Large-scale Finite Element Computations Research Articles

Consistent treatment and automation of the incremental Mori\u2013Tanaka scheme for\xa0elasto-plastic composites

A consistent algorithmic treatment of the incremental Mori–Tanaka (MT) model for elasto-plastic composites is proposed. The aim is to develop a computationally efficient and robust micromechanical constitutive model suitable for large-scale finite-element computations. The resulting overall computational scheme is a doubly-nested iteration-subiteration scheme. The Newton method is used to solve the nonlinear equations at each level involved. Exact linearization is thus performed at each level so that a quadratic convergence rate can be achieved. To this end, the automatic differentiation (AD) technique is used, and the corresponding AD-based formulation is provided. Excellent overall performance of the present MT scheme in three-dimensional finite-element computations is illustrated.

A comparison of hyperelastic constitutive models applicable to brain and fat tissues.

In some soft biological structures such as brain and fat tissues, strong experimental evidence suggests that the shear modulus increases significantly under increasing compressive strain, but not under tensile strain, whereas the apparent Young's elastic modulus increases or remains almost constant when compressive strain increases. These tissues also exhibit a predominantly isotropic, incompressible behaviour. Our aim is to capture these seemingly contradictory mechanical behaviours, both qualitatively and quantitatively, within the framework of finite elasticity, by modelling a soft tissue as a homogeneous, isotropic, incompressible, hyperelastic material and comparing our results with available experimental data. Our analysis reveals that the Fung and Gent models, which are typically used to model soft tissues, are inadequate for the modelling of brain or fat under combined stretch and shear, and so are the classical neo-Hookean and Mooney–Rivlin models used for elastomers. However, a subclass of Ogden hyperelastic models are found to be in excellent agreement with the experiments. Our findings provide explicit models suitable for integration in large-scale finite-element computations.

X-ray CT imaging and finite element computations of the elastic properties of a rigid organic foam compared to experimental measurements: insights into foam variability

A combined computational/experimental technique was developed to analyze the compressive elastic properties of a rigid organic foam. This technique combines X-ray computed tomography, image analysis, and large-scale finite element computations utilizing a new numerical technique. Predictions of Young’s modulus were validated with uniaxial compression testing. Good agreement was obtained between imaging/finite element computations and experimental mechanical measurements within experimental error, and the limited knowledge existing on the solid material comprising the backbone of the foam. Using the new combined experimental/theoretical procedures, it was found that the predicted Young’s modulus of the solid backbone differed by more than a factor of 100 % between two different grades of the foam, in accordance with the findings of other researchers. A significant variability of the backbone modulus was also found within the same grade. Density measurements identified the variability between different grades of foam and different as-received sample thicknesses within the same grade of foam.

Microplane Model M7 for Plain Concrete. II: Calibration and Verification

AbstractThe microplane material model for concrete, formulated mathematically in the companion paper, is calibrated by material test data from all the typical laboratory tests taken from the literature. Then, the model is verified by finite-element simulations of data for some characteristic tests with highly nonuniform strain fields. The scaling properties of model M7 are determined. With the volumetric stress effect taken from the previous load step, the M7 numerical algorithm is explicit, delivering in each load step the stress tensor from the strain tensor with no iterative loop. This makes the model robust and suitable for large-scale finite-element computations. There are five free, easily adjustable material parameters, which make it possible to match the given compressive strength, the corresponding strain, the given hydrostatic compression curve, and certain triaxial aspects. In addition, there are many fixed, hard-to-adjust parameters, which can be taken to be the same for all concretes. The opt...

Surface wrinkling of nanostructured thin films on a compliant substrate

The wrinkling of films on a soft substrate is a critical issue of many technologically important applications and thus has attracted considerable attentions. However, the effect of the surface roughness on the buckling mode of the film remains unclear. In the present paper, the buckling of a rough film, resting on a compliant substrate is theoretically investigated. Dimensional analysis and large-scale finite element computations are performed to explore the wrinkling behavior of a film with periodically triangular or sinusoidal nanostructured (rough) surface patterns. The dependence relationship of the wrinkling wavelength on the geometric parameters of surface nanostructures and the elastic properties of the film and substrate is established. Our study shows that the effects of various surface nanostructures on the film buckling can be well described by using the concept of the equivalent thickness. A relation between the equivalent thickness and the geometric parameters of the system are derived by fitting our computational results. The results reported here may be instructive for surface patterning and biomimetic design of novel materials and devices with specific surface properties. To demonstrate the potential application of the buckling method in the fabrication of hierarchical surface structures, we provide two examples inspired by the micro/nano-patterns on lotus leaves and mosquito legs.

