Explicit Integration Scheme Research Articles

ЭКСПЕРИМЕНТАЛЬНАЯ И РАСЧЕТНАЯ ОЦЕНКА КРАТКОВРЕМЕННОЙ ПРОЧНОСТИ ОБРАЗЦОВ ИЗ ПЛАСТИЧНОГО МАТЕРИАЛА С U- И V-ОБРАЗНЫМИ ОСТРЫМИ НАДРЕЗАМИ

In this work, the experimental and calculation studies of the short-time strength of tensile rods made of a plastic material with U- and V-shape sharp notches were made. Thermoplastic-acryl-butadiene-styrene (ABS) was chosen as the model material. Samples with a diameter of about 5 mm were obtained on a single-screw extruder by melting granules. In the first part of the paper, the dependence of the mechanical properties of ABS in a wide range of quasi-static strain rates (0.02 ... 10 min-1) was studied. With these conditions, under single-step loading, this material can be considered as an elastoplastic one with an elastic modulus of 2200 MPa, with the yield strength of about 41 MPa and independent of the given strain rates with an error of less than 5 %. For the tested smooth samples, the residual longitudinal strain at rupture was 15 ... 25 %, the residual decreasing of a cross-section (necking) was 30 ... 50 %. The next group of samples had U-notches with a radius of 1.6 mm. The angle of sharp V-notches was 60°. The depth of the single-sided notches was varied in the range of 0 ... 3.5 mm. It is obtained that the ultimate load held by the samples with V-notches exceeds the corresponding load of the samples with U-notches of the same depth due to a greater constraint of the plastic strains in a notch zone. Notches up to 1 mm depth practically do not reduce the ultimate load of the samples. In the second part of the work, with the help of the FEM, the elastic-plastic deformation and fracture kinetics were calculated using a non-local approach, an explicit integration scheme in the ANSYS Workbench package. The calculations showed that the ultimate load is determined only by the yield strength of the material and the configuration of the notch. Rupture of samples (in ANSYS this is the technology of removing critically deformed finite elements) occurred at lower loads, depending on the plasticity resource of the material and the configuration of the notch. The calculated values of the ultimate and rupture loads are in a good agreement with the experimental data. The technique can be recommended for evaluating the strength of complex shape samples of plastic materials with arbitrary stress concentrators.

Symbolic multibody methods for real-time simulation of railway vehicles

In this work, recently developed state-of-the-art symbolic multibody methods are tested to accurately model a complex railway vehicle. The model is generated using a symbolic implementation of the principle of virtual power. Creep forces are modeled using a direct symbolic implementation of the standard linear Kalker model. No simplifications, such as base parameter reduction, partial-linearization or lookup tables for contact kinematics, are used. An Implicit–Explicit integration scheme is proposed to efficiently deal with the stiff creep dynamics. Real-time performance is achieved: the CPU time required for a very robust $1~\text{ms}$ integration time step is 203 μs.

Hamiltonian Nodal Position Finite Element Method for Cable Dynamics

This paper developed a new Hamiltonian nodal position finite element method (FEM) to treat the nonlinear dynamics of cable system in which the large rigid-body motion is coupled with small elastic cable elongation. The FEM is derived from the Hamiltonian theory using canonical coordinates. The resulting Hamiltonian finite element model of cable contains low frequency mode of rigid-body motion and high frequency mode of axial elastic deformation, which is prone to numerical instability due to error accumulation over a very long period. A second-order explicit Symplectic integration scheme is used naturally to enforce the conservation of energy and momentum of the Hamiltonian finite element system. Numerical analyses are conducted and compared with theoretical and experimental results as well as the commercial software LS-DYNA. The comparisons demonstrate that the new Hamiltonian nodal position FEM is numerically efficient, stable and robust for simulation of long-period motion of cable systems.

