Large-scale Finite Element Simulations Research Articles

A rate-independent crystal plasticity model with a smooth elastic–plastic transition and no slip indeterminacy

A new crystal plasticity constitutive model is proposed that combines, for the first time, the following features: (i) multi-criterion formulation, (ii) exact strain rate-independence, (iii) absence of a consistency condition and (iv) smooth elastic–plastic transition. It is characterised by the existence of a rate-independent overstress that removes the usual possible indeterminacy of simultaneously activated slip systems. The performance of the new model compared to a reference crystal plasticity model by Meric and Cailletaud (1991) in its quasi-rate-independent limit was evaluated in the case of two significantly different materials, namely single crystalline copper and a nickel-based superalloy at room temperature. The provided material point simulations of complex loading paths and large scale finite element simulations do not show any spurious effect of the model, provided that the overstress remains small enough. The improved computational efficiency of the model is discussed.

Modelling flow stress of AISI 316L at high strain rates

Modelling of the material behaviour is crucial for machining simulations. Strain and strain rates can reach values of 1–10 and 103–106s−1 during the severe deformations associated with machining. An existing dislocation density model for AISI 316L based on a coupled set of evolution equations for dislocation density, mono vacancy concentration is enhanced in order to accommodate plastic deformation at high strain rates. Two mechanisms are evaluated with respect to their contribution in this respect. One is rate dependent cell formation and the other is dislocation drag due to phonons and electrons. Furthermore a temperature and strain rate dependent recovery and a proportionality interaction factor and short range component that both depends on the dislocation density are also considered. High strain rate compression tests are performed using Split-Hopkinson technique at various initial temperatures. Experimental results are then used to calibrate the models via an optimization procedure. Evaluation of various flow stress models shows that the flow stress behaviour of 316L stainless steel is best modelled by the model with a rate dependent cell formation. Its numerical solution is implemented in a format suitable for large-scale finite element simulations.

Numerical Verification Criteria for Coseismic and Postseismic Crustal Deformation Analysis with Large-scale High-fidelity Model

Abstract Numerical verification of postseismic crustal deformation analysis, computed using a large-scale finite element simulation, was carried out, by proposing new criteria that consider the characteristics of the target phenomenon. Specifically, pointwise displacement was used in the verification. In addition, the accuracy of the numerical solution was explicitly shown by considering the observation error of the data used for validation. The computational resource required for each analysis implies that high- performance computing techniques are necessary to obtain a verified numerical solution of crustal de- formation analysis for the Japanese Islands. Such verification in crustal deformation simulations should take on greater importance in the future, since continuous improvement in the quality and quantity of crustal deformation data is expected.

Impact of material processing and deformation on cell morphology and mechanical behavior of polyurethane and nickel foams

The cell morphology and mechanical behavior of open-cell polyurethane and nickel foams are investigated by means of combined 3D X-ray micro-tomography and large scale finite element simulations. Our quantitative 3D image analysis and finite element simulations demonstrate that the strongly anisotropic tensile behavior of nickel foams is due to the cell anisotropy induced by the deformation of PU precursor during the electroplating and heat treatment stages of nickel foam processing. In situ tensile tests on PU foams reveal that the initial main elongation axis of the cells evolves from the foam sheet normal direction to the rolling direction of the coils. Finite element simulations of the hyperelastic behavior of PU foams based on real cell morphology confirm the observation that cell struts do not experience significant elongation after 0.15 tensile straining, thus pointing out alternative deformation mechanisms like complex strut junctions deformation. The plastic behavior and the anisotropy of nickel foams are then satisfactorily retrieved from finite element simulations on a volume element containing eight cells with a detailed mesh of all the hollow struts and junctions. The experimental and computational strategy is considered as a first step toward optimization of process parameters to tailor anisotropy of cell shape and mechanical behavior for applications in batteries or Diesel particulate filtering.