Determination of the elastic modulus of micro- and nanowires/tubes using a buckling-based metrology

A buckling-based method for measuring the mechanical properties of micro- and nanowires/tubes with a general cross-sectional shape is investigated. For a wire/tube bonded to a soft elastic substrate, a simple scaling relation between the characteristic buckling wavelength and the material and geometric parameters of the system is established based on an approximated theoretical model. This relation is examined by using fully three-dimensional, large-scale finite-element computations with the guidance of dimensional analysis.

Three‐dimensional numerical simulation of g‐jitter induced convection and solute transport in magnetic fields

PurposeThe quality of crystals grown in space can be diversely affected by the melt flows induced by g‐jitter associated with a space vehicle. This paper presents a full three‐dimensional (3D) transient finite element analysis of the complex fluid flow and heat and mass transfer phenomena in a simplified Bridgman crystal growth configuration under the influence of g‐jitter perturbations and magnetic fields.Design/methodology/approachThe model development is based on the Galerkin finite element solution of the magnetohydrodynamic governing equations describing the thermal convection and heat and mass transfer in the melt. A physics‐based re‐numbering algorithm is used to make the formidable 3D simulations computationally feasible. Simulations are made using steady microgravity, synthetic and real g‐jitter data taken during a space flight.FindingsNumerical results show that g‐jitter drives a complex, 3D, time dependent thermal convection and that velocity spikes in response to real g‐jitter disturbances in space flights, resulting in irregular solute concentration distributions. An applied magnetic field provides an effective means to suppress the deleterious convection effects caused by g‐jitter. Based on the simulations with applied magnetic fields of various strengths and orientations, the magnetic field aligned with the thermal gradient provides an optimal damping effect, and the stronger magnetic field is more effective in suppressing the g‐jitter induced convection. While the convective flows and solute transport are complex and truly 3D, those in the symmetry plane parallel to the direction of g‐jitter are essentially two‐dimensional (2D), which may be approximated well by the widely used 2D models.Originality/valueThe physics‐based re‐numbering algorithm has made possible the large scale finite element computations for 3D g‐jitter flows in a magnetic field. The results indicate that an applied magnetic field can be effective in suppressing the g‐jitter driven flows and thus enhance the quality of crystals grown in space.

High-Performance Domainwise Parallel Direct Solver for Large-Scale Structural Analysis

Large-scale structural analysis using a finite element method requires a high-performance and efficient parallel algorithm that is scalable in terms of both performance and storage. Most of the research for large-scale parallel structural analysis has focused on iterative solution methods because they are much easier to parallelize. In contrast, direct solution methods have generally been considered in adequate for large-scale finite element computations because of many difficulties and disadvantages for carrying out large-scale problems. However, direct solution methods are still generally preferred due to their ease of use and the numerical robustness that guarantees the solution to be obtained within an estimated time without failure. Therefore, for the general application of large-scale structural analysis to a wide range of problems, an efficient parallel direct solution method that has scalability comparable to that of iterative methods is proposed. A new parallel direct solver for large-scale finite element analysis, the domainwise multifrontal solver, is proposed by realizing domainwise parallelism for a direct solver. By the use of the proposed solver with our own structural analysis code, good scalability can be shown as a direct method and can solve the largest problem ever known to be solved by direct solvers.

