Abaqus Implementation Research Articles

Time Domain Implementation of Transmitting Boundaries in ABAQUS for Discrete Soil-structure Interaction Systems

Soil-structure-interaction (SSI) analyses are essential to evaluate the seismic performance of important structures before finalizing their structural design. SSI under seismic condition involves much more complex interaction with soil compared to the dynamic loads having source on the structure. Seismic SSI analysis requires due consideration of site-specific and structure-specific properties to estimate the actual ground motion (scattered motion) experienced at the base of the structure, and subsequently the effects of the scattered motion on the structure. Most challenging aspect of seismic SSI analysis is to implement transmitting boundaries that absorb the artificial reflections of stress waves at the truncated interface of the finite and infinite domains, while allowing the seismic waves to enter the finite domain. In this paper, the time domain implementation of seismic analysis of a soil-structure system is presented using classical discrete models of structure and interactive force boundary conditions for soil. These models represent typical SSI systems- a single Degree of Freedom (DOF) of a spherical cavity with mass attached to its wall, a two DOF system consisting of a mass attached by a nonlinear spring to a semi-infinite rod on elastic foundation, and a three DOF system with additional DOFs for modelling the structural stiffness and damping. The convolution integral representing the force boundary condition on the truncated interface, is evaluated interactively using UAMP user-subroutine in ABAQUS and applied as concentrated forces at the interface (truncated interface) nodes of the bounded domain or generalized-structure domain. The verification problems presented in the paper show the satisfactory performance of the developed MATLAB code and ABAQUS implementation with FORTRAN user-subroutines. The classical phenomena associated with the dynamic soil-structure systems are discussed through the present work.

An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation

Brittle and ductile dynamic fracture in solids is a complex mechanical phenomenon which attracted much attention from both engineers and scientists due to its technological interests. Modeling cracks in dynamic cases based on a discontinuous description is difficult because it needs additional criteria for branching and widening. Due to the very short time scales and the spatial complexity of the dynamic problem, its experimental analysis is still very difficult. Therefore, researchers still have to rely on numerical simulations to find a deeper explanation for many observed phenomena. This study is set out to investigate the effect of plasticity on dynamic fracture propagation. On the other hand, the diffuse phase-field formulation makes it possible to initiate, propagate, arrest or even branch cracks while satisfying the basic principles of thermodynamics. An implicit, staggered elastoplastic version of the phase-field approach was implemented in the commercial finite element code Abaqus through the UEL option. By means of simple examples we show that localized ductile deformations first increase both resistance and toughness. Then, after a maximum value, the resistance starts to decrease with a significant increment in energy dissipation. By favoring shear deformation over tensile failure the fracture pattern changes. First the branching disappears, then the crack propagation angle changes and becomes a shear band. Finally, we observed the increment of the instantaneous dynamic stress intensity factor during the acceleration stage of the crack without introducing a rate dependent critical fracture energy. We explained this phenomenon with the increasing roughness of the fracture surface.

ABAQUS IMPLEMENTATION OF A COROTATIONAL PIEZOELECTRIC 3-NODE SHELL ELEMENT WITH DRILLING DEGREE OF FREEDOM

Integration of classical, passive structures and active elements based on multi-functional materials resulted in a novel structural concept denoted as active structures. The new structural systems are characterized by self-sensing and actuation. Coupling the two distinctive features by means of a controller enables a number of exquisite functionalities such as vibration suppression, noise attenuation, shape control, structural health monitoring, etc. Reliable, accurate and highly efficient modeling tools are an important ingredient of the active structure design. This paper addresses the Abaqus implementation of a recently developed piezoelectric 3-node shell element. The element uses co-rotational formulation to cover geometric nonlinearities. Special techniques are used to address the issues originating from low-order interpolation functions. The discrete shear gap is used to resolve the shear locking, while the assumed natural deviatoric strain technique improves the membrane behavior. Examples are computed in Abaqus upon implementation of the developed element.