Computationally-Optimized Bone Mechanical Modeling from High-Resolution Structural Images

Image-based mechanical modeling of the complex micro-structure of human bone has shown promise as a non-invasive method for characterizing bone strength and fracture risk in vivo. In particular, elastic moduli obtained from image-derived micro-finite element (μFE) simulations have been shown to correlate well with results obtained by mechanical testing of cadaveric bone. However, most existing large-scale finite-element simulation programs require significant computing resources, which hamper their use in common laboratory and clinical environments. In this work, we theoretically derive and computationally evaluate the resources needed to perform such simulations (in terms of computer memory and computation time), which are dependent on the number of finite elements in the image-derived bone model. A detailed description of our approach is provided, which is specifically optimized for μFE modeling of the complex three-dimensional architecture of trabecular bone. Our implementation includes domain decomposition for parallel computing, a novel stopping criterion, and a system for speeding up convergence by pre-iterating on coarser grids. The performance of the system is demonstrated on a dual quad-core Xeon 3.16 GHz CPUs equipped with 40 GB of RAM. Models of distal tibia derived from 3D in-vivo MR images in a patient comprising 200,000 elements required less than 30 seconds to converge (and 40 MB RAM). To illustrate the system's potential for large-scale μFE simulations, axial stiffness was estimated from high-resolution micro-CT images of a voxel array of 90 million elements comprising the human proximal femur in seven hours CPU time. In conclusion, the system described should enable image-based finite-element bone simulations in practical computation times on high-end desktop computers with applications to laboratory studies and clinical imaging.

Rockfall on the Slope of the Embankment of Finite Element Analysis of the Impact of the Impact

This article in a typical road slope model as an example, through large-scale general-purpose finite element simulation software ANSYS/LS-DYNA rockfall on the slope of the roadbed impact for three-dimensional dynamic analysis in the roadbed, slope geological parameters and falling stone initial state is not at the same time on the roadbed impact the results of comparative analysis. The result is the mountain slope of the road construction project provides reference.

A closed-form structural model of planar fibrous tissue mechanics

Structural models of tissue mechanics, in which the tissue is represented as a sum or integral of fiber contributions for a distribution of fiber orientations, are a popular tool to represent the complex mechanical behavior of soft tissues. A significant practical challenge, however, is evaluation of the integral that defines the stress. Numerical integration is accurate but computationally demanding, posing an impediment to incorporation of structural models into large-scale finite-element simulations. In this paper, a closed-form analytic evaluation of the integral is derived for fibers distributed according to a von Mises distribution and an exponential fiber stress–strain law.

Biotechnical means of soil stabilization using willow cuttings

Focus on the semi-arid and denuded loess plateau in Northwest China has resulted in emergence of biotechnical stabilization methods in response to the occurrence of severe soil erosion and numerous shallow slope failures. Green cuttings of easy-to-root species such as willow have been installed across a slope, which play an important role in preventing both surface erosion and shallow mass movements. However, the mechanical behavior of the cuttings in soil is not well understood so far. This paper presents a series of large-scale simple shear tests and finite element simulations of a soil reinforced by willow cuttings. The reinforced soils when subjected to simple shear exhibited strain-hardening behavior and failed along a horizontal plane. The shear strength of the reinforced soil increased with the cutting density and decreased with the soil water content. The finite element analysis, incorporating an elasto-plastic constitutive model for the soil, predicted shear strength parameters for the reinforced soil that agree well with those obtained from the simple shear tests. Significant stress concentrations occurred on the cuttings while the stresses in the soil were reduced—hence, the reinforced soil could withstand greater loadings.

An Improved Jacobi-Davidson Method With Multi-Level Startup Procedure

The Jacobi-Davidson method is very attractive for the large-scale finite element simulation of electromagnetic cavity problems, because it just requires approximate solutions to some auxiliary systems of linear equations, which are easily obtained by iterative solvers. Moreover, rates of convergence are quadratic to cubic. In consequence, the time spent within the pre-asymptotic region at the early stages of the iteration may have strong impact on overall performance, particularly when the number of eigenvalues sought is small. Therefore, we propose a startup procedure that utilizes p hierarchical finite element spaces to reduce the cost of bridging the pre-asymptotic region.

Large Scale Finite Element Modeling, Simulation and Visualization for Wind Flows in Urban Area Using Virtual Reality

A large-scale finite element modeling, simulation and visualization for wind flows are presented. The modeling method using GIS/CAD data is employed. The stabilized parallel finite element method based on SUPG/PSPG method is employed for the analysis of wind flows. The present method is applied to the simulation of wind flow and contaminant spread in urban area. The visualization based on virtual reality is employed to evaluate the mesh quality and computational results. The computed results are qualitatively in agreement with the experimental results and actual phenomena. The present method is shown to be a useful tool to simulate the wind flows in urban area.

