Showing papers by "Garth N. Wells published in 2004"

Cohesive-zone models, higher-order continuum theories and reliability methods for computational failure analysis

Abstract: A concise overview is given of various numerical methods that can be used to analyse localization and failure in engineering materials. The importance of the cohesive-zone approach is emphasized and various ways to incorporate the cohesive-zone methodology in discretization methods are discussed. Numerical representations of cohesive-zone models suffer from a certain mesh bias. For discrete representations this is caused by the initial mesh design, while for smeared representations it is rooted in the ill-posedness of the rate boundary value problem that arises upon the introduction of decohesion. A proper representation of the discrete character of cohesive-zone formulations which avoids any mesh bias can be obtained elegantly when exploiting the partition-of-unity property of finite element shape functions. The effectiveness of the approach is demonstrated for some examples at different scales. Moreover, examples are shown how this concept can be used to obtain a proper transition from a plastifying or damaging continuum to a shear band with gross sliding or to a fully open crack (true discontinuum). When adhering to a continuum description of failure, higher-order continuum models must be used. Meshless methods are ideally suited to assess the importance of the higher-order gradient terms, as will be shown. Finally, regularized strain-softening models are used in finite element reliability analyses to quantify the probability of the emergence of various possible failure modes.

Sensitivity of the scale partition for variational multiscale large-eddy simulation of channel flow

Abstract: The variational multiscale method has been shown to perform well for large-eddy simulation (LES) of turbulent flows. The method relies upon a partition of the resolved velocity field into large- and small-scale components. The subgrid model then acts only on the small scales of motion, unlike conventional LES models which act on all scales of motion. For homogeneous isotropic turbulence and turbulent channel flows, the multiscale model can outperform conventional LES formulations. An issue in the multiscale method for LES is choice of scale partition and sensitivity of the computed results to it. This is the topic of this investigation. The multiscale formulation for channel flows is briefly reviewed. Then, through the definition of an error measure relative to direct numerical simulation (DNS) results, the sensitivity of the method to the partition between large- and small-scale motions is examined. The error in channel flow simulations, relative to DNS results, is computed for various partitions between large- and small-scale spaces, and conclusions drawn from the results.

Energy transfers and spectral eddy viscosity in large-eddy simulations of homogeneous isotropic turbulence: Comparison of dynamic Smagorinsky and multiscale models over a range of discretizations

Abstract: Energy transfers within large-eddy simulation (LES) and direct numerical simulation (DNS) grids are studied. The spectral eddy viscosity for conventional dynamic Smagorinsky and variational multiscale LES methods are compared with DNS results. Both models underestimate the DNS results for a very coarse LES, but the dynamic Smagorinsky model is significantly better. For moderately to well-refined LES, the dynamic Smagorinsky model overestimates the spectral eddy viscosity at low wave numbers. The multiscale model is in good agreement with DNS for these cases. The convergence of the multiscale model to the DNS with grid refinement is more rapid than for the dynamic Smagorinsky model.

An experimental-computational investigation of fracture in brittle materials

Abstract: A combined experimental-computational study of a double edge-notched stone specimen subjected to tensile loading is presented. In the experimental part, the load-deformation response and the displacement field around the crack tip are recorded. An Electronic Speckle Pattern Interferometer (ESPI) is used to obtain the local displacement field. The experimental results are used to validate a numerical model for the description of fracture using finite elements. The numerical model uses displacement discontinuities to model cracks. At the discontinuity, a plasticity-based cohesive zone model is applied for monotonic loading and a combined damage-plasticity cohesive zone model is used for cyclic loading. Both local and global results from the numerical simulations are compared with experimental data. It is shown that local measurements add important information for the validation of the numerical model. Consequently, the numerical models are enhanced in order to correctly capture the experimentally observed behaviour.

A continuous/discontinuous Galerkin formulation for a strain gradient-dependent damage model: 2D results

Abstract: The numerical solution of strain gradient-dependent continuum problems has been hindered by continuity demands on the basis functions. The presence of terms in constitutive models that involve gradi- ents of the strain eld means that the C 0 continuity of standard nite element shape functions is insufcient. Despite a resurgence of research interest in strain gradient continuum models to represent micro-mechanical effects, a sound, effective and simple framework for the numerical solution of strain gradient-dependent problems is lacking. Here, a formulation is presented which allows the use of C 0 nite element shape func- tions for the solution of a prototype strain gradient-dependent damage model. The formulation is examined in two dimensions for the simulation of crack propagation. Particular attention is paid to the application of non-standard boundary conditions.

A continuous/discontinuous Galerkin formulation for a strain gradient-dependent damage model

Abstract: The numerical solution of strain gradient-dependent continuum problems has been hindered by continuity demands on the basis functions. The presence of terms in constitutive models which involve gradients of the strain eld means that the C 0 conti- nuity of standard nite element shape functions is insucient. In this work, a continu- ous/discontinuous Galerkin formulation is developed to solve a strain gradient-dependent damage problem in a rigorous manner. Potential discontinuities in the strain eld across element boundaries are incorporated in the weak form of the governing equations. The per- formance of the formulation is tested in one dimension for various interpolations, which provides guidance for two-dimensional simulations.