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The application of numerical techniques to the solution of practical problems which exist in rubber technology is described. Structures and components in the form of reinforced rubber shells are widely used in industry and prediction of their performance is complicated by both the anisotropic nature of composite construction and the incompressible behaviour of the basic material. A layered shell element is developed for the solution of such problems with general anisotropic behaviour independently permitted in each layer. The approach adopted permits the easy location of reinforcement patterns. Numerical solution is based on a single field formulation by eliminating at integrating point level the Lagrange multiplier imposing the incompressible constraint. Large deformation, including large rotation, behaviour is accommodated and a total Lagrangian solution process is adopted. The code developed permits the simulation of non‐conservative loading and its versatility is demonstrated by the solution of some practical examples.

Application of the finite element method to the simulation of glass forming processes is described. The forming process results in a coupled thermal/mechanical problem with interaction between the heat transfer analysis of the temperature distribution in the glass and the viscous flow formulation describing the deformation of molten glass being a dominant factor. Particular attention must be given to derivation of the appropriate non‐linear thermal boundary conditions and also to monitoring of the mechanical contact between the glass and mould. The technique described provides both the glass and temperature distribution at each instant of the forming process and thus can provide invaluable information for mould and plunger design, optimum operation times, etc. Numerical examples are provided for both wide neck and narrow neck press and blow forming processes and the results obtained compare well with commercial observations.

This paper focuses on the development of a new class of eight‐node solid finite elements, suitable for the treatment of volumetric and transverse shear locking problems. Doing so, the proposed elements can be used efficiently for 3D and thin shell applications. The starting point of the work relies on the analysis of the subspace of incompressible deformations associated with the standard (displacement‐based) fully integrated and reduced integrated hexahedral elements. Prediction capabilities for both formulations are defined related to nearly‐incompressible problems and an enhanced strain approach is developed to improve the performance of the earlier formulation in this case. With the insight into volumetric locking gained and benefiting from a recently proposed enhanced transverse shear strain procedure for shell applications, a new element conjugating both the capabilities of efficient solid and shell formulations is obtained. Numerical results attest the robustness and efficiency of the proposed approach, when compared to solid and shell elements well‐established in the literature.

Uses a rigid viscoplastic formulation to simulate hot and cold forging processes. The finite element solution uses mixed methods in which the independent variables can be velocities, pressures and deviatoric stresses. Uses interface elements both in the mechanical and the thermal analysis, to take into account the effects of contact and friction, thermal conductivity of lubricants and heat generated by friction. The code developed includes an adaptive mesh refinement, triggered by an error estimator based on energy norms evaluated from nodal stress values, recovered from a local continuous polynomial expansion, and those given by the numerical solution. Assesses the code developed, using experimental results.

An optimisation method for design of intermediate die shapes needed in some forging operations is presented. The basic problem consists of finding an optimal two‐step forging sequence by automatically designing the shape of the preforming tools. The optimisation problem is defined based on an inverse formulation. The objective function of the optimisation problem is a function describing the quality of the obtained part by measuring the die underfill. The finite element method is used to simulate the forging problem. The optimisation method is based on a modified sequential unconstrained minimisation technique and a gradient method. The sensitivity‐dependent algorithm requires computing the derivatives of the objective function with respect to the design variables defining the preform shapes. A direct differentiation method has been developed for this purpose. The optimisation scheme is demonstrated with two axisymmetric forging examples in which optimal preform dies are obtained.

The purpose of this paper is to perform a numerical assessment of two recently proposed extensions of the Gurson‐Tveegard‐Needleman ductile damage constitutive model under low stress triaxiality.

One of the most widely used ductile damage models is the so‐called Gurson‐Tveegard‐Needleman model, commonly known as GTN model. The GTN model has embedded into its damage formulation the effects of nucleation, growth and coalescence of micro‐voids. However, the GTN model does not include void distortion and inter‐void linking in the damage evolution. To overcome this limitation, some authors have proposed the introduction of different shear mechanisms based on micromechanical grounds or phenomenological assumptions. Two of these constitutive formulations are reviewed in this contribution, numerically implemented within a quasi‐static finite element framework and their results critically appraised.

Through the analysis of the evolution of internal variables, such as damage and effective plastic strain, obtained by performing a set of numerical tests using a Butterfly specimen, it is possible to conclude that the extended GTN models are in close agreement with experimental evidence.

Even though the results obtained with the modified GTN models have shown improvements, it can also be observed that both shear mechanisms have inherent limitations in the prediction of the location of fracture onset for some specific stress states.