Finite element solution of Poisson Equation over Polygonal Domains using a novel auto mesh generation technique and an explicit integration scheme for nine node linear convex quadrilateral of Lagrange family

This paper presents an explicit integration scheme to compute the stiffness matrix of a nine node linear convex quadrilateral element of Lagrange family using symbolic mathematics and discretisation of polygonal domain by such finite elements using a novel auto mesh generation technique , In finite element analysis, the boundary value problems governed by second order linear partial differential equations, the element stiffness matrices are expressed as integrals of the product of global derivatives over the linear convex quadrilateral region. These matrices can be shown to depend on the material properties and the matrix of integrals with integrands as rational functions with polynomial numerator and the linear denominator (4+ ) in the bivariates over a nine node 2-square (-1 ) with nodes at the points {(-1,-1),(1,-1),(1,1),(-1,1),(0,-1),(1,0).(0,1),(- 1,0),(0,0)} in local parametric space. In this paper, we have computed these integrals in exact forms using the symbolic mathematics capabilities of MATLAB. The proposed explicit finite element integration scheme can be applied to solve boundary value problems in continuum mechanics over convex polygonal domains. We have also developed a novel auto mesh generation technique of all nine node linear convex quadrilaterals for a polygonal domain which provides the nodal coordinates and element connectivity. We have used the explicit integration scheme and this novel auto mesh generation technique to solve the Poisson equation u ,where u is unknown physical variable and in with given Dirichlet boundary conditions over the given convex polygonal domain.

Application of mode superposition to hybrid simulation using Real Time Finite Element Method

The following paper presents methods for application of mode superposition to the analytical part of the hybrid simulation, when Real Time Finite Element Method is used to model the analytical substructure. Introducing mode superposition can bring significant computation time decrease in real time computations, by performing some calculations offline. The paper describes requirements, methods and algorithms for introducing mode superposition to explicit and implicit integration schemes. In explicit schemes mode superposition allows to increase the minimum time step often enabling real time computations that were not possible before. In implicit schemes mode superposition allows to reduce the time step of the analysis (and therefore increase accuracy). Numerical examples proving the effectiveness of the presented algorithms are given.DOI: http://dx.doi.org/10.5755/j01.mech.23.5.14642

A nonlocal continuum damage model for brittle fracture

The objective of this paper is to develop a nonlocal continuum damage model for brittle fracture. A nonlocal damage conjugate force tensor is obtained from the “local” one, using an integral-type regularization technique, and the thermodynamic equations are formulated in a nonlocally generalized standard manner. A nonlocal damage model is developed based on a recently developed “local” model, which can rigorously handle damage anisotropy, distinct tensile and compressive damage behavior, and damage deactivation, so that the nonlocal model not only handles brittle fracture well but also possesses the advantageous features of the “local” model. A fully explicit integration scheme for the present model is developed and then implemented in Abaqus/Explicit via VUMAT. The present model is validated through: 1. simulating cyclic uniaxial tests on a SiC–SiC woven composite; 2. calibrating its associated material parameters via single edge notched bend (SENB) tests on concrete beams. Its versatility is demonstrated through simulating a mixed-mode fracture test on a double edge notched (DEN) specimen. It is found to be capable of producing realistic fracture paths and capturing size effects in real materials. A wide variety of mechanical behavior can be incorporated into the present model in the future.

Asynchronous parallel algorithm for three-dimensional soil-structure interaction analysis based on explicit-implicit integration scheme

A computationally efficient explicit-implicit FEM in parallel manner to analyze the response of three-dimensional soil-structure system subjected to seismic wave is presented. The unbounded soil is modelled by lumped-mass explicit finite element method and viscoelastic artificial boundary, the structure is analysed through implicit finite element method, and response of the rigid foundation is calculated through explicit time integration scheme. The different time steps can be chosen for the explicit and implicit integration scheme, which can greatly improve the efficiency. The synchronous and asynchronous parallel algorithms using MPI are proposed for the soil-structure interaction analysis. The codes for this method are programmed. Example for seismic response analysis of a nuclear plant is given, which validates the feasibilty and efficiency of the proposed method.

