User-defined Element Research Articles

Stochastic analysis of dynamic fracture of concrete using CT-image based mesoscale models with a rate-dependent phase field method

Concrete structures are commonly exposed to dynamic loads spanning a wide range of strain rates, and the inherent mesoscale heterogeneities complicate stochastic dynamic fracture mechanisms even more. This work develops a numerical framework using mesoscale concrete models based on micro computed tomography (CT) images to investigate such mechanisms with meaningful stochastic analyses. A rate-dependent phase field model is proposed to characterise the dynamic initiation and propagation of cracks by incorporating both micro-viscosity and macroscopic viscoelasticity, which is described by two standard Maxwell elements with different relaxation times to consider a wide range of strain rates. Moreover, the viscoelastic constitutive relation is formulated in the full strain space, which allows for a spectral decomposition of the strain tensor to determine the effective damage driving force, thus effectively addressing the issue of compressive fracture. A numerical implementation scheme is developed by combining user-defined element and material subroutines in ABAQUS/Explicit solver. Extensive Monte Carlo simulations of dynamic tension up to a strain rate of 200 s−1 are performed with statistical analyses. This work reveals the intricate dynamics associated with mesoscale heterogeneities and identifies the critical transition state at 20 s−1. The transition is characterised by changing modes of fracture patterns, stress wave propagation, and load-carrying capacities. A new TDIF–strain rate–standard deviation relation is also proposed and aligns well with the increasing dispersion of experimental data. The relationship between void content and tensile strength reflects the formation characteristics of crack networks, with the void content exhibiting a positive correlation with the TDIF from 20 s−1 to 100 s−1.

Phase field modeling for composite material failure

AbstractA computational framework of anisotropic phase field model is used to investigate the effects of effective critical energy release rate, interface property, and hole shape on the failure of composite material in this paper. This model is implemented in ABAQUS using a user‐defined element (UEL). First of all, the model is validated through a benchmark model. Second, the effective critical energy release rate is introduced, which can improve the accuracy of the simulation result. Then, the influence of strong and weak interfaces on the failure of composite material is studied. It can be found that the interface properties can change the evolution mode of crack and the final load–displacement response. Finally, the effect of hole shapes on the failure of the composite material is also explored, which shows that the bearing capacity of model can be improved by changing the shape of the hole.

An ANSYS user cohesive element for the modelling of fatigue initiation and propagation of delaminations in composite structures

A deeper understanding of delamination growth under fatigue loading in composite wind turbine blades is required. A new cohesive model for delamination fatigue initiation, which uses initiation S-N curve data to calculate the number of cycles to the introduction of delaminations, is developed and tailored to a state-of-the-art model for fatigue propagation. Both models are implemented in a novel user-defined cohesive element for ANSYS Mechanical APDL. In fatigue propagation-dominated test cases, including with multiple delaminations, the crack growth rate evolution is accurately predicted. In fatigue initiation-dominated cases, a satisfactory prediction is achieved, also showcasing the ability to model fatigue propagation after initiation.

Linear and Nonlinear Formulation of Phase Field Model with Generalized Polynomial Degradation Functions for Brittle Fractures

The classical phase field model has wide applications for brittle materials, but nonlinearity and inelasticity are found in its stress–strain curve. The degradation function in the classical phase field model makes it a linear formulation of phase field and computationally attractive, but stiffness reduction happens even at low strain. In this paper, generalized polynomial degradation functions are investigated to solve this problem. The first derivative of degradation function at zero phase is added as an extra constraint, which renders higher-order polynomial degradation function and nonlinear formulation of phase field. Compared with other degradation functions (like algebraic fraction function, exponential function, and trigonometric function), this polynomial degradation function enables phase in [0, 1] (should still avoid the first derivative of degradation function at zero phase to be 0), so there is no Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document} convergence problem. The good and meaningful finding is that, under the same fracture strength, the proposed phase field model has a larger length scale, which means larger element size and better computational efficiency. This proposed phase field model is implemented in LS-DYNA user-defined element and user-defined material and solved by the Newton–Raphson method. A tensile test shows that the first derivative of degradation function at zero phase does impact stress–strain curve. Mode I, mode II, and mixed-mode examples show the feasibility of the proposed phase field model in simulating brittle fracture.

