Single Integration Point Research Articles

One-point quadrature of higher-order finite and virtual elements in nonlinear analysis

In the present article, a stability- and consistency-preserving integration scheme for polynomial Galerkin approaches of arbitrary order is presented. The basis is formed by Taylor series expansions of the stresses with respect to the strains, which in turn are expanded towards the spatial directions. With a split of the material and geometric nonlinearities and the assumption of a material behavior linearly variable within an element, the strain energy in elements of arbitrary shape and polynomial order can be evaluated exactly. Therefore, geometric moments have to be calculated in preprocessing, requiring only evaluations of derivatives at a single integration point during the analysis. The moments can be effectively integrated analytically over the boundary of the elements. As one of the manifold applications, the use in the context of second order virtual elements is elaborated for which the assembly time can be significantly reduced. The combination with the automatic differentiation and expression optimization software AceGen provides performant element routines. In the numerical examples, the integration scheme shows promising accuracy and makes the application in more complex material models up to computational homogenization attractive.

Single Point Integration a Monolithic Application for Versatile Multifunctionality

In today's digitally interconnected world, the management of multiple social media accounts has become increasingly complex. The need for a unified solution that simplifies access to diverse platforms and centralizes notifications has led to the development of a groundbreaking application. This application offers a seamless and user-friendly experience, enabling individuals and businesses to effortlessly consolidate their social media presence in one place. With the capability to access and switch between various social media accounts at the click of a button, users can streamline their online interactions, saving time and improving overall efficiency. This paper introduces the concept and features of this innovative application, highlighting its potential to revolutionize the way we engage with our digital networks while enhancing convenience and productivity. Keywords: Social Media Management, Unified Solution, Centralized Notifications, User-Friendly Interface, Consolidation of Accounts, Diverse Platforms, Efficiency Optimization, Digital Networks, Time-Saving, Online Interactions, Digital Presence, Seamless Access, Switching Between Accounts, Streamlining, Multifunctional Application, Interconnected World, Convenience Enhancem ent, Productivity Improvement, Ground breaking Technology, Social Media Engagement.

A single point integration rule for numerical manifold method without locking and hourglass issues

A single point integration rule for numerical manifold method without locking and hourglass issues

Voxel‐based finite elements with hourglass control in fast Fourier transform‐based computational homogenization

AbstractThe power of fast Fourier transform (FFT)‐based methods in computational micromechanics critically depends on a seamless integration of discretization scheme and solution method. In contrast to solution methods, where options are available that are fast, robust and memory‐efficient at the same time, choosing the underlying discretization scheme still requires the user to make compromises. Discretizations with trigonometric polynomials suffer from spurious oscillations in the solution fields and lead to ill‐conditioned systems for complex porous materials, but come with rather accurate effective properties for finitely contrasted materials. The staggered grid discretization, a finite‐volume scheme, is devoid of bulk artifacts in the solution fields and works robustly for porous materials, but does not handle anisotropic materials in a natural way. Fully integrated finite‐element discretizations share the advantages of the staggered grid, but involve a higher memory footprint, require a higher computational effort due to the increased number of integration points and typically overestimate the effective properties. Most widely used is the rotated staggered grid discretization, which may also be viewed as an underintegrated trilinear finite element discretization, which does not impose restrictions on the constitutive law, has fewer artifacts than Fourier‐type discretizations and leads to rather accurate effective properties. However, this discretization comes with two downsides. For a start, checkerboard artifacts are still present. Second, convergence problems occur for complex porous microstructures. The work at hand introduces FFT‐based solution techniques for underintegrated trilinear finite elements with hourglass control. The latter approach permits to suppress local hourglass modes, which stabilizes the convergence behavior of the solvers for porous materials and removes the checkerboards from the local solution field. Moreover, the hourglass‐control parameter can be adjusted to “soften” the material response compared to fully integrated elements, using only a single integration point for nonlinear analyses at the same time. To be effective, the introduced technology requires a displacement‐based implementation. The article exposes an efficient way for doing so, providing minimal interfaces to the most commonly used solution techniques and the appropriate convergence criterion.