Adaptive multigrid for finite element computations in plasticity

The solution of the system of equilibrium equations is the most time-consuming part in large-scale finite element computations of plasticity problems. The development of efficient solution methods are therefore of utmost importance to the field of computational plasticity. Traditionally, direct solvers have most frequently been used. However, recent developments of iterative solvers and preconditioners may impose a change. In particular, preconditioning by the multigrid technique is especially favorable in FE applications. The multigrid preconditioner uses a number of nested grid levels to improve the convergence of the iterative solver. Prolongation of fine-grid residual forces is done to coarser grids and computed corrections are interpolated to the fine grid such that the fine-grid solution successively is improved. By this technique, large 3D problems, invincible for solvers based on direct methods, can be solved in acceptable time at low memory requirements. By means of a posteriori error estimates the computational grid could successively be refined (adapted) until the solution fulfils a predefined accuracy level. In contrast to procedures where the preceding grids are erased, the previously generated grids are used in the multigrid algorithm to speed up the solution process. The paper presents results using the adaptive multigrid procedure to plasticity problems. In particular, different error indicators are tested.

Size-dependent sharp indentation—I: a closed-form expression of the indentation loading curve

In this paper, a closed-form expression of the size-dependent sharp indentation loading curve has been proposed based on dimensional analysis and the finite deformation Taylor-based nonlocal theory (TNT) of plasticity (Int. J. Plasticity 20 (2004) 831). The key issue is to link the results of FEM based on TNT plasticity with those obtained using conventional FEM by taking as the effective strain gradient, η , that presented in the work of Nix and Gao (J. Mech. Phys. Solids 46 (1998) 411), thus avoiding large-scale finite element computations using strain gradient plasticity theories. Two experiments carried out on 316 stainless-steel and pure titanium have been used to verify the effectiveness of the present analytical model; the results demonstrate that the present analytical expression of the size-dependent indentation loading curve corresponds very well to the experimental indentation loading curve. The empirical constant, α , in the Taylor model estimated from the experimental data has the correct order of magnitude. Also, the results presented in this part can be further applied to establish an analytical framework to extract the plastic properties of metallic materials with sharp indentation on a small scale where the size effect caused by geometrically necessary dislocations is significant. This will be discussed in detail in the second part of the paper.

An Extended Tube-Model for Rubber Elasticity: Statistical-Mechanical Theory and Finite Element Implementation

Abstract A novel model of rubber elasticity—the extended tube-model—is introduced. The model considers the topological constraints as well as the limited chain extensibility of network chains in filled rubbers. It is supplied by a formulation suitable for an implementation into a finite element code. Homogeneous states of deformation are evaluated analytically to yield expressions required e.g., for parameter identification algorithms. Finally, large scale finite element computations compare the extended tube-model with experimental investigations and with the phenomenological strain energy function of the Yeoh-model. The extended tube-model can be considered as an interesting approach introducing physical considerations on the molecular scale into the formulation of the strain energy function which is on the other hand the starting point for the numerical realization on the structural level. Thus, the gap between physics and numerics is bridged. Nevertheless, this study reveals the importance of a proper parameter identification and adapted experiments.

Large scale finite element computations with GMRES-like methods on a CRAY Y-MP

GMRES-like methods require the computation and storage of basis vectors of Krylov subspaces. The number of vectors that has to be computed and stored depends on the number of iterations that has to be performed, that is if no restart or truncation strategy is employed. The number of iterations can be reduced by performing more matrix-vector multiplications per iteration, for example by applying a polynomial preconditioner or by performing inner iterations. In this paper we discuss this approach and we compare some of the resulting GMRES methods. The experimental comparison has been made on a CRAY Y-MP, using the finite element code DIANA. The element-by-element matrix-vector multiplication is discussed in detail.

A Numerical Method for Free Vibration Analysis of Structures with Small Design Changes : 2nd Report: Analysis of Degenerate or Nearly Degenerate Cases by a Subspace Technique

This paper presents a numerical method for free vibration analysis of structures with small design changes or perturbations. The proposed method is an extension of the iteration scheme introduced in the first report of this paper. A subspace technique is employed to deal with variation of degenerate or nearly degenerate eigenvalues of the unperturbed problems. The algorithm is designed such that it can be easily implemented in large-scale finite element computations. To see the effectiveness and fundamental properties of the proposed method, some numerical results are given for lateral vibration problems of a cantilever beam, a circular plate, and a parallelogramic membrane. It is shown that the present approach can actually analyze the separation of degenerate eigenvalues. Furthermore, it can improve the convergence behavior of the iteration process when it is compared with the method in the first report.