Adrian J. Lew

Optimal BV estimates for a discontinuous Galerkin method for linear elasticity

We analyze a discontinuous Galerkin method for linear elasticity. The discrete formulation derives from the Hellinger-Reissner variational principle with the addition of stabilization terms analogous to those previously considered by others for the Navier-Stokes equations and a scalar Poisson equation. For our formulation, we first obtain convergence in a mesh-dependent norm and in the natural mesh-independent BD norm. We then prove a generalization of Korns second inequality which allows us to strengthen our results to an optimal, mesh-independent BV estimate for the error.

Role of Surface Roughness in Hysteresis during Adhesive Elastic Contact

In experiments that involve contact with adhesion between two surfaces, as found in atomic force microscopy or nanoindentation, two distinct contact force (P) versus indentation-depth (h) curves are often measured depending on whether the indenter moves towards or away from the sample. The origin of this hysteresis is not well understood and is often attributed to moisture, plasticity or viscoelasticity. Here we report experiments which show that hysteresis can exist in the absence of these effects, and that its magnitude depends on surface roughness. We develop a theoretical model in which the hysteresis appears as the result of a series of surface instabilities, in which the contact area grows or recedes by a finite amount. The model can be used to estimate material properties from contact experiments even when the measured P–h curves are not unique.

A Note on the Numerical Treatment of the k-epsilon Turbulence Model*

Numerical solution of the equations arising from the κ mdash; ε turbulence model has difficulties inherent to nonlinear convection-reaction-diffusion equations with strong reaction terms, resulting in that numerical schemes easily become unstable. We present a formulation that stresses on the robustness of the solution method, tackling common problems that produce instability. The main contribution concerns the loss of positivity of κ and ε, which is addressed by acting on the coefficients of the reaction and diffusion terms rather than on the turbulent variables themselves. In addition, a linearized implicit, non-iterative, treatment of the wall law is proposed.

Discontinuous Galerkin methods for nonlinear elasticity

In this talk we present a general formulation for discontinuous Galerkin methods for nonlinear elasticity. We discuss the efficiency, implementation, and stabilization of the method, and illustrate the results with numerical examples, including convergence rates, behavior under nearly incompressible conditions and under severely large deformations. We illustrate the performance of the method with applications to biomechanics problems.

Towards a dynamic data driven system for structural and material health monitoring

This paper outlines the initial motivations and implementation scope supporting a dynamic data driven application system for material and structural health monitoring as well as critical event prediction. The dynamic data driven paradigm is exploited to promote application advances, application measurement systems and methods, mathematical and statistical algorithms and finally systems software infrastructure relevant to this effort. These advances are intended to enable behavior monitoring and prediction as well as critical event avoidance on multiple time scales.

High-Order Finite Element Methods for Moving Boundary Problems with Prescribed Boundary Evolution

Abstract We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our approach is the use of a universal mesh: a stationary background mesh containing the domain of interest for all times that adapts to the geometry of the immersed domain by adjusting a small number of mesh elements in the neighborhood of the moving boundary. The resulting method maintains an exact representation of the (prescribed) moving boundary at the discrete level, or an approximation of the appropriate order, yet is immune to large distortions of the mesh under large deformations of the domain. The framework is general, making it possible to achieve any desired order of accuracy in space and time by selecting a preferred and suitable finite-element space on the universal mesh for the problem at hand, and a preferred and suitable time integrator for ordinary differential equations. We illustrate our approach by constructing a particular class of methods, and apply them to a prescribed-boundary variant of the Stefan problem. We present numerical evidence for the order of accuracy of our schemes in one and two dimensions.

An artificial viscosity method for the Lagrangian analysis of shocks in solids with strength on unstructured, arbitrary order tetrahedral meshes

We present an artificial viscosity scheme tailored to finite-deformation Lagrangian calculations of shocks in materials with or without strength on unstructured tetrahedral meshes of arbitrary order. The artificial viscous stresses are deviatoric and satisfy material-frame indifference exactly. We have assessed the performance of the method on selected tests, including: a two-dimensional shock tube problem on an ideal gas; a two-dimensional piston problem on tantalum without strength; and a three-dimensional plate impact problem on tantalum with strength. In all cases, the artificial viscosity scheme returns stable and ostensibly oscillation-free solutions on meshes which greatly underresolve the actual shock thickness. The scheme typically spreads the shock over 4 to 6 elements and captures accurately the shock velocities and jump conditions.

Analysis of a Method to Parameterize Planar Curves Immersed In Triangulations

We prove that a planar

Application of Assembly of Finite Element Methods on Graphics Processors for Real-Time Elastodynamics

C^2

Some Applications of Discontinuous Galerkin Methods in Solid Mechanics

-regular boundary