Modelling of materials problems

Summary A strategy is outlined for constructing models of material behaviour. It is described by a flow chart which identifies nine stages. They include identification of the purpose of the model, the construction of the model itself, and its implementation in a useful form.     

Solving anti-plane problems of piezoelectric materials by the Trefftz finite element approach

Applications of the Trefftz finite element method to anti-plane electroelastic problems are presented in this paper. A dual variational functional is constructed and used to derive Trefftz finite element formulation. Special trial functions which satisfy boundary conditions are also used to develop a special purpose element with local defects. The performance of the proposed element model is assessed by an example and comparison is made with results obtained by other approaches. The Trefftz finite element approach is demonstrated to be ideally suited for the analysis of the anti-plane problem.The work was performed under the auspices of an Australian Professorial Fellowship Program with grant number DP0209487 and 21st Century Education Promotion Key project from Tianjin University.     

Simulation of static recrystallization in non-isothermal annealing using a coupled cellular automata and finite element model

A coupled cellular automata and finite element model has been proposed to evaluate static recrystallization kinetics during non-isothermal annealing of cold deformed low carbon steels. The effects of various factors including heating rate, annealing temperature, and initial microstructures have been considered in the model to accurately predict the static recrystallization kinetics and the final microstructures. In order to examine the employed algorithm, the predicted results have been compared with the experimental observations and a good agreement was found between the two sets of results.     

An augmented finite element method for modeling arbitrary discontinuities in composite materials

An augmented finite element method (“A-FEM”) is presented that is a variant of the method of Hansbo and Hansbo (Comput Methods Appl Mech Eng, 193: 3523–3540, 2004), which can fully account for arbitrary discontinuities that traverse the interior of elements. Like the method of Hansbo and Hansbo, the A-FEM preserves elemental locality, because element augmentation is implemented within single elements and involves nodal information from the modified element only. The A-FEM offers the additional convenience that the augmentation is implemented via separable mathematical elements that employ standard finite element nodal interpolation only. Thus, the formulation is fully compatible with standard commercial finite element packages and can be incorporated as a user element without access to the source code. Because possible discontinuities include both elastic heterogeneity and cracks, the A-FEM is ideally suited to modeling damage evolution in structural or biological materials with complex morphology. Elements of a multi-scale approach to analyzing damage mechanisms in laminated or woven textile composites are used to validate the A-FEM and illustrate its possible uses. Key capabilities of the formulation include the use of meshes that need not conform to the surfaces of heterogeneities; the ability to apply the augmented element recursively, enabling modeling of multiple discontinuities arising on different, possibly intersecting surfaces within an element; and the ease with which cohesive zone models of nonlinear fracture can be incorporated.     

Influence of minimum element size to determine crack closure stress by the finite element method

Measuring opening or closure stress is a complex process that influences the low accuracy of obtained data. Finite element models have been one of the available ways to deal with this problem. The difficulty of modelling the whole process of crack growth (due to the great number of cycles implied) as the great complexity of the phenomenon itself (with a high plastic strain concentrated in a small area, with elevated stress gradients) has made the results to be quite varied, being influenced by a great number of modelling parameters. Of those parameters, the minimum size of the element used to mesh the area around the crack tip vicinity presents a great influence on the results.In this work, a detailed analysis of the influence of this parameter in the results in terms of closure or opening stress is presented. The effect that different meshing criteria can have on the result is complex and it has been necessary to reduce the element size around the crack tip to a size that had not been reached before. Procedures and modelling criteria stricter than the ones shown in the current bibliography are proposed. A methodology for the correct interpretation of the results is also established.     

The bi-potential method applied to the modeling of dynamic problems with friction

The bi-potential method has been successfully applied to the modeling of frictional contact problems in static cases. This paper presents an extension of this method for dynamic analysis of impact problems with deformable bodies. A first order algorithm is applied to the numerical integration of the time-discretized equation of motion. Using the Object-Oriented Programming (OOP) techniques in C++ and OpenGL graphical support, a finite element code including pre/postprocessor FER/Impact is developed. The numerical results show that, at the present stage of development, this approach is robust and efficient in terms of numerical stability and precision compared with the penalty method.     

