User-defined Element Subroutine Research Articles

A multi-mechanism model for cutting simulation: A Ginzburg-Landau type phase gradient and numerical implementations

Based on the concept of generalized stresses we developed a multi-mechanism model for cutting simulations, where the austenite phase fraction is treated as an extra degree of freedom and its first gradient is involved. In this work we show a new aspect on the phase gradient according to Ginzburg-Landau equation, whose derivation is based on the definition of the free energy being a gradient part and a potential part. In a further part of this work we show some numerical aspects for implementation of the bulk model. We formulate the strong and weak formulations of the model and build the finite element matrix using the isoparametric concept for quadrilateral elements. After that we introduce the integration scheme and the local iteration. To this end, the model is implemented as a user-defined element subroutine for explicit (VUEL) and linked to the FE-program ABAQUS for investigating cutting simulations. At the end, the visualisation with ABAQUS/Viewer is introduced, which is not supported for user-defined element.

Time-domain PML formulation for modeling viscoelastic waves with Rayleigh-type damping in an unbounded domain: Theory and application in ABAQUS

The Perfectly Matched Layer (PML) method is a powerful approach to absorb outgoing waves from a finite computational domain in various media, such as elastic, poroelastic, anisotropic, and viscoelastic, by means of layers of artificial material placed at the finite domain boundaries. However, its use in most finite-element method (FEM) codes, which take into account viscous damping by employing only the Rayleigh and Lindsday damping formulation, is inadequate. This paper introduces a viscoelastic Perfectly Matched Layer (PML) formulation with Rayleigh-type damping for finite-element time-domain analyses. The PML formulations in the frequency- and time-domain are derived using a two-parameter complex coordinate stretching function. The displacement field is the only unknown variable in the formulation, so that the approach can be readily implemented in general finite-element codes. The weak form formulation in the time-domain is implemented in ABAQUS/Standard by merging it with a user-defined element (UEL) subroutine in Fortran90. The UEL is developed for 2D plane-strain (PE4ML) and plane-stress (PS4ML) four-node, linear, isoparametric, quadrilateral elements. The Hilber-Hughes-Taylor implicit time integration scheme is used to evaluate the unknown displacements, velocities, and accelerations. The validity and efficiency of the viscoelastic PML formulation and the UEL subroutine are examined with two numerical examples, namely a single-layer and a multi-layered soil profile with different damping ratios and properties. The results also highlight the poor performance of elastic PML layers, when they are placed at the boundaries of a viscoelastic interior domain, because, as the damping ratio increases, the reflection at the interface of the interior domain and the elastic PML domain increases. Long-time stability of the model is also examined, and no instabilities are observed.

Point-wise evaluation of the growth driving direction for arbitrarily shaped delamination fronts using cohesive elements

Abstract The identification of the delamination propagation direction in three-dimensional structures with arbitrarily shaped fronts is needed in many applications. In the cohesive element framework, the propagation direction may be computed as the normal direction to a numerical damage isoline. The damage isoline tracking requires to exchange information between neighboring elements, thus post-processing global data, which is computationally expensive. This work presents a novel approach for the evaluation of the growth driving direction, only using local element information. The method can be directly implemented in a user-defined element subroutine and be evaluated at the execution time of the analysis. The presented formulation and its implementation in the commercial Finite Element code Abaqus is validated by comparison to the damage isoline shape rendering using global information.

A Finite Element Implementation of a Fully Coupled Mechanical–Chemical Theory

A finite element implementation with UEL user-defined element (UEL) subroutines in ABAQUS for fully coupled mechanical–chemical processes, which accounts for deformation, mass diffusion, and chemical reactions based on irreversible thermodynamics, is presented. The finite element formulations are deduced from the Gibbs function variational principle. To demonstrate the robustness of the numerical implementation, one- and two-dimensional numerical simulations with different boundary conditions are conducted. The results present the validity and capability of the UEL subroutines and the coupled theory, and show the interaction among deformation, mass diffusion and chemical reaction. This work provides a valuable tool to the researchers for the study of coupled problems.

A finite element method for light activated shape‐memory polymers

SummaryShape‐memory polymers (SMPs) belong to a class of smart materials that have shown promise for a wide range of applications. They are characterized by their ability to maintain a temporary deformed shape and return to an original parent permanent shape. In this paper, we consider the coupled photomechanical behavior of light activated shape‐memory polymers (LASMPs), focusing on the numerical aspects for finite element simulations at the engineering scale. The photomechanical continuum framework is summarized, and some specific constitutive equations for LASMPs are described. Numerical implementation of the multiphysics governing partial differential equations takes the form of a user defined element subroutine within the commercial software package ABAQUS. We verify our two‐dimensional and three‐dimensional finite element procedure for multiple analytically tractable cases. To show the robustness of the numerical implementation, simulations are performed under various geometries and complex photomechanical loading. Copyright © 2016 John Wiley & Sons, Ltd.

