An object-oriented programming of an explicit dynamics code: application to impact simulation

During the last fifty years, the development of better numerical methods and more powerful computers has been a major enterprise for the scientific community. Recent advances in computational softwares have lead to the possibility of solving more physical and complex problems (coupled problems, nonlinearities, high strain and high strain rate problems, etc.). The development of object-oriented programming leads to better structured codes for the finite element method and facilitates the development, the maintainability and the expandability of such codes. This paper presents an implementation in C++ of an explicit finite element program dedicated to the simulation of impacts. We first present a brief overview of the kinematics, the conservative and constitutive laws related to large deformation inelasticity. Then we present the design and the numerical implementation of some aspects developed with an emphasis on the object-oriented programming adopted. Finally, the efficiency and accuracy of the program are investigated through some benchmark tests

Parallelization of an object-oriented FEM dynamics code: influence of the strategies on the Speedup

This paper presents an implementation in C++ of an explicit parallel finite element code dedicated to the simulation of impacts. We first present a brief overview of the kinematics and the explicit integration scheme with details concerning some particular points. Then we present the OpenMP parallelization toolkit used in order to parallelize our FEM code, and we focus on how the parallelization of the DynELA FEM code has been conducted for a shared memory system using OpenMP. Some examples are then presented to demonstrate the efficiency and accuracy of the proposed implementations concerning the Speedup of the code. Finally, an impact simulation application is presented and results are compared with the ones obtained by the commercial Abaqus explicit FEM code

Influence of the constitutive flow law in FEM simulation of the Radial forging process

Radial forging is a widely used forming process for manufacturing hollow products in transport industry. As the deformation of the workpiece, during the process, is a consequence of a large number of high-speed strokes, the Johnson-Cook constitutive law (taking into account the strain rate) seems to be well adapted for representing the material behavior even if the process is performed under cold conditions. But numerous contributions concerning radial forging analysis, in the literature, are based on a simple elastic-plastic formulation. As far as we know, this assumption has yet not been validated for the radial forging process. Because of the importance of the flow law in the effectiveness of the model, our purpose in this paper is to analyze the influence of the use of an elastic-viscoplastic formulation instead of an elastic-plastic one for modeling the cold radial forging process. In this paper we have selected two different laws for the simulations: the Johnson-Cook and the Ludwik ones, and we have compared the results in terms of forging force, product’s thickness, strains, stresses, and CPU time. For the presented study we use an AISI 4140 steel, and we denote a fairly good agreement between the results obtained using both laws

Influence of Process and Material Parameters on Impact Response in Composite Structure: Methodology Using Design of Experiments

Even if the mechanical performances of composite materials give new perspectives for the aircraft and space design, the variability of their behavior, linked to the presence of initial microscopic defects or led in service, constitute however a still important brake in their development. As regards particularly the response to fatigue loads or ageing, the behavior of these materials is affected by several sources of uncertainties, notably on the nature of the physical mechanisms of degradation, which are translated by a strong dispersion in life time. In aerospace industry, low energy impact phenomenon is not well known concerning composite materials and composite structures. Many manufacturers use important safety factors to design structures. The aim of this work is to define the most predominant parameters which permit a good response of damage using experiences plans. The differences of these parameters by using Resin Transfer Molding (RTM) or Liquid Resin Infusion (LRI) process than prepreg one is also studied in this work

Numerical implementation of the eXtended Finite Element Method for dynamic crack analysis

A numerical implementation of the eXtended Finite Element Method (X-FEM) to analyze crack propagation in a structure under dynamic loading is presented in this paper. The arbitrary crack is treated by the X-FEM method without re-meshing but using an enrichment of the classical displacement-based finite element approximation in the framework of the partition of unity method. Several algorithms have been implemented, within an Oriented Object framework in C++, in the home made explicit FEM code. The new module, called DynaCrack, included in the dynamic FEM code DynELA, evaluates the crack geometry, the propagation of the crack and allow the post-processing of the numerical results. The module solves the system of discrete equations using an explicit integration scheme. Some numerical examples illustrating the main features and the computational efficiency of the DynaCrack module for dynamic crack propagation are presented in the last section of the paper

Micromechanical modeling of brittle damage in composite materials: primary anisotropy, induced anisotropy and opening-closure effects