Static, free vibrational and buckling analysis of laminated composite beams using isogeometric collocation method

Isogeometric collocation (IGA-C) method is a computational approach to solve boundary value problems. In this method (IGA-C), the differential equations are solved in strong form instead of the weak form approach adopted by Galerkin based formulations. IGA-C method is computationally efficient in comparison to conventional finite element method and Galerkin-Isogeometric approaches. IGA-C method does not involve the process of assembling global stiffness matrix from element stiffness matrix. Another advantage of IGA-C is that it requires a single integration point per element irrespective of the order of Non-Uniform Rational B-Spline functions (NURBS) adopted. Isogeometric collocation has also been demonstrated as a stable, efficient and accurate higher order computational method for explicit problems. For a wider adoption of isogeometric collocation method, beam/plate/shell finite elements within the framework of IGA-C method need to be formulated. Owing to the extensive adoption of laminated composites in structural components, development of beam finite elements for laminated composite beams based on isogeometric collocation method will prove useful during analysis of composite structures. IGA-C method is proposed in this study for the static bending, free vibration and buckling analysis of laminated composite beams. Classical laminated plate theory (CLPT), first order shear deformation theory (FSDT) and higher order shear deformation theory (HSDT) are considered for all the three analyses. The computational approach proposed for laminated beam based on HSDT contains two Degrees of Freedom (DOF) per node. Computational approach for analysing laminated composite beams based on each of these kinematic theories and using IGA-C method is presented. Accuracy of the proposed computational approaches is checked by solving different numerical examples. Values of normalized transverse displacement, normalized stresses, normalized natural frequencies and normalized critical buckling loads are compared with results from the literature and are found to be accurate.

A hyper-reduction computational method for accelerated modeling of thermal cycling-induced plastic deformations

For materials under cyclic thermal loadings, temperature and strain rate-dependent creep deformation can occur due to the thermal expansion mismatch near material interfaces, leading to deterioration of fatigue life. Simulation of the nonlinear mechanical deformation processes of materials subjected to thermal cycling with high-fidelity numerical models often consume high computational costs due to material nonlinearities and long thermal loading period. To accelerate such thermal cycling simulation, an efficient reduced-order modeling framework is proposed. We adopt the reproducing kernel particle method (RKPM) to generate offline high-fidelity model snapshots, which are utilized to create low-dimensional surrogate models based on the proper orthogonal decomposition under Galerkin projection. Based on the stabilized conforming nodal integration technique, gradient smoothing at single integration point per integration cell is employed in conjunction with a least-squares stabilization for high computational efficiency. To further speed up the simulation, a hyper-reduction method is introduced to avoid the full domain integration during the elastoplastic online simulation. Numerical examples on modeling of thermal cycling-induced plastic deformation and thermal fatigue life prediction of a flip chip assembly are analyzed to demonstrate the effectiveness of the present hyper-reduced-order model in significant reduction of computational time while preserving desired accuracy.

Thermomechanical model for solidification and cooling simulation of Ni-based superalloy components

One of the challenges encountered in the industrialization of new single-crystal superalloys parts (like high-pressure turbine blades and vanes for aircraft engines) is to limit the mechanical stresses during the solidification and cooling of the metal. In order to accurately predict the viscoplastic flow as well as the thermo-mechanical behaviour of Ni-based superalloy during its cooling, in this study a thermodynamically-consistent thermo-elasto-viscoplastic model was developed. This model takes into account the solid-liquid transition occurring in the material during the cooling phase. This is done by introducing a compressible-type viscoplastic yield function based on appropriate equivalent stress depending on volume fraction of the solid phase formed by the propagation of dendrites inside the liquid phase of the material. This model was implemented in Abaqus/Standard© F.E. code and applied to the identification of material parameters of Ni-based superalloy using isothermal tensile-relaxation tests driven for different strain rates and temperatures. First, anisothermal tensile-compression test was simulated on a single integration point. A comparison of the experimental and numerical stress-strain response partially validate the model. Second, a benchmark test involving casting of a rectangular Ni-based superalloy bar in a sand mold was simulated and analyzed.