Phase field fracture in elasto-plastic solids: Abaqus implementation and case studies

Phase field modelling for fracture has been extended from elastic solids to elasto-plastic solids. In this study, we present the implementation procedures of a staggered scheme for phase field fracture of elasto-plastic solids in commercial finite element software Abaqus using subroutines UEL and UMAT. The UMAT is written for the constitutive behaviour of elasto-plastic solids, while the UEL is written for the phase field fracture. The phase field and displacement field are solved separately using the Newton-Raphson iteration method. In each iteration, one field is computed by freezing the other field at the last loading increment. A number of benchmark examples are tested from one single element up to 3D problems. The correctness of the staggered scheme is verified analytically in terms of the stress-strain curve and the evolution of the phase field in the one single element example. In the 2D and 3D problems, the fracture behaviour of elasto-plastic solids can be reproduced in terms of reaction force curve and crack propagation, which exhibit good agreement with the experimental observations and numerical results in literature. Not only can the proposed implementation help attract more academic researchers, but also engineering practitioners to take the advantages of phase field modelling for fracture in elasto-plastic solids. The Abaqus subroutine codes can be downloaded online from Mendeley data repository linked to this work (The link is provided in Supplementary material).

Flutter Suppression for Damaged High-Aspect-Ratio Wings: Implementation in Abaqus

An Abaqus implementation of a flutter suppression control system for a joined three-dimensional (3D)/one-dimensional (1D) finite element model of damaged high-aspect-ratio wings is presented. By doing so, one can exploit the modeling, solution, and postprocessing capabilities of Abaqus in aeroservoelastic analysis and design. To benefit from the computational efficiency of 1D modeling and the accuracy of 3D finite element analysis, a small area close to the boundary is modeled as a full 3D continuum and the rest of the beam is modeled as a 1D beam model. A geometrically exact beam model is then coupled with a two-dimensional finite-state unsteady aerodynamic theory and has been coded into a nonlinear UEL for Abaqus. A test case is presented in which the reduced-order model is exploited to design a flutter suppression control system in a linear-quadratic-Gaussian framework. The controller is also coded into Abaqus as a UAMP user subroutine and its performance is evaluated through nonlinear time simulation.

An XFEM implementation in Abaqus to model intersections between fractures in porous rocks

This paper presents the key aspects of the implementation of an XFEM element for hydraulic fracturing in porous medium in Abaqus. The implemented element has the capability of intersecting fractures inside an element and includes coupled hydro-mechanical behaviour and fluid exchange between fracture and the porous medium. The algorithm has three main steps: fracture geometry pre-processing, local matrix assembling, and post-processing. The first computes all the geometrical parameters of the XFEM. The second computes the jacobian and the right-hand-side matrices for each mesh element. The third checks for fracture propagation and the direction and length for propagating segments. Considering that Abaqus is a commercial software, adaptations were necessary, such as an algorithm for consideration of in-situ stress states, positioning of the degrees of freedom and numerical integration. A discussion on the limitations of the tool and of the use of the User Subroutine feature closes the implementation description. Then, we present the consolidation of a multi-fractured medium, comparing the results with a model with interface elements. In a second example, we simulate an injection in a fracture that propagates and intersects a naturally fractured model. The simulations show that the capabilities of Abaqus were considerably extended with this implementation.

A comparative study and ABAQUS implementation of conventional and localizing gradient enhanced damage models

The conventional gradient models based on continuum damage mechanics are found to exhibit inconsistencies in terms of damage initiation and growth. With the decrease in non-local interactions, localizing gradient damage model describes the failure phenomena in a physically meaningful manner. In the present study, both conventional and localizing gradient damage models are implemented in the commercial finite element package ABAQUS through user subroutines. The motivation behind the implementation is the popularity and computational efficiency of the ABAQUS. It is demonstrated through various numerical examples that the localizing gradient damage model is more effective and efficient than the conventional gradient damage model. A detailed stress oscillation study is carried out to provide more insight on the localizing gradient damage model. A new approach is proposed for an implicit representation of initial notch/crack in the gradient damage models. The enhanced capability of the present implementation is demonstrated by solving the problems with complicated geometry under complex loading. A detailed description of the working of the user subroutines (UEL and UMAT) and other associated activities is elucidated. The source codes of the present implementation are provided for better understanding and further development.