A robust explicit integration of elasto-plastic constitutive models, based on simple subincrement size estimation

PurposeThe purpose of this study, which is designed for the implementation of models in the implicit finite element framework, is to propose a robust, stable and efficient explicit integration algorithm for rate-independent elasto-plastic constitutive models.Design/methodology/approachThe proposed automatic substepping algorithm is founded on an explicit integration scheme. The estimation of the maximal subincrement size is based on the stability analysis.FindingsIn contrast to other explicit substepping schemes, the algorithm is self-correcting by definition and generates no cumulative drift. Although the integration proceeds with maximal possible subincrements, high level of accuracy is attained. Algorithmic tangent stiffness is calculated in explicit form and optionally no analytical second-order derivatives are needed.Research limitations/implicationsThe algorithm is convenient for elasto-plastic constitutive models, described with an algebraic constraint and a set of differential equations. This covers a large family of materials in the field of metal plasticity, damage mechanics, etc. However, it cannot be directly used for a general material model, because the presented algorithm is convenient for solving a set of equations of a particular type.Practical implicationsThe estimation of the maximal stable subincrement size is computationally cheap. All expressions in the algorithm are in explicit form, thus the implementation is simple and straightforward. The overall performance of the approach (i.e. accuracy, time consumption) is fully comparable with a default (built-in) ABAQUS/Standard algorithm.Originality/valueThe estimated maximal subincrement size enables the algorithm to be stable by definition. Subincrements are much larger than those in conventional substepping algorithms. No error control, error correction or local iterations are required even in the case of large increments.

Excitation and decay of surface plasmon polaritons in n-GaN

We report on the studies of the surface plasmon polaritons in n-GaN epitaxial layers. The grating etched on the surface of the epitaxial layer is used to excite surface plasmon polaritons by means of terahertz photons. The experimental reflectivity spectrum for p-polarized radiation demonstrates a set of resonances associated with excitation of different surface plasmon polariton modes. Spectral peculiarities due to the diffraction effect have been also revealed. Emission of terahertz radiation is investigated under epilayer temperature modulation by electric current. The emissivity spectrum of the epitaxial layer with surface-relief grating shows peaks in the frequency ranges corresponding to the decay of the surface plasmon polariton modes. The characteristic features of the reflectivity and emissivity spectra are well described theoretically by a differential method with explicit integration scheme.

Numerical analysis of crimping and inflation process of balloon-expandable coronary stent using implicit solution.

The paper presents an applied methodology for numerical finite element analysis of coronary stent crimping and the free inflation process with the use of a folded noncompliant angioplasty balloon. The use of an implicit scheme is considered as the most original part of the work, as an explicit finite element procedure is very often preferred. Hitherto, when the implicit solution was used for the finite element solution, the simulated issue was largely simplified. Therefore, the authors focused on the modelling methodology with minimum possible simplification, ie, a full load path (compression and inflation in single analysis), solid element discretization, and sophisticated contact models (bodies with highly different stiffness). The obtained results are partially compared with experimental data (radial force during the crimping procedure) and present satisfactory compliance. The authors believe that presented methodology allow for significant improvement of the obtained results, as well as potential extension of the research scope, compared to previous efforts performed using the explicit integration scheme. Moreover, the presented methodology is believed to be suitable for sensitivity and optimization studies.

Realization and Discretization of Asymptotically Stable Homogeneous Systems

Sufficient conditions for the existence and convergence to zero of numeric approximations to solutions of asymptotically stable homogeneous systems are obtained for the explicit and implicit Euler integration schemes. It is shown that the explicit Euler method has certain drawbacks for the global approximation of homogeneous systems with nonzero degrees, whereas the implicit Euler scheme ensures convergence of the approximating solutions to zero. Properties of absolute and relative errors of the respective discretizations are investigated.

On the efficiency and accuracy of stress integration algorithms for constitutive models based on non-associated flow rule

Constitutive models based on non-associated flow rule enable the accurate description of complex anisotropy phenomena by using distinct, but relatively simple, mathematical description for yield function and plastic potential. The computational complexity of stress integration procedure may thus be significantly reduced. The amount by which this advantage is reflected to the total computation time is, however, a function of the nonlinearity of the problem at hand. The present work aims to make a systematic comparison of two different stress integration algorithms, used in conjunction to non-associated flow rule. A fully explicit and semi-implicit integration scheme are analyzed in terms of accuracy and speed. The implemented yield model is Yld2000-2d with isotropic hardening. The validity of the stress-integration approaches is assessed based on the ability to reproduce stress-ratios, r-values and tensile test results. Additionally, measured earing profiles in cup drawing experiments are compared. The fully explicit implementation shows significant advantages in terms of speed.