Inelastic deformation of various brittle materials such as concrete, rocks or composites has been widely explained by the existence, nucleation and growth of microcracks. The oriented nature of these microdefects, coupled with the unilateral contact of their lips (i.e. microcracks can be either open or closed depending on loading), leads to a complex anisotropic behaviour notably characterized by a recovery of some effective properties at the closure of microcracks. For composite materials, the interaction of these both features with their primary (structural) anisotropy makes things even more complex. Experimental investigations through ultrasonic measures on ceramic matrix composites confirm the stiffness modifications due to degradation process, both on the amplitude (when loading axes correspond to initial material axes) and on the type of resulting material symmetry, especially in the case of off-axis loadings [3]. Concerning the unilateral effect, some authors have put in evidence the partial recovery of elastic properties at the closure of microcracks but these studies are often restricted to axial properties or to defects configurations coinciding with to the structural anisotropy of the material [1,8]. In terms of representation, the simultaneous description of the damage induced anisotropy and of the activation-deactivation process (the so-called unilateral effect) within a consistent modeling still remains a difficult and open research field, even in the context of initially isotropic materials. Indeed, mathematical or thermodynamical inconsistencies have been pointed out in existing formulations, such as discontinuities of the stress-strain response or non-uniqueness of the thermodynamic potential [4-5]. Concerning anisotropic microcracked materials, the analysis of their overall elastic properties is limited to configurations of open defects [6,7,9]. This paper aims to introduce a novel and original modeling approach for this problem within the framework of Continuum Damage Mechanics. In view of the lack of exhaustive experimental data on such aspects, we propose a micromechanics-based formulation of the resulting -generally fully- anisotropic multilinear response of orthotropic materials containing microcracks. On the basis of works by [2] for isotropic media, a strain-based homogenization approach is developed. This leads to a closed-form expression of the macroscopic free energy corresponding to 2D initially orthotropic materials weakened by arbitrarily oriented microcrack systems with account of closure effects. The consideration of such unilateral behavior constitutes one of the main contribution of the study. The explicit expressions obtained provide then a complete quantification of interaction effects both between primary and microcracks-induced anisotropies and between opening/closure states of cracks on the materials elastic properties. The thermodynamics framework finally gives a standard procedure for the formulation of the damage evolution law that ensures in all cases the verification of the thermodynamics second principle. Moreover, the association of the overall free energy expression derived with the standard evolution law introduces both oriented and closure effects due to microcracks in the material response and damage evolution. The model has been implemented within the finite-element code ABAQUS and various numerical simulations illustrate the representation capacities. Indeed, the formulation can account for the main features of brittle cracking kinetics, especially the load-induced anisotropy and the dissymmetry between initial damage thresholds in tension and compression

Effect of Ductile Damage Evolution in Sheet Metal Forming: Experimental and Numerical Investigations

The numerical simulation based on the Finite Element Method (FEM) is widely used in academic institutes and in the industry. It is a useful tool to predict many phenomena present in the classical manufacturing forming processes such as necking, fracture, springback, buckling and wrinkling. But, the results of such numerical model depend strongly on the parameters of the constitutive behavior model. In the first part of this work, we focus on the traditional identification of the constitutive law using oriented tensile tests (0°, 45°, and 90° with respect to the rolling direction). A Digital Image Correlation (DIC) method is used in order to measure the displacements on the surface of the specimen and to analyze the necking evolution and the instability along the shear band. Therefore, bulge tests involving a number of die shapes (circular and elliptic) were developed. In a second step, a mixed numerical–experimental method is used for the identification of the plastic behavior of the stainless steel metal sheet. The initial parameters of the inverse identification were extracted from a uniaxial tensile test. The optimization procedure uses a combination of a Monte-Carlo and a Levenberg-Marquardt algorithm. In the second part of this work, according to some results obtained by SEM (Scaning Electron Microscopy) of the crack zones on the tensile specimens, a Gurson Tvergaard Needleman (GTN) ductile model of damage has been selected for the numerical simulations. This model was introduced in order to give informations concerning crack initiations during hydroforming. At the end of the paper, experimental and numerical comparisons of sheet metal forming applications are presented and validate the proposed approach

Finite Element Simulation of Low Velocity Impact Damage on an Aeronautical Carbon Composite Structure

Low velocity barely visible impact damage (BVID) in laminated carbon composite structures has a major importance for aeronautical industries. This contribution leads with the development of finite element models to simulate the initiation and the propagation of internal damage inside a carbon composite structure due by a low velocity impact. Composite plates made from liquid resin infusion process (LRI) have been subjected to low energy impacts (around 25 J) using a drop weight machine. In the experimental procedure, the internal damage is evaluated using an infrared thermographic camera while the indentation depth of the face is measured by optical measurement technique. In a first time we developed a robust model using homogenised shells based on degenerated tri-dimensional brick elements and in a second time we decided to modelize the whole stacking sequence of homogeneous layers and cohesive interlaminar interfaces in order to compare and validate the obtained results. Both layer and interface damage initiation and propagation models based on the Hashin and the Benzeggagh-Kenane criteria have been used for the numerical simulations. Comparison of numerical results and experiments has shown the accuracy of the proposed models

[Rp] Parallelization of an object-oriented FEM dynamics code

Between 1997 and 2005, the Laboratoire Génie de Production of the National Engineering School of Tarbes developed an Explicit Finite Elements Code for the numerical simulation of the behavior of mechanical structures subjected to impacts in large thermomechanical deformations: the DynELA FEM code. This academic FEM code has been used in support of different Ph.D. theses and several scientific publications among which, one was focused on the parallelization of the DynELA FEM code using the OpenMP library. The purpose of this paper is to present the steps that were necessary to allow the reproduction of the results presented in the original article using the 2005 version of the DynELA code

Mechanical properties of the elemental nanocomponents of nacre structure

Sheet nacre is a nanocomposite with a multiscale structure displaying a lamellar “bricks and mortar” microarchitecture. In this latter, the brick refer to aragonite platelets and the mortar to a soft organic biopolymer. However, it appears that each brick is also a nanocomposite constituted as CaCO3 nanoparticles reinforced organic composite material. What is the role of this “intracrystalline” organic phase in the deformation of platelet? How does this nanostructure control the mechanical behaviour of sheet nacre at the macroscale? To answer these questions, the mechanical properties of each nanocomponents are successively investigated and computed using spherical and sharp nanoindentation tests combined with a structural model of the organomineral platelets built from AFM investigations