Kidney damage in extracorporeal shock wave lithotripsy: a numerical approach for different shock profiles

In shock-wave lithotripsy--a medical procedure to fragment kidney stones--the patient is subjected to hypersonic waves focused at the kidney stone. Although this procedure is widely applied, the physics behind this medical treatment, in particular the question of how the injuries to the surrounding kidney tissue arise, is still under investigation. To contribute to the solution of this problem, two- and three-dimensional numerical simulations of a human kidney under shock-wave loading are presented. For this purpose a constitutive model of the bio-mechanical system kidney is introduced, which is able to map large visco-elastic deformations and, in particular, material damage. The specific phenomena of cavitation induced oscillating bubbles is modeled here as an evolution of spherical pores within the soft kidney tissue. By means of large scale finite element simulations, we study the shock-wave propagation into the kidney tissue, adapt unknown material parameters and analyze the resulting stress states. The simulations predict localized damage in the human kidney in the same regions as observed in animal experiments. Furthermore, the numerical results suggest that in first instance the pressure amplitude of the shock wave impulse (and not so much its exact time-pressure profile) is responsible for damaging the kidney tissue.

Dislocations, vacancies and solute diffusion in physical based plasticity model for AISI 316L

A physical based model for the evolution of flow stress of AISI 316L from room temperature up to 1300 °C, strains up to 0.6 and strain rates from 0.0005 up to 10 s −1 is developed. One set of tests have been used for model calibration and another more complex set of tests for its validation. The model is based on a coupled set of evolution equations for dislocation density and (mono) vacancy concentration. Furthermore, it includes the effect of diffusing solutes in order to describe dynamic strain ageing (DSA). The model described the overall flow stress evolution well with exception of the details of the effect of the DSA phenomenon. Its numerical solution is implemented in a format suitable for large-scale finite element simulations.

A computational method to predict strip profile in rolling mills

Presented is a new computational method for predicting the static cross-sectional thickness profile of rolled metal strip. Methods to model the strip profile and related flatness with improved efficiency and accuracy remain central for achieving high quality flat-rolled products. The new method involves a novel combination of Timoshenko beam finite elements with multiple coupled Winkler elastic foundations. It applies to simple mill configurations, such as the common 4-high rolling mill, in addition to complex mill types, such as the 20-high Sendzimir mill. The inherent benefits over traditional strip profile models include non-discrete elastic foundations, cubic displacement fields, rapid solution, and mixed boundary conditions. The flexible nature of the model allows it to readily accommodate typical mechanisms used in industry to control strip profile, such as roll crowning, roll bending, roll shifting, and roll crossing. Comparison of the predicted displacement for a 4-high mill with that obtained using a large-scale finite element simulation provides validation of the presented strip profile calculation method for real-time industrial applications.

Hierarchical hybrid grids: achieving TERAFLOP performance on large scale finite element simulations

The design of the hierarchical hybrid grids (HHG) framework is motivated by the desire to achieve high performance on large-scale, parallel, finite element simulations on super computers. In order to realize this goal, careful analysis of the low-level, computationally intensive algorithms used in implementing the library is necessary. This analysis is primarily concerned with identifying and removing bottlenecks that limit the serial performance of multigrid component algorithms such as smoothing and residual error calculation. To aid in this investigation, two metrics have been developed: the balance metric (BM), and the loads per miss metric (LPMM). Each of these metrics makes assumptions about the interaction of various data structures and algorithms with the underlying memory subsystems and processors of the architectures on which they are implemented. Applying these metrics generates performance predictions that can then be compared to measured results to determine the actual characteristics of an algorithm/data structure on a given platform. This information can then be used to increase performance. In this paper, we first present an overview of the HHG framework. Next, we introduce the details of the two performance metrics. These metrics are then applied to three different data structures used to implement a Gauß–Seidel smoothing algorithm. Performance results and an interpretation of the underlying interactions of the data structures with several relevant supercomputing architectures are given. Finally, we present a brief discussion of some performance results of the HHG framework, followed by some concluding remarks.

On gradient-enhanced damage and plasticity models for failure in quasi-brittle and frictional materials

Gradient-enhanced damage and plasticity approaches are reviewed with regard to their ability to model localization phenomena in quasi-brittle and frictional materials. Emphasis is put on the algorithmic aspects. For the purpose of carrying out large-scale finite element simulations efficient numerical treatments are outlined for gradient-enhanced damage and gradient-enhanced plasticity models. For the latter class of models a full dispersion analysis is presented at the end of the paper. In this analysis the fundamental role of dispersion in setting the width of localization bands is highlighted.