An advanced meshless technique for large deformation analysis of metal forming

The large deformation analysis is one of major challenges in numerical modelling and simulation of metal forming. Although the finite element method (FEM) is a well-established method for modeling nonlinear problems, it often encounters difficulties for large deformation analyses due to the mesh distortion issues. Because no mesh is used, the meshless methods show very good potential for the large deformation analysis. In this paper, a local meshless formulation is developed for the large deformation analysis. The Radial Basis Function (RBF) is employed to construct the meshless shape functions, and the spline function with high continuity is used as the weight function in the construction of the local weak form. The discrete equations for large deformation of solids are obtained using the local weak-forms, RBF shape functions, and the total Lagrangian (TL) approach, which refers all variables to the initial (undeformed) configuration. This formulation requires no explicit mesh in computation and therefore fully avoids mesh distortion difficulties in the large deformation analysis of metal forming. Several example problems are presented to demonstrate the effectiveness of the developed meshless technique. It has been found that the developed meshless technique provides a superior performance to the conventional FEM in dealing with large deformation problems in metal forming

Comparison of a Material Point Method and a Galerkin meshfree method for the simulation of cohesive-frictional materials

The simulation of large deformation problems, involving complex history-dependent constitutive laws, is of paramount importance in several engineering fields. Particular attention has to be paid to the choice of a suitable numerical technique such that reliable results can be obtained. In this paper, a Material Point Method (MPM) and a Galerkin Meshfree Method (GMM) are presented and verified against classical benchmarks in solid mechanics. The aim is to demonstrate the good behavior of the methods in the simulation of cohesive-frictional materials, both in static and dynamic regimes and in problems dealing with large deformations. The vast majority of MPM techniques in the literature are based on some sort of explicit time integration. The techniques proposed in the current work, on the contrary, are based on implicit approaches, which can also be easily adapted to the simulation of static cases. The two methods are presented so as to highlight the similarities to rather than the differences fromPeer ReviewedPostprint (published version

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)

Numerical methods for the modelling of chip formation

The modeling of metal cutting has proved to be particularly complex due to the diversity of physical phenomena involved, including thermo-mechanical coupling, contact/friction and material failure. During the last few decades, there has been significant progress in the development of numerical methods for modeling machining operations. Furthermore, the most relevant techniques have been implemented in the the relevant commercial codes creating tools for the engineers working in the design of processes and cutting devices. This paper presents a review on the numerical modeling methods and techniques used for the simulation of machining processes. The main purpose is to identify the strengths and weaknesses of each method and strategy developed up-to-now. Moreover the review covers the classical Finite Element Method covering mesh-less methods, particle-based methods and different possibilities of Eulerian and Lagrangian approaches.Postprint (author's final draft

Meshless Mechanics and Point-Based Visualization Methods for Surgical Simulations

Computer-based modeling and simulation practices have become an integral part of the medical education field. For surgical simulation applications, realistic constitutive modeling of soft tissue is considered to be one of the most challenging aspects of the problem, because biomechanical soft-tissue models need to reflect the correct elastic response, have to be efficient in order to run at interactive simulation rates, and be able to support operations such as cuts and sutures. Mesh-based solutions, where the connections between the individual degrees of freedom (DoF) are defined explicitly, have been the traditional choice to approach these problems. However, when the problem under investigation contains a discontinuity that disrupts the connectivity between the DoFs, the underlying mesh structure has to be reconfigured in order to handle the newly introduced discontinuity correctly. This reconfiguration for mesh-based techniques is typically called dynamic remeshing, and most of the time it causes the performance bottleneck in the simulation. In this dissertation, the efficiency of point-based meshless methods is investigated for both constitutive modeling of elastic soft tissues and visualization of simulation objects, where arbitrary discontinuities/cuts are applied to the objects in the context of surgical simulation. The point-based deformable object modeling problem is examined in three functional aspects: modeling continuous elastic deformations with, handling discontinuities in, and visualizing a point-based object. Algorithmic and implementation details of the presented techniques are discussed in the dissertation. The presented point-based techniques are implemented as separate components and integrated into the open-source software framework SOFA. The presented meshless continuum mechanics model of elastic tissue were verified by comparing it to the Hertzian non-adhesive frictionless contact theory. Virtual experiments were setup with a point-based deformable block and a rigid indenter, and force-displacement curves obtained from the virtual experiments were compared to the theoretical solutions. The meshless mechanics model of soft tissue and the integrated novel discontinuity treatment technique discussed in this dissertation allows handling cuts of arbitrary shape. The implemented enrichment technique not only modifies the internal mechanics of the soft tissue model, but also updates the point-based visual representation in an efficient way preventing the use of costly dynamic remeshing operations