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The analysis of the interpolation error is particularly important for the error analysis of the finite element methods. In the previous paper, we proved that the finite element solution converges to an exact solution if the maximum circumradius of the triangular elements converges to zero. We call such situation "circumradius condition" and claimed that the circumradius condition is more essential than the well-known maximum angle condition. It is considered that the better finite element solution can be obtained by using the mesh division consists of "good" triangles. However, the generation of such mesh division is time consuming task within the simulation process of the finite element method. On the other hand, the effecient algorithm is known for computing Delaunay triangulation. However, the mesh division produced by Delaunay triangulation sometimes contains collapsed triangles. In this paper, we will introduce "circumradius condition" and show that the effecient error estimate can be obtained by the circumradius condition with Delaunay triangulation. [ABSTRACT FROM AUTHOR]

In order to describe the meso-damage of the refractories more accurately, and to study of the relationship between the mesostructured of the refractories and the macro-mechanics, this paper takes the magnesia-carbon refractories as the research object and uses the molecular dynamics method to instead the traditional sequential algorithm to establish the meso-particles filling model including small and large particles. Finally, the finite element software-ABAQUS is used to conducts numerical simulation on the meso-damage evolution process of refractory materials. From the results, the process of initiation and propagation of microscopic interface cracks can be observed intuitively, and the macroscopic stress-strain curve of the refractory material is obtained. The results show that the combination of molecular dynamics modeling and the use of Python in the interface to insert the cohesive element numerical simulation, obtaining of more accurate interface parameters through parameter inversion, can be more accurate to observe the interface of the meso-damage evolution process and effective to consider the effect of the mesostructured of the refractory material on its macroscopic mechanical properties. [ABSTRACT FROM AUTHOR]

Drop test simulation via finite element methods can help simulate the effects of high impact and shock. It has become an indispensable tool during the virtual product design processes to reduce the cost of experimental test and to help improve the durability of products. The choice of a reliable contact method is critical for drop test simulation. Of all the contact algorithms, the penalty method has the advantage of taking the contact constraint into account without increasing the degrees of freedom while being easy to implement into existing software. The implicit analysis is generally known to be more accurate than the explicit analysis, but has convergence issues. This paper presents a penalty finite element method based on dynamic implicit scheme to implement impact planes for drop test simulation. An idea of impact element groups, which allows multiple impact planes with different normal directions, is presented. Two impact plane types are implemented: 'Full general' and 'Slide/no bounce'. The general drop process is divided into three durations with different time step sizes to efficiently and accurately capture the fast change within the microtime of the impact. Typical and interesting drop test models are simulated and discussed for the presented method. [ABSTRACT FROM AUTHOR]

The paper focuses on the miniaturization of the bulging test for material characterization of micro tubes. For the design of the experimental device, numerical simulations are conducted first. Even if no scale effect is taken into account in material modeling, numerical results give some information before designing the set-up and performing experimental works: level of pressure inside the tube, volume of fluid necessary to create such a level of pressure and bulge height to measure. The main results are a design of the experimental device and choices for its instrumentation. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the simulation of linear elastic behaviour of plates using a 3D approach which numerical cost only scales like a 2D one. In the case of plates, the kinematic hypothesis introduced in plate theories to go from 3D to 2D is usually unsatisfactory where one cannot rely on St Venant's principle (usually close to the plate edges). We propose to apply the PGD (Proper Generalized Decomposition) method [1] to the simulation of the linear elastic behavior of plates. This method allows us to separately search for the in-plane and the out-of plane contributions to the 3D solution, yielding significant savings in computational cost. The method is validated on a simple case and its full potential is then presented for the simulation of the behavior of laminated composite plates. [ABSTRACT FROM AUTHOR]

This paper presents the formulation of an axi-symmetric element based on an efficient method called 'Inverse Approach' (I.A.) for the numerical modeling of cold forging process. In contrast to the classical incremental methods, the Inverse Approach exploits the known shape of the final part and executes the calculation from the final part to the initial billet. The assumptions of the proportional loading and the simplified tool actions make the I.A. calculation very fast. The metal's incompressibility is ensured by the penalty method. The comparison with ABAQUS® and FORGE® shows the efficiency and limitations of the I.A. This simplified method will be a good tool for the preliminary preform design. [ABSTRACT FROM AUTHOR]

The simulation of high-velocity impact and penetration is inhibited by complex material behavior and large deformations. Lagrangian formulations best model complex materials because history-dependent variables and material boundaries are not advected. However, Lagrangian finite elements are limited by large deformations. Recently, meshfree particle methods have been used to avoid such limitations, and have demonstrated greater accuracy than traditional erosion methods (wherein deformed elements are removed). Though the variable connectivity of particles enables them to model large deformations, it requires more computational effort than (fixed-connectivity) elements. Therefore, an algorithm was designed to convert deformed elements to particles, thus providing the ability to model large deformations where needed, while maintaining the efficiency of elements elsewhere. This combination is essential in three dimensions, where problem size demands efficiency. In this paper, the conversion algorithm is demonstrated for several three-dimensional simulations of high-velocity impact and penetration. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]