Explicit integration scheme of a subloading surface plasticity model for unsaturated soils

An adaptive substepping explicit integration scheme is proposed for a subloading surface plasticity (SSP) model for unsaturated soils. The SSP model is referred to as the modified σ Θ model, the constitutive laws of which are established in the space of Bishop's effective stress ( σ ) and effective degree of saturation (Θ ). The modified σ Θ model includes a convex subloading surface in the p-q plane and a nonconvex subloading surface in the p- Θ plane. The convex/nonconvex subloading surface in the model may cause problems of incorrect loading-unloading decisions during the stress update. A Double Cosine loading-unloading decision method (DC method) is revised and embedded into the explicit integration scheme for the modified σ Θ model. The local error of the effective degree of saturation ( Θ ) is introduced in the error control for each substep. The performance of the DC method for the modified σ Θ model is discussed. The importance of involving the effective saturation ( Θ ) in the error control is also demonstrated via numerical examples.

Assessment tools for numerical resolution of a contact dynamic problem with modal basis reduction.

This paper is devoted to the study of the modal basis reduction method in the framework of the dynamical behavior of a mechanical system with multiple joint clearances. The final objective is to estimate contact forces in a confined tube bundle during a dynamic loading for nuclear components sizing. The modal basis reduction combined with an explicit integration scheme is envisioned to deal with the large number of tubes and potential contact zones. In this paper, method is first applied to the example of a clamped-free beam impacting on a spring on its free edge. A semi-analytical resolution allows assessing the validity of the modal basis reduction method depending of some parameters, like frequency truncation and ratio between the bending stiffness and the spring stiffness. This study leads to criteria on numerical parameters which have to be respected to ensure stability and accuracy of results.

An All Quadrilateral Automesh Generation Technique and Explicit Integration Scheme for Finite Elements to Solve Some Elliptic Boundary Value Problems in Two Space

This paper proposes the explicit integration scheme for a unique linear convex quadrilateral which can be obtained from an arbitrary linear triangle by joining the centroid to the midpoints of sides of the triangle. The explicit integration scheme proposed for these unique linear convex quadrilaterals is derived by using the standard transformations in two steps. We first map an arbitrary triangle into a standard right isosceles triangle by using an affine linear transformation from global (x, y) space into a local space (u, v). We discretise the standard right isosceles triangle in (u, v) space into three unique linear convex quadrilaterals. We have shown that any unique linear convex quadrilateral in (x, y) space can be mapped into one of the unique quadrilaterals in (u, v) space. We can always map these linear convex quadrilaterals into a 2-aquare in a natural space by an appropriate bilinear transformation. Using these two mappings, we have established an integral derivative product relation between the linear convex quadrilaterals in the (x, y) space interior to the arbitrary triangle and the linear convex quadrilaterals of the local space (u, v) interior to the standard right isosceles triangle. Further , we have shown that the product of global derivative integrals in (x, y) space can be expressed as a matrix triple product P ( X (2 * area of the arbitrary triangle in (x, y) space ) in which P is a geometric properties matrix and is the product of global derivative integrals in (u, v) space.We have shown that the explicit integration of the product of local derivative integrals in (u, v) space over the unique quadrilateral spanning vertices (1/3 ,1/3), (0, ½), (0, 0) , (1/2, 0) is now possible by use of symbolic processing capabilities in MATLAB which are based on Maple – V software package. In a similar manner we have found explicit integrals of ihe shape function and global derivative products as well as the product of shape functions.We use these integral values in computing stiffness matrix for some elliptic equations with constant coefficients.The proposed explicit integration scheme is a useful technique for boundary value problems governed by either a single equation or a system of second order partial differential equations. The physical applications of such problems are numerous in science, and engineering, the examples of single equations are the well known Laplace and Poisson equations with suitable boundary conditions. These problems are already studied in authors recent paper. We have demonstrated the proposed explicit integration scheme to solve the elliptic equations with constant coefficients subject to Dirichlet boundary conditions over simple polygonal domains like 1-square and 2-square.We have demonstrated the propsed scheme and technique to study five typical elliptic boundary value problems.Three FEM models with 2400,5400 and 7776 elements and 2481,5521 and 7921 nodes respectively are used.Tables of fem computed values,theoretical values at selected nodes and the finite element meshes are appended.The findings confirm with surface plots of exact solutions for the considered elliptic boundary value problems. Key words: Explicit Integration, Finite Element Method, Matlab Symbolic Mathematics, All Quadrilateral Mesh Generation Technique,Elliptic equations with constant coefficients ,Dirichlet Boundary Conditions ,Polygonal Domain,2-square,1-square