One-dimensional Eikonal Non-Local (ENL) damage models: Influence of the integration rule for computing interaction distances and indirect loading control on damage localization

The Eikonal Non-Local approach models damage dependent non-local interactions by considering that interaction distances between material points are computed from solving an eikonal equation with an isotropic/anisotropic damage dependent metric Riemann function. In the finite element context, such a formulation exhibits good regularization properties and naturally allows one to model strain localization when non-local interactions vanish. In an isotropic damage mechanics framework, the damage variable tends to unity on a single integration point, and no damage diffusion occurs. In a one-dimensional context, evaluating the interaction distance between two points comes into computing an integral where the integrated function depends on the damage field between them. Desmorat et al. [9] performed the integration using a trapezoidal rule (under the assumption that the damage field is constant between adjacent integration points). Conversely, Jirásek and Desmorat [19] assumed that the damage field is linear between nearby integration points. Mainly motivated by improved integration accuracy, this method leads to a more gradual damaging process and makes it easier to follow the structural response when damage localizes. In this contribution, we show that despite these advantages, such a choice induces parasite damage diffusion issues, making the use of a standard trapezoidal rule more relevant. Moreover, once this choice is made, the structural response during damage localization can be conveniently described using a path-following method based on controlling the non-local strain variation of the localizing element instead of the local strain as in the works cited above.

Towards the incorporation of damage into solid‐shells based on reduced integration

AbstractSome years ago, a family of continuum finite elements based on reduced integration [1], [2], [3] was investigated. Many structural components with different kinds of elastic and inelastic material behaviour were considered and these elements showed accurate results while beeing more efficient than similar three‐dimensional formulations based on full integration. The objective of the present contribution is to extend the analysis to damage and fracture. To this end, we present the incorporation of a modified version of a gradient‐extended damage model [4] based on the micromorphic approach [5] into solids with only a single integration point. Due to the analogy to fully‐coupled thermomechanical problems, we adapt the derivation of a consistent hourglass stabilization from an earlier contribution for multi‐field problems [6]. A numerical benchmark problem of quasi‐brittle fracture reveals the accuracy and efficiency of the proposed approach. Besides the ability to deliver mesh‐independent results, the framework is especially suitable for highly constrained situations in which conventional low‐order finite elements suffer from well known locking phenomena.

On a robust FE2 model for delamination analysis in composite structures

The present paper deals with a robust two-scale delamination model based on a FE2 formulation, whereby a finite element model on the macro- and meso-scale are solved simultaneously. For a correct modeling of the delamination kinematics, the composite structure on macro-scale is discretized by a combined element. Only one single integration point over the full height of the composite structure contains the information about shell and interfacial kinematics, allowing a straight forward enhancement to the FE2 model. On the meso-scale, the combined kinematics are applied to a coupled representative volume element (cRVE), which describes the entire stacking sequence including an interfacial layer. The coupling between the shell and the interfacial kinematics results in a more robust delamination model. Numerical examples demonstrate the applicability and the improvements by reducing the oscillations of the load displacement curve during the softening process and the influence of the macroscopic mesh discretization under single and mixed mode loading.

A stabilized single-point finite element formulation for three-dimensional dynamic analysis of saturated soils

A low-order single-point quadrature finite element suitable of dynamic 3D analysis of saturated soils is presented. The new element uses a u-p formulation to consider the interaction of the pore fluid and solid skeleton. An hourglass stabilization scheme facilitates single-point integration for the solid phase terms, and non-residual pressure field stabilization is used to facilitate equal-order interpolation for the two phases and improve element behavior in the incompressible–impermeable limit. Several numerical examples are presented to verify the new element formulation and demonstrate its response in a geotechnical application.