Finite element method of bond-based peridynamics and its ABAQUS implementation

Based on the principle of minimum potential energy, the peridynamic finite element method (PDFEM) is presented, in which the peridynamic (PD) multi-bond element stiffness matrix and the unbalanced force vector are established. An adjusting technique of PD element stiffness matrix is introduced to realize sharing of physical information at joint points between PD elements and classical continuum mechanics (CCM) elements in a unified finite element framework. Applying PDFEM, a new PD element type can be developed through UEL subroutine in ABAQUS to model fracture and damage in the light of PD theory and couple PD grids with CCM meshes. The numerical examples illustrate the availability of PDFEM in ABAQUS, which opens up the prospect of application of peridynamics to practical engineering analysis.

An iteration scheme for phase field model for cohesive fracture and its implementation in Abaqus

Recently, phase field modelling of fracture has gained much attentions because of its benefits in predicting cracks initiation and propagation without any ad-hoc criterion. In the model cracks are smeared into the surrounding areas by introducing an auxiliary crack phase field which should be solved either by iteration or using sufficiently small loading increment, and this makes the method be computationally demanding. The introduction of other complex models e.g. cohesive zone model results in nonlinear damage sub-problems which may further increase the number of iteration steps. In this study, an improved staggered iteration scheme by which the nonlinear sub-problems are solved by a one-pass procedure is proposed. Such that the computational costs can be reduced and the stability of iteration can be improved. In particular, a unified phase field model which integrates varies cohesive relationships is investigated. The phase field model as well as the iteration scheme are implemented through Abaqus subroutine UEL (user defined element). The present study is validated through comparing both of crack propagation path and load-displacement curve with existing results. Moreover, comparisons on total iteration steps and the elapsed total computational time are made between the proposed iteration scheme and the existing scheme, and the results demonstrate that the proposed iteration scheme is very suitable for the considered problem.

2D and 3D Abaqus implementation of a robust staggered phase-field solution for modeling brittle fracture

In order to model brittle fracture, we have implemented a two and three dimensional phase-field method in the commercial finite element code Abaqus/Standard. The method is based on the rate-independent variational principle of diffuse fracture. The phase-field is a scalar variable between 0 and 1 which connects broken and unbroken regions. If its value reaches one the material is fully broken, thus both its stiffness and stress are reduced to zero. The elastic displacement and the fracture problem are decoupled and solved separately as a staggered solution.The approach does not need predefined cracks and it can simulate curvilinear fracture paths, branching and even crack coalescence. Several examples are provided to explain the advantages and disadvantages of the method. The provided source codes and the tutorials make it easy for practicing engineers and scientists to model diffuse crack propagation in a familiar computational environment.

On strength analysis of highly porous materials within the framework of the micropolar elasticity

We discuss the finite element approach to modelling of static deformations of porous materials such as foams, beam lattices, and others within the linear micropolar elasticity. It is known that the micropolar elasticity may be used for microstructured solids and fluids since it can forecast size-effect near geometrical singularities such as holes, notches, small contact areas of two solids. Within the micropolar elasticity the translational and rotational interactions of the material particles can be taken into account. Here we present the recent developments in the theory of finite elements calculations for micropolar solids in order to capture the stress behaviour in the vicinity of geometric singularities such as holes, notches, imperfections or contact areas. The fundamental equations of the micropolar continuum are presented. The FEM implementation in micropolar elasticity is given. The new 8-node hybrid micropolar isoparametric element and its implementation in ABAQUS are introduced. The solutions of few 3D benchmark problems of the micropolar elasticity are given. Among them are analysis of stresses and couple stresses near notches and holes, contact problem of parabolic stamp and half space. The main attention is paid to modelling of interaction between a biodegradable porous implant and a trabecular bone. Comparison of classical and micropolar solutions is carefully discussed. Comparison of classical and micropolar solutions is discussed. Numerical tests have shown that couple stress appears almost in the vicinity of geometrical singularities. It is shown that micropolar elasticity allows to obtain better results for domains with microstructures and singularities than classical theory of elasticity.