The role of non‐coaxiality in the simulation of strain localization based on classical and Cosserat continua

SummaryIt is normally accepted that materials inside the shear band undergo severe rotation of the principal stress direction, which causes non‐coaxiality between the principal stress and principal plastic strain rate. However, classical plasticity flow theory implicitly assumes that the principal stress and the principal plastic strain rate are coaxial; thus, it may not correctly predict the onset of the shear band. In addition, classical continuum does not contain any internal length scales; as a result, it cannot provide a reasonable shear band thickness. In this study, the original vertex non‐coaxial plastic model based on the classical continuum is extended to the Cosserat continuum. The corresponding codes are implemented via the interface of the user defined element subroutine in ABAQUS. Through a simple shear test, the effectiveness of the user's codes is verified. Through a uniaxial compression test, the influence of non‐coaxiality on the onset, the orientation, and the thickness of the shear band is investigated. Results show that the onset of the shear localization is delayed, and the thickness of the shear band is widened when the non‐coaxial degree increases, while the orientation of the shear band is little affected by the non‐coaxial degree. In addition, it is found that the non‐coaxiality can weaken the micro‐polar effect to some extent; nonetheless, the Cosserat non‐coaxial model still has its advantage over the classical non‐coaxial model in capturing the pre‐bifurcation as well as the post‐bifurcation behaviors of strain localization. Copyright © 2016 John Wiley & Sons, Ltd.

An efficient FE–SBFE coupled method for mesoscale cohesive fracture modelling of concrete

This study develops a method coupling the finite element method (FEM) and the scaled boundary finite element method (SBFEM) for efficient meso-scale fracture modelling of concrete for the first time. In this method, the aggregates are modelled by SBFE polygons with boundaries discretised only, while the mortar matrix is modelled by conventional finite elements. The semi-analytical SBFEM is implemented in ABAQUS by a user-defined element subroutine for the first time. Nonlinear cohesive interface elements with normal and shear traction-separation constitutive laws are pre-inserted within the mortar and on the aggregate-mortar interfaces to simulate potential cracks. Various meso-structures generated from both random aggregates and X-ray computed tomography images are modelled. The results demonstrate that the coupled method leads to considerable reductions in degrees of freedom and computational time against the conventional FEM, and these reductions become more significant when the aggregate volume fraction increases. The modelled crack paths and load-carrying capacities of a three-point bending beam and an L-shaped panel are in excellent agreement with the experimental data.

A finite element implementation of a coupled diffusion-deformation theory for elastomeric gels

The theory of Chester and Anand (2011) for fluid diffusion and large deformations of elastomeric gels is implemented as a user-defined element (UEL) subroutine in the commercial finite element software package ABAQUS. A specialized form of the constitutive equations and the governing partial differential equations of the theory are summarized, and the numerical implementation is described in detail. To demonstrate the robustness of the numerical implementation a few illustrative numerical simulation examples for axisymmetric, plane strain, and three-dimensional geometries are shown. For educational purposes, and also to facilitate the numerical implementation of other coupled multiphysics theories, the source code for the UEL is provided as an online supplement to this paper.

Cohesive Zone Model Based Numerical Analysis of Steel-Concrete Composite Structure Push-Out Tests

Push-out tests were widely used to determine the shear bearing capacity and shear stiffness of shear connectors in steel-concrete composite structures. The finite element method was one efficient alternative to push-out testing. This paper focused on a simulation analysis of the interface between concrete slabs and steel girder flanges as well as the interface of the shear connectors and the surrounding concrete. A cohesive zone model was used to simulate the tangential sliding and normal separation of the interfaces. Then, a zero-thickness cohesive element was implemented via the user-defined element subroutine UEL in the software ABAQUS, and a multiple broken line mode was used to define the constitutive relations of the cohesive zone. A three-dimensional numerical analysis model was established for push-out testing to analyze the load-displacement curves of the push-out test process, interface relative displacement, and interface stress distribution. This method was found to accurately calculate the shear capacity and shear stiffness of shear connectors. The numerical results showed that the multiple broken lines mode cohesive zone model could describe the nonlinear mechanical behavior of the interface between steel and concrete and that a discontinuous deformation numerical simulation could be implemented.

