An integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials. The integral may be evaluated almost by inspection for a few notch configurations. Also, for materials of the elastic-plastic type (treated through a deformation rather than incremental formulation), with a linear re-sponse to small stresses followed by non-linear yielding, the integral may be evaluated in terms of Irwin's stress intensity factor when yielding occurs on a scale small in comparison to notch size. On the other hand, the integral may be expressed in terms of the concentrated deformation field in the vicinity of the notch tip. This implies that some information on strain concentrations is obtainable without recorse to detailed non-linear analyses. Such an approach is exploited here. Applications are made to: 1) Approximate estimates of strain concentrations at smooth ended notch tips in elastic and elastic-plastic materials, 2) A general solution for crack tip separation in the Barenblatt-Dugdale crack model, leading to a proof of the identity of the Griffith theory and Barenblatt cohesive theory for elastic brittle fracture and to the inclusion of strain hardening behavior in the Dugdale model for plane stress yielding, and 3) An approximate perfectly plastic plane strain analysis, based on the slip line theory, of contained plastic deformation at a crack tip and of crack blunting.

. We develop and test an algorithmic approach for the boundary design of elastic structures. The goal of our approach is two-fold. First, to develop a method which allows one to rapidly solve the two-dimensional Lame equations in abitrary domains and compute for example the stresses, and second, to develop a systematic way of modifying the design towards optimizing chosen properties. At the core, our approach relies on two distinct steps. Given a design, we rst apply an Explicit Jump Immersed Interface Method for computing the stresses for a given design shape. We then use a narrow band level set method to perturb this shape and progress towards an improved design. The equations of 2D linear elastostatics in the displacement formulation on arbitrary domains are solved quickly by domain embedding and the use of fast elastostatic solvers. This eectively reduces the dimensionality of the problem by one. Once the stresses are found, the level set method, which represents the...

Haptic interaction is an increasingly common form of interaction in virtual environment (VE) simulations. This medium introduces some new challenges. In this paper we study the problem arising from the difference between the sampling rate requirements of haptic interfaces and the significantly lower update rates of the physical models being manipulated. We propose a multirate simulation approach which uses a local lin-ear approximation. The treatment includes a detailed analysis and experimental verification of the approach. The proposed method is also shown to improve the sta-bility of the haptic interaction.

A method has been developed for modeling structure-property relationships of nano-stmctured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with an equivalent-continuum model. It has been shown that this substitution may be accomplished by equating the vibrational potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As an important example with direct application to the development and characterization of single-walled carbon nanotubes, the model has been applied to determine the effective continuum geometry of a graphene sheet. A representative volume element of the equivalentcontinuum model has been developed with an effective thickness. This effective thickness has been shown to be similar to, but slightly smaller than, the interatomic spacing of graphite.

A probabilistic approach to the brain image matching problem is proposed in which no assumptions are made about the nature of the intensity relationship between the two brain images. Instead the correspondence between the two intensities is represented by a conditional probability, which is iteratively determined as part of the matching problem. This paper presents the theory and describes its finite element implementation. The results of preliminary experiments indicate that there remain several aspects of the algorithm that require further investigation and refinement. 1.

This paper presents a systematic approach to quantifying the effectiveness of compliant grasps and fixtures of an object. The approach is physically motivated and applies to the grasping of 2D and 3D objects by any number of fingers. The approach is based on a characterization of the frame-invariant features of a grasp or fixture stiffness matrix. In particular, we define a set of frame-invariant characteristic stiffness parameters, and provide physical and geometric interpretation for these parameters. Using a physically meaningful scheme to make the rotational and translational stiffness parameters comparable, we define a frame-invariant quality measure, which we call the stiffness quality measure. An example of a frictional grasp illustrates the effectiveness of the quality measure. We then consider the optimal grasping of frictionless polygonal objects by three and four fingers. Such frictionless grasps are useful in high-load fixturing applications, and their relative simplicity allows ...

Abstract—This paper reports on the design, fabrication, and testing of a low-actuation voltage Microelectromechanical systems (MEMS) switch for high-frequency applications. The mechanical design of low spring-constant folded-suspension beams is presented first, and switches using these beams are demonstrated with measured actuation voltages of as low as 6 V. Furthermore, common nonidealities such as residual in-plane and gradient stress, as well as down-state stiction problems are addressed, and possible solutions are discussed. Finally, both experimental and theoretical data for the dynamic behavior of these devices are presented. The results of this paper clearly underline the need of an integrated design approach for the development of ultra low-voltage RF MEMS switches. Index Terms—Low actuation voltage, microelectromechanical systems (MEMS) switches, residual stress, spring constant, switching speed, top-electrode switches. I.

. Image matching has emerged as an important area of investigation in medical image analysis. In particular, much attention has been focused on the atlas problem, in which a template representing the structural anatomy of the human brain is deformed to match anatomic brain images from a given individual. The problem is made difficult because there are important differences in both the gross and local morphology of the brain among normal individuals. We have formulated the image matching problem under a Bayesian framework. The Bayesian methodology facilitates a principled approach to the development of a matching model. Of special interest is its capacity to deal with uncertainty in the estimates, a potentially important but generally ignored aspect of the solution. In the construction of a reference system for the human brain, the Bayesian approach is well suited to the task of modeling variation in morphology. Statistical information about morphological variability, accumulated over p...

This paper presents an approach to animate elastic deformable materials at interactive rates using space-time adaptive resolution. We propose a new computational model, based on the conventional Hooke's law, that uses a discrete approximation of derivative operators on irregular sample points. It allows local refinement or simplification of the computational model based on local error measurement. We in effect minimize calculations while ensuring a realistic and scale-independent behavior within a given accuracy threshold. We demonstrate this technique on a real-time virtual liver surgery application. 1 Introduction Although simple interactive animation techniques exist and are used in virtual reality systems for instance, they mainly simulate rigid bodies. Using simplified solid mechanics laws, they focus on issues like collision detection and contact modeling, where naive approaches are computationally intensive [Bar96, Fau98]. A smaller amount of effort has been put into deformabl...

This paper discusses a Finite Element approach for volumetric soft tissue modeling in the context of facial surgery simulation. We elaborate on the underlying physics and address some computational aspects of the finite element discretization. In contrast to existing approaches speed is not our first concern, but we strive for the highest possible accuracy of simulation. We therefore propose an extension of linear elasticity towards incompressibility and nonlinear material behavior, in order to describe the complex properties of human soft tissue more accurately. Furthermore, we incorporate higher order interpolation functions using a Bernstein-Bézier formulation, which has various advantageous properties, such as its integral polynomial form of arbitrary degree, efficient subdivision schemes, and suitability for geometric modeling and rendering. In addition, the use of tetrahedral Finite Elements does not put any restriction on the geometry of the simulated volumes. Experimental results obtained from a synthetic block of soft tissue and from the Visible Human Data Set illustrate the performance of the envisioned model.