NUMERICAL MODELLING AND VALIDATION OF 12.7 MM FSP IMPACT INTO ALFC SHIELD – ARMOX 500T STEEL PLATE SYSTEM

The study develops a methodology for numerical modelling and simulation of a 12.7 mm 13.4 g FSP fragment impact into the ALFC shield – ARMOX 500T steel plate system. The ALFC shield is composed of the ALF energyabsorbing subsystem and a 10 mm-thick 99,7% Al 2O3 alumina ceramic layer. The ALF subsystem is designed to absorb blast wave impact energy induced by explosive materials up to 10 kg TNT. The ceramic layer is designed to stop fragments from IED explosion. The 5 mm-thick Armox 500T steel plate constitutes the body bottom segment of a light armoured vehicle. The ALF subsystem has the following layered structure: Al2024 aluminium alloy plate, SCACS hybrid laminate plate, ALPORAS aluminium foam, SCACS hybrid laminate plate. The layers are joined with Soudaseal 2K chemoset glue. SCACS hybrid laminate contains the following components: VE 11-M modified vinylester resin (matrix), SWR800 S-glass plain weave fabric, Tenax HTA40 6K carbon plain weave fabric, Kevlar 49 T 968 aramid plain weave fabric. The total thickness of the ALFC shield amounts to 90 mm. Proof ground tests of a 12.7 mm 13.4 g FSP fragment impact into the ALFC shield – ARMOX 500T steel plate system have been performed at impact velocity 715 m/s and used for experimental validation of numerical modelling and simulation. In the numerical modelling, the aluminium alloy plate and Armox 500T steel plate are working in the elasto-plastic range according to Johnson–Cook model. The 99.7% Al 2O3 alumina ceramic is working in elasto-short range according to JH-2 Johnson–Holmquist model. The simulations correspond to large displacements, large deformations and potential contact among all the components of the system. In FE mesh, the 8-node 24 DOF hexahedral finite elements with single integration point have been used. Failure criteria governing ad-hoc erosion of finite elements have been applied. The FEM modelling, simulation and postprocessing have been carried out using Catia, HyperMesh, LS-DYNA and LS-PrePost systems. The simulation results in the form of displacement/penetration contours and the FSP final deformation have been compared with the experimental results.

NUMERICAL MODELLING AND DESIGN OF ALFC SHIELD LOADED BY 20 MM FSP FRAGMENT

The study develops numerical modelling and design of the ALFC shield loaded by the 20 mm 54 g FSP fragment moving at impact velocity of 1800 m/s (fragmentation simulation of IED devices), used to protect 5 mm-thick Armox 500T steel plate. The ALFC shield is composed of the ALF energy-absorbing subsystem and a 99.7% Al 2O3 alumina ceramic layer. The ALF subsystem is designed to absorb blast wave impact energy induced by explosive materials up to 10 kg TNT. The ceramic layer is aimed at stopping FSP fragments. The 5 mm-thick Armox 500T steel plate reflects the body bottom segment of a light armoured vehicle. The main purpose of the study is to determine the minimum thickness of the ceramic layer at which the 5 mm-thick Armox 500T steel plate is fully protected from perforation. The ALF subsystem has the following layered structure: Al2024 aluminium alloy plate, SCACS hybrid laminate plate, ALPORAS aluminium foam, SCACS hybrid laminate plate. The layers are joined with Soudaseal 2K chemoset glue. SCACS hybrid laminate contains the following components: VE 11-M modified vinylester resin (matrix), SWR800 glass S plain weave fabric, Tenax HTA40 6K carbon plain weave fabric, Kevlar 49 T 968 aramid plain weave fabric. The total thickness of the ALF shield amounts to 76 mm. In the numerical modelling, the aluminium alloy plate and Armox 500T steel plate are working in the elasto-plastic range according to Johnson–Cook model. The 99.7% Al 2O3 alumina ceramic is working in elasto-short range according to JH-2 Johnson–Holmquist model. The simulations correspond to large displacements, large deformations and contact among all the components of the system. In FE mesh, the 8-node 24 DOF hexahedral finite elements with single integration point have been used. Additional failure criteria governing ad-hoc erosion of finite elements have been applied. The FEM modelling, simulation and postprocessing have been carried out using Catia, HyperMesh, LS-DYNA and LS-PrePost systems. The simulation results are presented in the form of displacement – perforation contours and the FSP final deformation for both the FSP–shield–plate and the FSP–plate systems. It has been pointed out that 18 mm-thick ceramic layer protects the LAV body bottom plate from perforation.