Effects of grain boundary heterogeneities on creep fracture studied by rate-dependent cohesive model

To simulate creep fracture of ceramics at high temperatures, we have developed a user-defined element (UEL) subroutine and a user-defined material properties (UMAT) subroutine to analyze the rate-dependent cohesive behavior of the grain boundary and the creep deformation of the grain, respectively, and implemented them in ABAQUS. The model presented here accounts for grain boundary sliding, nucleation of grain boundary cavities, their growth by diffusion and creep, and link up of microcracks to form macrocracks. Numerical examples demonstrate that the rate-dependent cohesive element has a better numerical stability than the existing work and the entire cavity growth process can be simulated. Also, in the presence of grain boundary heterogeneities, stress distribution becomes localized which, in turn, induces localized grain boundary cavitation and promotes creep fracture.

Numerical Investigation on Galloping of Iced Quad Bundle Conductors

The aerodynamic coefficients of each subconductor in an iced quad bundle conductor covered with crescent-shaped and sector-shaped cross-sections were determined by the wind tunnel test. A cable element with torsional degree of freedom used to simulate the iced conductor is obtained in ABAQUS software by releasing the two bending degrees of freedom and setting the material to be incompressible. The aerodynamic loads varying with the angle of attack during moving of the bundle conductor are applied on the cable elements used to discretize the iced subconductors through the user-defined element subroutine UEL in ABAQUS. The numerical method verified by two examples is employed to investigate galloping of iced quad bundle conductors at different wind speed, initial angle of attack, ice thickness, ice shape, and span length, and the results reflect the influences of these parameters on the galloping behavior of the quad bundle conductor, which is important for the development of anti-galloping technology.

Computational implementation of the PPR potential-based cohesive model in ABAQUS: Educational perspective

A potential-based cohesive zone model, so called the PPR model, is implemented in a commercial software, e.g. ABAQUS, as a user-defined element (UEL) subroutine. The intrinsic cohesive zone modeling approach is employed because it can be formulated within the standard finite element framework. The implementation procedure for a two-dimensional linear cohesive element and the algorithm for the PPR potential-based model are presented in-detail. The source code of the UEL subroutine is provided in Appendix for educational purposes. Three computational examples are investigated to verify the PPR model and its implementation. The computational results of the model agree well with the analytical solutions.

A three-dimensional edge-crack finite element for fracture mechanics applications

A three-dimensional extension of a previously published two-dimensional cracked finite element [Potirniche, G.P., Hearndon, J., Daniewicz, S.R., Parker, D., Cuevas, P., Wang, P.T., Horstemeyer, M.F., 2008. A two-dimensional damaged finite element for fracture applications. Engineering Fracture Mechanics 17(13), 3895–3908] is presented in this paper. The new element has an embedded edge crack, and was developed to model damage in three-dimensional structures using the finite element method. The element simulates the presence of a crack without physically inserting it in the three-dimensional finite element mesh. The method involves the derivation of a modified stiffness matrix that accounts for the change in the element flexibility due to the crack presence. The cracked element was analytically formulated and implemented in the finite element code ABAQUS Standard as a User-defined Element (UEL) subroutine. Tests of various cracked beam configurations were used to estimate the accuracy of the element by comparing two models: one with a UEL and another with an embedded edge crack. Beam deflections and natural frequencies were analyzed and compared for the two models. The results indicate that the new element has a good potential in modeling cracks in three-dimensional parts. Moreover, the method using this UEL computes the global response of damaged structures, in which cracks can be placed at various locations and in an unlimited number.

Fiber Heat Transfer Element for Modeling the Thermal Response of Structures in Fire

This paper introduces a novel type of heat transfer finite element that can be used to model the three-dimensional thermal response of structural beams and columns subjected to elevated temperatures associated with fire. The element is a three-node heat transfer element that uses a fiber discretization to account for both transverse and longitudinal temperature variations in a structural member. This fiber heat transfer element is purposely formulated to be compatible with any fiber beam-column finite element in a sequentially coupled thermal-mechanical analysis of a structural frame subjected to fire. The element is implemented in ABAQUS using a user-defined element subroutine. To demonstrate the capabilities of the fiber heat transfer element, analyses are performed on members with various types of thermal boundary conditions. Results indicate that the fiber heat transfer element offers excellent accuracy with minimal computational expense, making the fiber heat transfer element a valuable tool for modeling the behavior of frame structures in fire.