Atherosclerotic plaque delamination: Experiments and 2D finite element model to simulate plaque peeling in two strains of transgenic mice

Finite element analyses using cohesive zone models (CZM) can be used to predict the fracture of atherosclerotic plaques but this requires setting appropriate values of the model parameters. In this study, material parameters of a CZM were identified for the first time on two groups of mice (ApoE-/- and ApoE-/- Col8-/-) using the measured force-displacement curves acquired during delamination tests. To this end, a 2D finite-element model of each plaque was solved using an explicit integration scheme. Each constituent of the plaque was modeled with a neo-Hookean strain energy density function and a CZM was used for the interface. The model parameters were calibrated by minimizing the quadratic deviation between the experimental force displacement curves and the model predictions. The elastic parameter of the plaque and the CZM interfacial parameter were successfully identified for a cohort of 11 mice. The results revealed that only the elastic parameter was significantly different between the two groups, ApoE-/- Col8-/- plaques being less stiff than ApoE-/- plaques. Finally, this study demonstrated that a simple 2D finite element model with cohesive elements can reproduce fairly well the plaque peeling global response. Future work will focus on understanding the main biological determinants of regional and inter-individual variations of the material parameters used in the model.

Finite Element Analysis Of Linear Elastic Torsion For Regular Polygons

This paper presents an explicit finite element integration scheme to compute the stiffness matrices for linear convex quadrilaterals. Finite element formulationals express stiffness matrices as double integrals of the products of global derivatives. These integrals can be shown to depend on triple products of the geometric properties matrix and the matrix of integrals containing the rational functions with polynomial numerators and linear denominator in bivariates as integrands over a 2-square. These integrals are computed explicitely by using symbolic mathematics capabilities of MATLAB. The proposed explicit finite element integration scheme can be applied to solve boundary value problems in continuum mechanics over convex polygonal domains.We have also developed an automatic all quadrilateral mesh generation technique for convex polygonal domain which provides the nodal coordinates and element connectivity.We have demonstrated the proposed explicit integration scheme to solve the Poisson Boundary Value Problem for a linear elastic torsion of a non-circular bar with cross sections having profiles of equilateral triangle, a square and regular polygons (pentagon(5-gon)to icosagon(20gon)) which are inscribed in a circle of unit radius. Monotonic convergence from below is observed with known analytical solutions for the Prandtl stress function and torsional constant .We have shown the solutions in Tables which list both the FEM and exact solutions. The graphical solutions of contour level curves and the corresponding finite element meshes are also displayed.

A simple procedure to improve the explicit integration of Cam-Clay models

A simple procedure is proposed to reduce the error in the calculation of the stresses when simulating stress paths applying explicit stress integration schemes in Cam-Clay models with an associated flow rule. The procedure consists of defining the value of the preconsolidation stress (the hardening parameter of a Cam-Clay model) so that the drift of the yield surface is zero at each calculation step. The results demonstrate the efficiency of the proposed procedure, especially along softening paths. The method can easily be implemented in existing explicit integration modules, which facilitates its practical application.

Finite Element Solution of Poisson Equation over Polygonal Domains using an Explicit Integration Scheme and a novel Auto Mesh Generation Technique

Finite Element Solution of Poisson Equation over Polygonal Domains using an Explicit Integration Scheme and a novel Auto Mesh Generation Technique

Explicit stress integration with streamlined drift reduction

The paper proposes an efficient method of drift correction in explicit stress integration schemes. The new method does not require significant changes to existing implementations and may, in fact, be regarded as a streamlining modification to standard drift correction schemes which may be used in tandem.