Accelerating crystal plasticity simulations using GPU multiprocessors

SUMMARYCrystal plasticity models are often used to model the deformation behavior of polycrystalline materials. One major drawback with such models is that they are computationally very demanding. Adopting the common Taylor assumption requires calculation of the response of several hundreds of individual grains to obtain the stress in a single integration point in the overlying FEM structure. However, a large part of the operations can be executed in parallel to reduce the computation time. One emerging technology for running massively parallel computations without having to rely on the availability of large computer clusters is to port the parallel parts of the calculations to a graphical processing unit (GPU). GPUs are designed to handle vast numbers of floating point operations in parallel. In the present work, different strategies for the numerical implementation of crystal plasticity are investigated as well as a number of approaches to parallelization of the program execution. It is identified that a major concern is the limited amount of memory available on the GPU. However, significant reductions in computational time‐up to 100 times speedup‐are achieved in the present study, and possible also on a standard desktop computer equipped with a GPU. Copyright © 2014 John Wiley & Sons, Ltd.

Stabilized single-point 4-node quadrilateral element for dynamic analysis of fluid saturated porous media

An accurate and efficient low-order quadrilateral mixed u–p element suitable for dynamic analysis of fluid saturated porous media is presented. The element uses physical hourglass stabilization to facilitate single-point integration for the solid phase, and non-residual stabilization of the fluid phase to circumvent instability in the incompressible-impermeable limit due to the use of equal-order interpolation for the displacement and pressure fields. Element behavior is verified and demonstrated through several numerical examples.

The Research on Thermal-Mechanical Coupling Simulation of Steam Turbine Vane Material’s Cutting Process

In order to explore the cutting rules of the 43-inch vane material --1Cr12Ni3Mo2VNbN on the turbine vane, and research the stress in cutting area, the strain as well as the temperature distribution and the variation, providing the reference data for the large-scale vane-root milling cutter's geometric parameter design and the cutting parameter optimization, the authors employed ANSYS / LS-DYNA finite element method to simulate and research the cutting process of the vane material. The authors adopted the two-dimensional plane element 2D SOLID l62 of the single-point integration Lagrange algorithm to establish the finite element cutting model, and established the Cowper-Symonds constitutive models based on the vane material, applied the 2D-r adaptive meshing to simulate the separation of the chip and workpiece. Obtain the distribution and rules of the stress, the strain as well as the temperature in the cutting area, and greatly shorten the period of the vane root milling cutter’s designing and trial-production.

Modelling of hydro‐fracture flow in porous media

PurposeThe mechanical response of the skeleton of a porous medium is highly dependent on its seepage behaviour as pore pressure modifications affect the in situ stress field. The purpose of this paper is to describe how u‐p formulation is employed using an explicit time integration scheme where fully saturated and single‐phase partially saturated analyse are incorporated for 2D and 3D cases.Design/methodology/approachOwing to their inherent simplicity, low‐order elements provide an excellent framework in which contact conditions coupled with crack propagation can be dealt with in an effective manner. For linear elements this implies single point integration which, however, can result in spurious zero‐energy modes which necessitates introduction of a stabilization technique to provide reliable results.FindingsThe success of the modelling strategy ultimately depends on the inter‐dependence of different phenomena. The linking between the displacements components, network and pore pressures represents an important role in the efficiency of the overall coupling procedure. Therefore, a master‐slave technique is proposed to link seepage and network fields, proving to be particularly attractive from a computational cost point of view. Another development that has provided substantial savings in CPU times is the use of an explicit‐explicit subcycling scheme.Originality/valueSignificant reduction in computational cost is achievable using a master‐slave procedure to link seepage and fracture network‐flows and an explicit‐explicit subcycling scheme. Special attention is focused on the investigation of the influence of plastic zones in oil production problems.