From the results reported, it is possible to identify some shortcomings in the recently proposed extensions of the GTN model and point out the direction of further improvements.

The simulation of real industry metal forming processes often requires the presence of adaptive procedures. With that purpose a quadrilateral mesh generator was developed. The algorithm is based on the simple fact that it is always possible to subdivide a region into quadrilaterals whenever the polygonal line that forms its boundary has an even number of sides and that, by joining two contiguous triangles, a quadrilateral may be formed. Rather than using an advancing front technique a cloud of nodal points is initially formed based on error estimators and criteria to define an optimal element size. With this procedure, using an adaptive process, the refinement is created where it will be needed.

Incremental sheet forming represents a promising process in the manufacturing of metallic components, particularly its variant known as single point incremental forming (SPIF). The purpose of this paper is to test and validate the results coming from numerical simulation of SPIF processes using the reduced enhanced solid‐shell formulation, when compared to the solid finite elements available in ABAQUS software. The use of SPIF techniques in the production of small batch components has a potential wide application in fields such as rapid prototyping and biomechanical devices.

Incremental forming processes differ from conventional stamping by not using a press and by requiring a lower number of tools, since no dedicated punches and dies are necessary, which lowers the overall production costs. In addition, it shows relative simplicity and flexible setup for complex parts, when compared with conventional technologies. However, the low speed of production and low‐dimensional accuracy levels are still the main obstacles for a wider application of this technique in the context of large production batches.

In this sense, the use of numerical simulation tools based on the finite element method (FEM) can provide a better understanding of the process' peculiarities. However, there are differences on using distinct finite element formulations, regarding accuracy as well as CPU times during simulations, which can be prohibitive in some cases.

Aiming to provide sounding improvements in these two fields (robustness and cost effectiveness of FEM solutions), the present work encloses a preliminary study about some relevant parameters in the FEM simulation of SPIF. Special focus is given to the use of solid‐shell and solid finite elements, for the sake of generality in modelling, as well as implicit solution schemes for the sake of accuracy. Finally, results coming from both experimental data and commercial FEM packages are compared to those obtained by a reliable and cost‐effective solid‐shell finite element formulation developed and implemented by the authors.

The purpose of this paper is to use PAM-CRASH, a finite element analysis solver, to assess the performance of a mass production vehicle cross car beam (CCB) under an overlap frontal crash scenario (crashworthiness). Simulation results were reviewed according to what is plausible to register regarding some critical points displacements and, moreover, to identify its stress concentrations zones. Furthermore, it was also computed the CCB modal analysis (noise, vibration and harshness (NVH) assessment) in order to examine if its natural modes are within with the original equipment manufacturer (OEM) design targets.

The available data at the beginning of the present study consisted of the structure CAD file and performance requirements stated by the OEM for NVH. No technical information was available concerning crashworthiness. Taking into account these limitations, it was decided to adapt the requirements for other mass production cars of the same category, as regards dynamic loading. A dynamic explicit code finite element analysis was performed throughout the CCB structure simulating the 120e−3 s crash event. For the modal analysis, there were some necessary modifications to the explicit finite element model in order to perform the analysis in implicit code. In addition, the car body in white stiffness was assigned at the boundaries. These stiffness values are withdrawn from the points where the CCB is attached to the car body’s sheet metal components.

Although the unavailability of published results for this particular CCB model prevents a comparison of the present results, the trends and order of magnitude of the crash simulation results are within the expectations for this type of product. Concerning modal analysis, the steering column first natural frequency has a percent deviation from the design lower bound value of 5.09 percent when local body stiffness is considered and of 1.94 percent with fixed boundary conditions. The other requirement of the NVH assessment regarding a 5 Hz minimum interval between first vehicle CCB mode and the first mode of the steering column was indeed achieved with both boundary configurations.

This study is a further confirmation of the interest of numerical modeling as a first step before actual experimental testing, saving time and money in an automotive industry that has seen an enormous increase of the demand for new car models in the last decade.

Contact problems are among the most difficult ones in mechanics. Due to its practical importance, the problem has been receiving extensive research work over the years. The finite element method has been widely used to solve contact problems with various grades of complexity. Great progress has been made on both theoretical studies and engineering applications. This paper reviews some of the main developments in contact theories and finite element solution techniques for static contact problems. Classical and variational formulations of the problem are first given and then finite element solution techniques are reviewed. Available constraint methods, friction laws and contact searching algorithms are also briefly described. At the end of the paper, a bibliography is included, listing about seven hundred papers which are related to static contact problems and have been published in various journals and conference proceedings from 1976.