New methodology for calculating damage variables evolution in Plastic Damage Model for RC structures

The behavior of reinforced concrete (RC) structures under severe demands, as strong ground motions, is highly complex; this is mainly due to joint operation of concrete and steel, with several coupled failure modes. Furthermore, given the increasing awareness and concern for the important seismic worldwide risk, new developments have arisen in earthquake engineering. Nonetheless, simplified numerical models are widely used (given their moderate computational cost), and many developments rely mainly on them. The authors have started a long-term research whose final objective is to provide, by using advanced numerical models, solid basis for these developments. Those models are based on continuum mechanics, and consider Plastic Damage Model to simulate concrete behavior. Within this context, this paper presents a new methodology to calculate damage variables evolution; the proposed approach is based in the Lubliner/Lee/Fenves formulation and provides closed-form expressions of the compressive and tensile damage variables in terms of the corresponding strains. This methodology does not require calibration with experimental results and incorporates a strategy to avoid mesh-sensitivity. A particular algorithm, suitable for implementation in Abaqus, is described. Mesh-insensitivity is validated in a simple tension example. Accuracy and reliability are verified by simulating a cyclic experiment on a plain concrete specimen. Two laboratory experiments consisting in pushing until failure two 2-D RC frames are simulated with the proposed approach to investigate its ability to reproduce actual monotonic behavior of RC structures; the obtained results are also compared with the aforementioned simplified models that are commonly employed in earthquake engineering.

Abaqus implementation of monolithic and staggered schemes for quasi-static and dynamic fracture phase-field model

The phase-field model for fractures regularizes crack diffusion using a length-scale parameter. The displacement fields and the phase-field in a coupled system can be solved as either fully coupled “monolithic” or sequentially coupled “staggered” fields. In this paper, we employ the commercial finite-element software Abaqus to solve the monolithic and staggered phase-field models using a user-defined element (UEL) and user-defined material (UMAT/VUMAT) subroutines in two- and three-dimensions for quasi-static and dynamic fractures. We present the implementation procedures for both strategies, and make a detailed comparison using different applications. By comparing the phase-field model as a diffusive crack model and the extended finite-element method (XFEM) as a discrete crack model, we obtain good agreement. We investigate the influence of the model-regularization parameter based on experimental results. We adopt the thread-parallel execution and mutexes of Abaqus solvers.

Modeling Dynamic Recrystallization in Polycrystalline Materials via Probability Distribution Functions

AbstractA model of dynamic recrystallization in polycrystalline materials is investigated in this work. Within this model a probability distribution function representing a polycrystalline aggregate is introduced. This function characterizes the state of individual grains by grain size and dislocation density. By specifying free energy and dissipation within the polycrystalline aggregate an evolution equation for the probability density function is derived via a thermodynamic extremum principle. For distribution functions describing a state of dynamic equilibrium we obtain a partial differential equation in parameter space. To facilitate numerical treatment of this equation, the equation is further modified by introducing an appropriately rescaled variable. In this the source term is considered to account for nucleation of grains. Then the differential equation is solved by an implicit time‐integration scheme based on a marching algorithm [2]. From the obtained distribution function macroscopic quantities like average strain and stress can be calculated. Numerical results of the theory are subsequently presented. The model is compared to an existing implementation in Abaqus as well. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Abaqus implementation of phase-field model for brittle fracture

A phase-field model for brittle fracture is implemented in the commercial finite element software Abaqus by means of UEL and UMAT subroutines. The phase-field method considerably reduces the implementation complexity for fracture problems as it removes the need for numerical tracking of discontinuities in the displacement field that are characteristic of discrete crack methods. This is accomplished by replacing the sharp discontinuities with a scalar damage phase-field representing the diffuse crack topology wherein the amount of diffusion is controlled by a regularization parameter. The nonlinear coupled system consisting of the linear momentum equation and a diffusion-type equation governing the phase-field evolution is solved simultaneously via a Newton–Raphson approach. The implemented crack propagation model does not require predefined paths for crack growth or user-defined surfaces to simulate crack debonding. Post-processing of simulation results is performed via an additional subroutine implemented in the visualization module.