A reduced integration solid‐shell finite element based on the EAS and the ANS concept—Geometrically linear problems

AbstractIn this paper a new reduced integration eight‐node solid‐shell finite element is presented. The enhanced assumed strain (EAS) concept based on the Hu–Washizu variational principle requires only one EAS degree‐of‐freedom to cure volumetric and Poisson thickness locking. One key point of the derivation is the Taylor expansion of the inverse Jacobian with respect to the element center, which closely approximates the element shape and allows us to implement the assumed natural strain (ANS) concept to eliminate the curvature thickness and the transverse shear locking. The second crucial point is a combined Taylor expansion of the compatible strain with respect to the center of the element and the normal through the element center leading to an efficient and locking‐free hourglass stabilization without rank deficiency. Hence, the element requires only a single integration point in the shell plane and at least two integration points in thickness direction. The formulation fulfills both the membrane and the bending patch test exactly, which has, to the authors' knowledge, not yet been achieved for reduced integration eight‐node solid‐shell elements in the literature. Owing to the three‐dimensional modeling of the structure, fully three‐dimensional material models can be implemented without additional assumptions. Copyright © 2009 John Wiley & Sons, Ltd.

Atomic-scale finite-element model of tension in nanoscale thin film

In this paper, a 2D atomic-scale finite-element model of tension in nanoscale thin film is developed in which Morse’s potential energy function is used to model the interactive forces between atoms. The model is fed into the finite-element package LS-DYNA and both a single integration point and an explicit solution method are used for solving the tension process rapidly to investigate the size effect of different film thicknesses and the effect of different atomic vacancy ratios on nanoscale thin film under tension. The results show that since the applied displacement is exerted at both ends for different thickness of a perfect crystal, a neutral line is formed at the middle of the material. The material slides along the easiest slip direction to cause a “necking” feature on both sides. The stress initially increases with the gradual increase of strain and thicker film shows a larger tensile stress. After the film experiences the peak stress, the stress then decreases with the gradual increase of strain. While the applied displacement is applied at both ends for different vacancies, a neutral line is formed at the middle of material, but this is not apparent due to the random scattered vacancies. The material slides along the easiest slip direction from left to right, and the stress concentration areas near the constrained ends form “necking” features. Stresses are not zero at zero strain. Tension tests for different vacancy ratios show different maximum stresses. Film with a larger vacancy ratio shows a lower stress at the same strain. As the vacancy ratio of the film under tension increases, the strength and elastic modulus reduces.

Direct computation of general chemical energy differences: Application to ionization potentials, excitation, and bond energies

Chemists are mainly interested in energy differences. In contrast, most quantum chemical methods yield the total energy which is a large number compared to the difference and has therefore to be computed to a higher relative precision than would be necessary for the difference alone. Hence, it is desirable to compute energy differences directly, thereby avoiding the precision problem. Whenever it is possible to find a parameter which transforms smoothly from an initial to a final state, the energy difference can be obtained by integrating the energy derivative with respect to that parameter (cf. thermodynamic integration or adiabatic connection methods). If the dependence on the parameter is predominantly linear, accurate results can be obtained by single-point integration. In density functional theory and Hartree-Fock, we applied the formalism to ionization potentials, excitation energies, and chemical bond breaking. Example calculations for ionization potentials and excitation energies showed that accurate results could be obtained with a linear estimate. For breaking bonds, we introduce a nongeometrical parameter which gradually turns the interaction between two fragments of a molecule on. The interaction changes the potentials used to determine the orbitals as well as the constraint on the orbitals to be orthogonal.