Mixed-Mode Dynamic Crack Growth in a Functionally Graded Particulate Composite: Experimental Measurements and Finite Element Simulations

Mixed-mode dynamic crack growth behavior in a compositionally graded particle filled polymer is studied experimentally and computationally. Beams with single edge cracks initially aligned in the direction of the compositional gradient and subjected to one-point eccentric impact loading are examined. Optical interferometry along with high-speed photography is used to measure surface deformations around the crack tip. Two configurations, one with a crack on the stiffer side of a graded sheet and the second with a crack on the compliant side, are tested. The observed crack paths are distinctly different for these two configurations. Furthermore, the crack speed and stress intensity factor variations between the two configurations show significant differences. The optical measurements are examined with the aid of crack-tip fields, which incorporate local elastic modulus variations. To understand the role of material gradation on the observed crack paths, finite element models with cohesive elements are developed. A user-defined element subroutine for cohesive elements based on a bilinear traction-separation law is developed and implemented in a structural analysis environment. The necessary spatial variation of material properties is introduced into the continuum elements by first performing a thermal analysis and then by prescribing material properties as temperature dependent quantities. The simulated crack paths and crack speeds are found to be in qualitative agreement with the observed ones. The simulations also reveal differences in the energy dissipation in the two functionally graded material (FGM) cases. T-stresses and hence the crack-tip constraint are significantly different. Prior to crack initiation, larger negative T-stresses near the crack tip are seen when the crack is situated on the compliant side of the FGM.

3D FEA of Size Effects in Deformation of Thin Metallic Films

AbstractThe purpose of this work is to analyze size effects in the deformation occurring during nanoindentation‐tests of thin metallic films on ceramic substrates. It is well known that classical phenomenological theories of plasticity are hardly applicable in cases of very small dimensions of a body [1]. Thus, the dependency of the mechanical behavior of thin films on the thickness can not be studied in the framework of classical theories. In order to simulate numerically the deformation, a specific material model has been chosen which is able to account for size effects. It bases on the theory of ”Mechanism Strain Gradient” (MSG) plasticity [2] in conjunction with the deformation theory of plasticity. The material model has been implemented via the user defined element subroutine (UEL) in the commercial FE code ABAQUS/Standard as a ten‐node tetrahedron‐element. With the developed subroutine the deformation of thin copper films on Si substrates during nanoindentation‐tests has been simulated. Different material models of the indentor (rigid and elastic) as well as different friction conditions between the film and the pyramidal indentor were tested. Furthermore, the influence of an additional oxide layer on the films surface has been analysed. In order to verify the numerical investigations, results from nanoindentation experiments have been used for comparison [4]. The FE simulations for different thicknesses in the range of 100‐600nm showed a very good agreement with the experiments. In particular, the size dependency of the force‐displacement curves, calculated by using the developed subroutine, is in rather good agreement with experiments. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Multiaxial softening hinge model for tubular vehicle roll-over protective structures

The purpose of the work described in this paper is to provide a computational tool for the design of roll-over protective structures (ROPS) comprised of thin-walled rectangular tubes. This tool simulates the multi-stage, regulatory quasi-static loading test (SAE Standard, SAE J1040 APR88) that new designs must pass. These tests are claimed to be indications of the performance of a ROPS under real (dynamic) roll-over conditions. The collapse of the framework involves large, three-dimensional deformation, which results mainly from large rotations in each member due to bending and torsion. To establish constitutive relationships for a framework model, biaxial bending collapse behaviour of thin-walled rectangular tubes was investigated using a kinematic approach to generate the bending interaction curves. The interaction between bending and torsion was examined separately using extensive finite element analyses of cantilevers modelled by the commercial finite element code ABAQUS. Approximate constitutive relationships were then formulated for a ‘hinge super-element’ to be implemented via the user-defined element subroutine UEL in ABAQUS. The hinge element consists of two nodes separated by a small distance. Each node has six degrees of freedom and the components of stiffness at each node are initially set to sufficiently large values to provide rigid response in the pre-collapse stage. When the collapse criterion is satisfied for the first time, the hinge element is switched to ‘softening’ hinge response and thereafter follows the local softening behaviour of a closed-section tube by modifying the stiffness of the three rotational components according to the constitutive relationships. To test the validity of the hinge model, the response of a simple, scaled ROPS to a simulated prescribed regulatory test load history (SAE Standard) was compared with the results from the analysis of an equivalent shell element model. Good agreement is demonstrated between the two models.