An Efficient Seepage Element Containing Drainage Pipe

Drainage pipes are often positioned downstream of embankments to mitigate pore pressure, thereby reducing the risk of dam failure. Considering that the size of drainage pipes is much smaller than that of embankment dams, directly discretizing the drainage pipes will generate a huge number of elements. Therefore, this paper proposes a seepage element containing drainage pipes. In this element, the permeability of the drainage pipe is taken as the third type of permeable conductivity condition, and it is considered in the energy functional. The governing equations for the steady-state and the transient seepage element containing drainage pipe are derived using the variational principle, and the infiltration matrix, equivalent nodal seepage array, and water storage matrix of the seepage element containing drainage pipe are obtained. In conjunction with the user-defined element module UEL of ABAQUS 2016 software, the established seepage element containing drainage pipe is programmed. The accuracy and efficiency of the proposed seepage element containing drainage pipe are verified through seepage field simulations of three examples. Finally, the influence of the permeable conductivity of drainage pipes on the pressure reduction effect is investigated, providing a reference for the layout of drainage pipes in embankment defense systems.

Study on the fracture behavior in clayey geomaterials under moisture diffusion by phase field modeling

Clayey geomaterials are prone to cracking under changing moisture conditions, which substantially compromises their engineering properties. When moisture intrusion and boundary constraints act in tandem on geomaterials, the relevance of multi-physics field processes to complex cracking phenomena remains underexplored. To provide deeper insight into the effect of moisture transport on the cracking behavior of clayey geomaterials, a theoretical model for moisture-induced fracture is proposed. The model combines moisture diffusion, volume deformation dependent on moisture conditions, and phase field fracture, and is solved using the finite element method with a user-defined element subroutine. The developed subroutine is applied to simulate soil desiccation experiments and mudstone water absorption tests. The results reveal that moisture gradients induce non-uniform expansion or shrinkage within the clayey geomaterials. The neighboring geomaterial particles mutually constrain these deformations, resulting in an internal stress field that serves as the primary cause of cracking. Stability and sensitivity analyses validate the reliability of the numerical framework. The proposed model can effectively simulate crack initiation, extension, and convergence during humidification or desiccation processes in both two and three dimensions. This study charts a feasible path for numerical simulation and mechanical mechanism exploration of cracking behaviors in clayey geomaterials during water migration.

Numerical Simulation of Fracture Propagation during Temporary Plugging Staged Fracturing in Tight-Oil Horizontal Wells.

Fracture propagation with temporary plugging hydraulic fracturing in tight-oil reservoirs is simulated in this study. The research considers dynamic fluid redistribution, with stress differences among multiple fractures. The fracture morphology during temporary plugging staged fracturing (TPSF) is investigated by using a user-defined perforation element combined with a pore-pressure finite-element model. The precision of the integrated model is verified by using the standard finite-element approach. Then, case studies are presented to investigate the influence of cluster spacing, horizontal stress difference coefficients (SDC), injection rates, and barrier tensile strengths. The simulation results show that central cluster fractures are hampered by side-cluster fractures, while TPSF can alleviate the effect and lead to a more uniform propagation of all fractures. Stress interference weakens as cluster spacing increases, and propagation patterns are minimally influenced once spacing reaches 40 m. Higher injection rates can improve the injection pressure, enlarging fracture width, and potentially increasing the risk of fracture penetration. Barrier tensile strength and horizontal SDC can modify fracture geometries and determine the penetration behavior of multiple fractures.

Integration of brake block thermal equations within a railway vehicle multibody model: a multiphysics approach

ABSTRACT The paper shows the development of a finite-difference (FD) railway brake block thermal model and its integration within the multibody (MB) formalism of the Simpack commercial code. The block nodal temperatures are included among the dynamic states computed by the MB solver, through the definition of a user-defined force element, which determines the braking torque based on the applied brake cylinder pressure. The proposed approach overcomes the main limitations of existing detailed railway vehicle models, which solve the thermal and vehicle dynamics equations in different computational environments. Furthermore, the new strategy can thrust the development of models able to account for the coupling between the wheel and block thermal behaviour and the whole vehicle dynamics. Preliminary simulations of drag and stop braking operations of a reference European freight waggon prove that the proposed model is able to effectively consider the main heat fluxes and nonlinearities involved in tread braking operations.