Finite element modeling of GTA weld surfacing applied to hot-work tooling

A finite element modeling of GTA weld-surfacing process is performed using computer code. The model is used to optimize welding parameters by analyzing temperature transients during welding, as well as deformation and residual stresses as a result of repair-weld surfacing of complex-geometry H13 tooling. In addition to computational analysis, an extensive experimental study is performed. Both remelting and surfacing are performed by GTA welding. A series of welds are prepared using different welding parameters. The temperature transients are measured at a number of positions in the material and macrosections of the welds are prepared. The data are used to develop a relationship between the welding parameters and characteristic weld dimensions, to select the most appropriate geometry of the heat source, and finally to verify the model. The model developed is applied to predict deformation and residual stresses and detect areas critical to cracking at repair-welding of complex-geometry tooling. Understanding these parameters is significant for quality improvement of weld-surfaced tooling and thus essential for extension of in-service life of refurbished tooling.     

Investigation of asphalt concrete rutting mechanisms by X-ray computed tomography imaging and micromechanical finite element modeling

This paper systematically investigates the changes in asphalt concrete (AC) microstructure caused by full-scale accelerated pavement testing with a heavy vehicle simulator (HVS), using X-ray computed tomography images taken before and after HVS rutting tests. A viscoelastic micromechanical finite element modeling was also used to investigate effects of bitumen mastic and aggregate skeleton properties on shear resistance. The primary purpose was to determine the reasons behind the earlier failure of the rubberized gap graded AC mix used in the test compared to the polymer modified dense graded mix also included in the experiment. Shear related deformation appears to control the long term rutting performance of the test sections while densification was primarily an initial contributor at the very early stages of trafficking. A high concentration of aggregate interlock in the polymer modified mix, as a result of the dense gradation and larger aggregate sizes, appears to have resulted in greater dissipation of shear stresses and therefore greater shear resistance. The lack of this interlocking effect for the rubberized gap graded mix is proposed to have caused the earlier failure on HVS test sections.     

Multiscale finite element modeling of superelasticity in Nitinol polycrystals

An efficient method is proposed for modeling superelastic polycrystalline NiTi by solving a two-scale problem. The RVE size of the fine scale is determined using a statistics-based approach. Both problems are discretized in space using the finite element method and their communication is effected using MPI. Representative simulations illustrate the modeling capabilities of the proposed approach.     

Using finite element modeling to examine the flow processes in quasi-constrained high-pressure torsion

Finite element modeling was used to examine the flow processes in high-pressure torsion (HPT) when using quasi-constrained conditions where disks are contained within depressions on the inner surfaces of the upper and lower anvils. Separate simulations were performed using applied pressures from 0.5 to 2.0 GPa, rotations up to 1.5 turns and friction coefficients from 0 to 1.0 outside of the depressions. The simulations demonstrate the distribution of effective strain within the depressions is comparable to the prediction by ideal torsion, and the applied pressure and the friction coefficient outside the depressions play only a minor role in the distribution of effective strain. The mean stresses during processing vary linearly with the distance from the center of the disk such that there are higher compressive stresses in the disk centers and lower stresses at the edges. The torque required for rotation of the anvil is strongly dependent upon the friction coefficient between the sample and the anvil outside the depressions.     

Delamination modelling of GLARE using the extended finite element method

In this paper, an application of the Extended Finite Element Method (XFEM) for simulation of delamination in fibre metal laminates is presented. The study consider a double cantilever beam made of fibre metal laminate in which crack opening in mode I and crack propagation were studied. Comparison with the solution by standard Finite Element Method (FEM) as well as with experimental tests is provided. To the authors’ knowledge, this is the first time that XFEM is used in the fracture analysis of fibre metal laminates such as GLARE. The results indicated that XFEM could be a promising technique for the failure analysis of composite structures.     

Rapid implementation of material models within finite element analysis

This paper presents a simple procedure for obtaining a numerical approximation to the consistent tangent matrix, together with a straightforward implicit (Euler backward) integration algorithm. The combined algorithm is used to incorporate four models into the commercial finite element package ABAQUS/Standard; illustrating how it can be used to rapidly implement material models within finite element analysis. The models have been chosen, not only because they help to illuminate the structure of the algorithm, but also because they illustrate its wide ranging applicability and permit the procedure to be tested against analytical results and an existing, well established, model.     

Micromechanical formulation and 3D finite element modeling of microinstabilities in composites

A 3D micromechanical formulation and a FE-model of fiber micro-buckling in materials with isotropic and transversal isotropic fibers in compression is presented. Three variants of geometrical modeling of the characteristic cell are proposed and compared. An appropriate one is then selected. An eigenvalue analysis of a characteristic cell is performed. The results show that the fiber anisotropy reduces significantly the critical loads and must be taken into account.     

