A priori error for unilateral contact problems with Lagrange multiplier and IsoGeometric Analysis

In this paper, we consider unilateral contact problem without friction between a rigid body and deformable one in the framework of isogeometric analysis. We present the theoretical analysis of the mixed problem using an active-set strategy and for a primal space of NURBS of degree $p$ and $p-2$ for a dual space of B-Spline. A inf-sup stability is proved to ensure a good property of the method. An optimal a priori error estimate is demonstrated without assumption on the unknown contact set. Several numerical examples in two- and three-dimensional and in small and large deformation demonstrate the accuracy of the proposed method

Finite element based surface roughness study for ohmic contact of microswitches

Finite element method (FEM) is used to model ohmic contact in microswitches. A determinist approach is adopted, including atomic force microscope (AFM) scanning real contact surfaces and generating rough surfaces with three-dimensional mesh. FE frictionless models are set up with the elastoplastic material and the simulations are performed with a loading-unloading cycle. Two material properties, gold and ruthenium, are studied in the simulations. The effect of roughness is investigated by comparing the models with several smoothing intensities and asperity heights. The comparison is quantitatively analyzed with relations of force vs. displacement, force vs. contact area and force vs. electrical contact resistance (ECR); further the evolution of spots in contact during a loading-unloading cycle is studied

Multiscale analysis of the effect of debris on fretting wear process using a semi-concurrent method

Fretting wear is a phenomenon, in which wear happens between two oscillatory moving contact surfaces in microscale amplitude. In this paper, the effect of debris between pad and specimen is analyzed by using a semi-concurrent multiscale method. Firstly, the macroscale fretting wear model is performed. Secondly, the part with the wear profile is imported from the macroscale model to a microscale model after running in stage. Thirdly, an effective pad's radius is extracted by analyzing the contact pressure in order to take into account the effect of the debris. Finally, the effective radius is up-scaled from the microscale model to the macroscale model, which is used after running in stage. In this way, the effect of debris is considered by changing the radius of the pad in the macroscale model. Due to the smaller number of elements in the microscale model compared with the macroscale model containing the debris layer, the semi-concurrent method proposed in this paper is more computationally efficient. Moreover, the results of this semi-concurrent method show a better agreement with experimental data, compared to the results of the model ignoring the effect of debris

Three-dimensional analysis of surface crack-Hertzian stress field interaction

The results are presented of a stress intensity factor analysis of semicircular surface cracks in the inner raceway of an engine bearing. The loading consists of a moving spherical Hertzian contact load and an axial stress due to rotation and shrink fit. A 3-D linear elastic Boundary Element Method code was developed to perform the stress analysis. The element library includes linear and quadratic isoparametric surface elements. Singular quarter point elements were employed to capture the square root displacement variation and the inverse square root stress singularity along the crack front. The program also possesses the capability to separate the whole domain into two subregions. This procedure enables one to solve nonsymmetric fracture mechanics problems without having to separate the crack surfaces a priori. A wide range of configuration parameters was investigated. The ratio of crack depth to bearing thickness was varied from one-sixtieth to one-fifth for several different locations of the Hertzian load. The stress intensity factors for several crack inclinations were also investigated. The results demonstrate the efficiency and accuracy of the Boundary Element Method. Moreover, the results can provide the basis for crack growth calculations and fatigue life prediction

Statistical Mechanics of Self-Avoiding Manifolds (Part II)

We consider a model of a D-dimensional tethered manifold interacting by excluded volume in R^d with a single point. Use of intrinsic distance geometry provides a rigorous definition of the analytic continuation of the perturbative expansion for arbitrary D, 0 < D < 2. Its one-loop renormalizability is first established by direct resummation. A renormalization operation R is then described, which ensures renormalizability to all orders. The similar question of the renormalizability of the self-avoiding manifold (SAM) Edwards model is then considered, first at one-loop, then to all orders. We describe a short-distance multi-local operator product expansion, which extends methods of local field theories to a large class of models with non-local singular interactions. It vindicates the direct renormalization method used earlier in part I of these lectures, as well as the corresponding scaling laws.Comment: 32 pages, 9 figures, Second Part and extensive update of Lecture Notes originally given in ``Statistical Mechanics of Membranes and Surfaces'', Fifth Jerusalem Winter School for Theoretical Physics (1987), D. R. Nelson, T. Piran,and S. Weinberg ed