A finite element framework for modeling internal frictional contact in three-dimensional fractured media using unstructured tetrahedral meshes

AbstractThis paper introduces a three-dimensional finite element (FE) formulation to accurately model the linear elastic deformation of fractured media under compressive loading. The presented method applies the classic Augmented Lagrangian(AL)-Uzawa method, to evaluate the growth of multiple interacting and intersecting discrete fractures. The volume and surfaces are discretized by unstructured quadratic triangle-tetrahedral meshes; quarter-point triangles and tetrahedra are placed around fracture tips. Frictional contact between crack faces for high contact precisions is modeled using isoparametric integration point-to-integration point contact discretization, and a gap-based augmentation procedure. Contact forces are updated by interpolating tractions over elements that are adjacent to fracture tips, and have boundaries that are excluded from the contact region. Stress intensity factors are computed numerically using the methods of displacement correlation and disk-shaped domain integral. A novel square-root singular variation of the penalty parameter near the crack front is proposed to accurately model the contact tractions near the crack front. Tractions and compressive stress intensity factors are validated against analytical solutions. Numerical examples of cubes containing one, two, twenty four and seventy interacting and intersecting fractures are presented

A Comparison of Numerical Methods used for\ud Finite Element Modelling of Soft Tissue\ud Deformation

Soft tissue deformation is often modelled using incompressible nonlinear elasticity, with solutions computed using the finite element method. There are a range of options available when using the finite element method, in particular, the polynomial degree of the basis functions used for interpolating position and pressure, and the type of element making up the mesh. We investigate the effect of these choices on the accuracy of the computed solution, using a selection of model problems motivated by typical deformations seen in soft tissue modelling. We set up model problems with discontinuous material properties (as is the case for the breast), steeply changing gradients in the body force (as found in contracting cardiac tissue), and discontinuous first derivatives in the solution at the boundary, caused by a discontinuous applied force (as in the breast during mammography). We find that the choice of pressure basis functions are vital in the presence of a material interface, higher-order schemes do not perform as well as may be expected when there are sharp gradients, and in general that it is important to take the expected regularity of the solution into account when choosing a numerical scheme

Hyperelastic modelling of nonlinear running surfaces

Accurate, 3-D analyses of running impact require a constitutive model of the running surface that includes the material nonlinearity shown by many modern surfaces. This paper describes a hyperelastic continuum that mimics the experimentally measured response of a particular treadmill surface. The material model sacrifices a little accuracy to admit a robust, low-order hyperelastic strain-energy functional. This helps prevent the premature termination of finite element simulations, due to numerical or material instabilities, that can occur with higher-order functionals. With only two free constants, it is also a more practical design tool. The best fit to the quasi-static response of the treadmill was achieved with an initial shear modulus =2 MPa and a power-stiffening index =25. The paper outlines the method used to derive the material constants for the treadmill, a device that is not amenable to the usual materials laboratory tests and must be reverse-engineered. Finite element analyses were then performed to ensure that the treadmill model interacts with the other components of the multibody running system in a numerically stable and physically realistic manner. The model surface was struck by a rigid heel, cushioned by a hyperfoam material that represents a shoe midsole. The results show that, while the ground reaction force is similar to that obtained with a rigid surface, the maximum principal stress in the shoe is reduced by 15%. Such a reduction, particularly when endured over many load cycles, may have a significant effect on comfort and damage to nearby tissue

Strip yield modelling of fatigue crack under variable amplitude loading

The results from 'strip yield' approach of the FASTRAN type models of plasticity induced crack closure effects of fatigue cracks subjected to variable amplitude loadings are presented. The strip yield results are compared with authors' finite element (FE) and experimental results. It has been observed that the strip yield model is seen to be fundamentally limited by choice of alpha (constraint factor) and corresponding to treat baseline closure effects. Double overload closure behavior is functionally similar for both strip yield and FE models. Under multiple overloads, an important functional difference is seen between FE and strip yield models. This has been linked to the absence of in-plane constraint in the strip yield model, which is seen to have a distinct decreasing influence on on-going closure effects.Peer reviewedFinal Accepted Versio

Avalanches, loading and finite size effects in 2D amorphous plasticity: results from a finite element model

Crystalline plasticity is strongly interlinked with dislocation mechanics and nowadays is relatively well understood. Concepts and physical models of plastic deformation in amorphous materials on the other hand - where the concept of linear lattice defects is not applicable - still are lagging behind. We introduce an eigenstrain-based finite element lattice model for simulations of shear band formation and strain avalanches. Our model allows us to study the influence of surfaces and finite size effects on the statistics of avalanches. We find that even with relatively complex loading conditions and open boundary conditions, critical exponents describing avalanche statistics are unchanged, which validates the use of simpler scalar lattice-based models to study these phenomena.Comment: Journal of Statistical Mechanics: Theory and Experiment, 2015, P0201

Guidelines to select suitable parameters for contour method stress measurements

The contour method is one of the promising techniques for the measurement of residual stresses in engineering components. In this method, the cut surfaces deform, owing to the relaxation of residual stresses. The deformations of the two cut surfaces are then measured and used to back calculate the 2-dimensional map of original residual stresses normal to the plane of the cut. Thus, it involves four main steps; specimen cutting, surface contour measurement, data analysis and finite element simulation. These steps should perform in a manner that they do not change the underlying features of surface deformation especially where the residual stress distribution varies over short distances. Therefore, to carefully implement these steps, it is important to select appropriate parameters such as surface deformation measurement spacing, data smoothing parameters (‘knot spacing’ for example cubic spline smoothing) and finite element mesh size. This research covers an investigation of these important parameters. A simple approach for choosing initial parameters is developed based on an idealised cosine displacement function (giving a self-equilibrated one-dimensional residual stress profile). In this research, guidelines are proposed to help the measurer to select the most suitable choice of these parameters based on the estimated wavelength of the residual stress field

SPH method applied to high speed cutting modelling

The purpose of this study is to introduce a new approach of high speed cutting numerical modelling. A Lagrangian smoothed particle hydrodynamics (SPH)- based model is arried out using the Ls-Dyna software. SPH is a meshless method, thus large material distortions that occur in the cutting problem are easily managed and SPH contact control permits a "natural" workpiece/chip separation. The developed approach is compared to machining dedicated code results and experimental data. The SPH cutting model has proved is ability to account for continuous to shear localized chip formation and also correctly estimates the cutting forces, as illustrated in some orthogonal cutting examples. Thus, comparable results to machining dedicated codes are obtained without introducing any adjusting numerical parameters (friction coefficient, fracture control parameter)