Investigation of finite element mesh independence in rate dependent materials

Crystal plasticity theory is commonly used in finite element analyses to predict large strain ductility in single crystal and polycrystal deformation. In the rate-dependent formulation of the theory it is possible, for cases of simple deformation, to achieve an analytical solution that is independent of any effects due to the finite element mesh spacing. In this study single crystal and polycrystal models were subjected to alternative loading conditions. The effect of the mesh density on the generation of strain localisations and shear bands was investigated with regard to consistency of results. It was found that, prior to the initiation of a narrow shear band, it was possible to achieve a numerical result independent of mesh spacing. In the larger polycrystal analyses, an element size was identified that enabled the generation of a mesh independent solution. This allowed the accurate prediction of the mechanical behaviour of the model up to, and including, the failure point. The implications of this for small-scale metallic device design are discussed.     

Solving thermal and phase change problems with the eXtended finite element method

 The application of the eXtended finite element method (X-FEM) to thermal problems with moving heat sources and phase boundaries is presented. Of particular interest is the ability of the method to capture the highly localized, transient solution in the vicinity of a heat source or material interface. This is effected through the use of a time-dependent basis formed from the union of traditional shape functions with a set of evolving enrichment functions. The enrichment is constructed through the partition of unity framework, so that the system of equations remains sparse and the resulting approximation is conforming. In this manner, local solutions and arbitrary discontinuities that cannot be represented by the standard shape functions are captured with the enrichment functions. A standard time-projection algorithm is employed to account for the time-dependence of the enrichment, and an iterative strategy is adopted to satisfy local interface conditions. The separation of the approximation into classical shape functions that remain fixed in time and the evolving enrichment leads to a very efficient solution strategy. The robustness and utility of the method is demonstrated with several benchmark problems involving moving heat sources and phase transformations. Received 20 May 2001 / Accepted 19 December 2001     

Finite element treatment of soft elastohydrodynamic lubrication problems in the finite deformation regime

Soft elastohydrodynamic lubrication (EHL) problem is studied for a reciprocating elastomeric seal with full account of finite configuration changes. The fluid part is described by the Reynolds equation which is formulated on the deformed boundary of the seal treated as a hyperelastic body. The paper is concerned with the finite element (FE) treatment of this soft EHL problem. Displacement-based FE discretization is applied for the solid part. The Reynolds equation is discretized using the FE method or, alternatively, the discontinuous Galerkin method, both employing higher-order interpolation of pressure. The performance of both methods is assessed by studying convergence and stability of the solution for a benchmark problem of an O-ring seal. It is shown that the solution may exhibit spurious oscillations which occur in severe lubrication conditions. Mesh refinement results in reduction of these oscillations, while increasing the pressure interpolation order or application of the discontinuous Galerkin method does not help significantly.     

Non-isothermal finite element modeling of a shape memory alloy actuator using ANSYS

Many applications involve actuated devices made of shape memory alloys, but the lack of efficient numerical tools hinders the development of such technologies. Software using a finite element method like ANSYS allows the user to predict complex responses of a system without extensive programming. In this paper, a homemade phenomenological 1D bilinear model is programmed through the USERMAT procedure in ANSYS. The model allows the representation of both mechanical and thermal hystereses. The martensitic transformation is controlled by transformation criteria similar to those used in conventional plasticity, and subcycles are modeled by a simple elastic return through the hysteresis. The model is validated through isothermal tensile testing, assisted two-way shape memory testing and stress generation testing, and a good agreement with experimental results is shown. Finally, thermomechanical response of a single-degree-of-freedom actuator is simulated as a typical application and a case study involving the shape change of a radio controlled aircraft wing shows the potential of the numerical simulations.     

Accurate finite element modeling of linear elastodynamics problems with the reduced dispersion error

It is known that the reduction in the finite element space discretization error for elastodynamics problems is related to the reduction in numerical dispersion of finite elements. In the paper, we extend the modified integration rule technique for the mass and stiffness matrices to the dispersion reduction of linear finite elements for linear elastodynamics. The analytical study of numerical dispersion for the modified integration rule technique and for the averaged mass matrix technique is carried out in the 1-D, 2-D and 3-D cases for harmonic plane waves. In the general case of loading, the numerical study of the effectiveness of the dispersion reduction techniques includes the filtering technique (developed in our previous papers) that identifies and removes spurious high-frequency oscillations. 1-D, 2-D and 3-D impact problems for which all frequencies of the semi-discrete system are excited are solved with the standard approach and with the new dispersion reduction technique. Numerical results show that compared with the standard mass and stiffness matrices, the simple dispersion reduction techniques lead to a considerable decrease in the number of degrees of freedom and computation time at the same accuracy, especially for multi-dimensional problems. A simple quantitative estimation of the effectiveness of the finite element formulations with reduced numerical dispersion compared with the formulation based on the standard mass and stiffness matrices is suggested.