to a bimaterial CFRP-Adhesive bimaterial corner and the generalized fracture toughness values have been obtained. The testing of mixed modes has permitted a failure envelope based on the generalized fracture toughness values at the corner tip to be defined. Previously published results, with different geometries, but involving the same corner, have shown that the failure envelope can predict accurately the failure initiation at these corners.Junta de Andalucía y Fondo Social Europeo P08-TEP-4071Junta de Andalucía y Fondo Social Europeo P08-TEP-4051Ministerio de Ciencia e Innovación MAT2009-14022CAPES Ministerio de Educación de Brasi

Ambiguity of the Moment Tensor

An earthquake on a fault separating two dissimilar materials does not have a well-defined moment density tensor. We present a complete characterization of this bimaterial ambiguity in the general case of slip on a fault in an anisotropic medium. The ambiguity can be eliminated by utilizing a potency density rather than a moment density representation of a bimaterial source

Green's functions for dislocations in bonded strips and related crack problems

Green's functions are derived for the plane elastostatics problem of a dislocation in a bimaterial strip. Using these fundamental solutions as kernels, various problems involving cracks in a bimaterial strip are analyzed using singular integral equations. For each problem considered, stress intensity factors are calculated for several combinations of the parameters which describe loading, geometry and material mismatch

A boundary integral equation method in the frequency domain for cracks under transient loading

Acknowledgments The financial support of the German Academic Exchange Service (DAAD), Engineering and Physical Sciences Research Council (EPSRC) and Advanced Research Collaboration (ARC) Programme (funded by the British Council and DAAD) is gratefully acknowledged.Peer reviewedPublisher PD