Abaqus implementation of extended finite element method using a level set representation for three-dimensional fatigue crack growth and life predictions

A three-dimensional extended finite element method (X-FEM) coupled with a narrow band fast marching method (FMM) is developed and implemented in the Abaqus finite element package for curvilinear fatigue crack growth and life prediction analysis of metallic structures. Given the level set representation of arbitrary crack geometry, the narrow band FMM provides an efficient way to update the level set values of its evolving crack front. In order to capture the plasticity induced crack closure effect, an element partition and state recovery algorithm for dynamically allocated Gauss points is adopted for efficient integration of historical state variables in the near-tip plastic zone. An element-based penalty approach is also developed to model crack closure and friction. The proposed technique allows arbitrary insertion of initial cracks, independent of a base 3D model, and allows non-self-similar crack growth pattern without conforming to the existing mesh or local remeshing. Several validation examples are presented to demonstrate the extraction of accurate stress intensity factors for both static and growing cracks. Fatigue life prediction of a flawed helicopter lift frame under the ASTERIX spectrum load is presented to demonstrate the analysis procedure and capabilities of the method.

Non-isothermal thermomechanical metallurgical model and its application to welding simulations

This paper presents a thermomechanical metallurgical macroscopic model for steels. The model is based on an existing model that is extended for non-isothermal behaviour in combination with phase transformations. The model and its numerical implementation in ABAQUS are described using vector notation for stress and strain tensors. Model parameters are presented for the dual phase steel DP600 and the structural steel S355. For DP600, thermomechanical model parameters, i.e. hardening and strain rate dependency, have been obtained by fitting temperature and strain rate dependent tensile tests. A metallurgical model was implemented using data obtained from phase field models for the austenite growth and continuous cooling transition diagrams for phase transformations from austenite to low temperature phases. The model is applied to welding simulations of DP600 overlap joints and S355 T joints. The final distortion is compared to experiments and it is shown that the model presented is able to reproduce the experimental results very well.

An Abaqus implementation of the extended finite element method

In this paper, we introduce an implementation of the extended finite element method for fracture problems within the finite element software ABAQUS TM. User subroutine ( UEL) in Abaqus is used to enable the incorporation of extended finite element capabilities. We provide details on the data input format together with the proposed user element subroutine, which constitutes the core of the finite element analysis; however, pre-processing tools that are necessary for an X-FEM implementation, but not directly related to Abaqus, are not provided. In addition to problems in linear elastic fracture mechanics, non-linear frictional contact analyses are also realized. Several numerical examples in fracture mechanics are presented to demonstrate the benefits of the proposed implementation.

Toward realization of computational homogenization in practice

AbstractWe present a computational homogenization approach for linear and non‐linear solid mechanics problems, which is fully compatible with conventional finite element code architecture. A seamless implementation in ABAQUS is presented including Python script, validation problems and a web‐link where script files, user‐defined subroutines and input files can be accessed. For linear problems, we demonstrate how to utilize ABAQUS existing facilities to develop analysis attributes required for solving a unit‐cell problem. For non‐linear problems, a Python script invoked by a coarse‐scale stress update procedure is introduced to carry out the scale bridging. The purpose of this paper is twofold: (i) to motivate practitioners to adopt the computational homogenization as an integral part of their analysis and design process; and (ii) to encourage commercial code vendors to seamlessly integrate the architectures proposed in their legacy codes. Copyright © 2007 John Wiley & Sons, Ltd.