Simulation of crack propagation in piping components using phase field approach

Understanding the fracture behaviour in pipelines transporting steam and other resources is vital for its longevity and structural integrity. The prediction of crack initiation and propagation, involving crack branching, and the nucleation of new cracks, etc. in fracture processes are challenging tasks. The phase field method (PFM), based on variational formulation, emerged as a competitive mathematical tool to address fracture mechanics problems. PFM does not require the presence of predefined cracks, handles the crack initiation and propagation within the same system. This feature provides an added advantage to PFM and overcomes the limitations of Griffith’s approach-based linear elastic fracture mechanics (LEFM). In the present work, simulation of the crack propagation in the piping components by employing phase field methodologies has been carried out. Two parameters namely; a phase field parameter (ϕ) that varies between 0 and 1 differentiating between broken and intact material, and a length scale parameter (l_0) that approximates the sharp crack into the diffused crack with exponential distribution are introduced in the mathematical modeling. Numerical modeling is solved using the staggered algorithm in three layered scheme defining the displacement field and phase field within a 3-D finite element framework and implemented in Abaqus via user-defined element (UEL) subroutine codes. PFM simulates the crack path and predicts the load-displacement response, which is validated with benchmark problems, and extended for piping components under monotonic loading. The proposed study accurately captures the crack growth behaviour as observed in experiments on SA312 Type 304LN stainless steel pipes and hence, demonstrated the robustness of the proposed formulation.

FINITE ELEMENT MODELLING AND ANALYSIS OF FREE VIBRATIONS OF AXIALLY FUNCTIONALY GRADED BEAMS WITH NON-UNIFORM CROSS-SECTIONS

The finite element package Abaqus is used for modeling and analysis of free vibrations of axially functional graded beams with non-uniform cross-sections. Considerable attention has been paid to this aspect of the geometry, as it has a significant effect on the behavior of the beam as a structural component. User-defined material model subroutines (UMAT) were developed in a unified way for one- and three-dimensional models of the specified beams to provide numerical implementation of functional material gradients within each finite element. UMAT procedures were programmed in FORTRAN in the MS Visual Studio environment and compiled with the main program package using the Intel Fortran Compiler. In the procedures, material heterogeneity was assigned to each material integration point of appropriate standard one- and three-dimensional finite elements, eliminating the need to design graded finite elements via user-defined element subroutine. Frequencies and mode shapes of free vibrations of one- and three-dimensional axially functional graded beams with non-uniform cross-sections were found using the Lanczos method in Abaqus. An analysis of the accuracy and effectiveness of the proposed modeling approach was carried out, comparing the obtained results with data known in the literature. The presented modeling technique based on user-defined material subroutines provides valuable opportunities for scientists and engineers engaged in the dynamic analysis of structural components made of functionally gradient materials and having variable geometry along the axial direction. Keywords: axially functionally graded beams; non-uniform cross-section beams; free vibrations; graded finite element; Abaqus user defined subroutines

A 3D cohesive‐frictional coupled interface model for mesoscale simulation of steel fibre‐reinforced concrete

AbstractA 3D mesoscale finite element modelling approach is developed for simulating complicated damage and fracture behaviour in steel fibre‐reinforced concrete (SFRC) with explicit modelling of fibre–matrix interfaces. In this approach, a new 3D four‐noded cohesive‐frictional coupled interface element is developed to model the nonlinear interfacial bond‐slip behaviour, supplemented by a kinematic multiple‐point‐constraint (kMPC) algorithm to simulate the wrapping effect of the mortar around the fibres. They are implemented as a user‐defined element (UEL) and a user‐defined MPC subroutine in ABAQUS, respectively. Three cohesive‐frictional constitutive relationships are proposed to describe the nonlinear bond‐slip behaviour of different fibre–matrix compositions. The new approach is validated by single fibre pullout tests, direct tensile tests and three‐point bending tests of SFRC specimens with randomly distributed fibres. The results show that the new approach is capable of effectively capturing typical failure mechanisms in SFRC, such as fibre yielding, matrix failure, and fibre–matrix debonding and slipping.

Development of an innovative three-dimensional vibration isolation bearing

This paper presented an innovative three-dimensional vibration isolation bearing (3D-VIB) to mitigate horizontal seismic action and rail-induced vertical vibration. The 3D-VIB was composed of a thick laminated rubber bearing acting as the vertical vibration isolation module and a friction pendulum acting as the horizontal seismic isolation module. The thick laminated rubber bearing was used as a part of the slider in the friction pendulum. The compression performance of 3D-VIB was decoupled from its shear performance by concentrating the compressive deformation into the thick rubber bearing while shear deformation occurred independently in the friction pendulum module. The bearing capacity, vertical and horizontal properties of a full-scale 3D-VIB specimen were tested. In the test, the ultimate bearing capacity of 3D-VIB was 7 times that of the design compressive load of normal service condition. The vertical stiffness of the specimen under seismic vibration and vertical rail-induced vibration were tested separately. It was found that the vertical stiffness of the specimen under rail-induced vibration was 1.55 times higher than the vertical stiffness under seismic vibration. The horizontal performance of the 3D-VIB was characterized by stable parallelogram-shaped hysteretic curves similar to that of the traditional friction pendulum system. A user-defined element was developed and incorporated into ABAQUS to simulate the mechanical behavior of the 3D-VIB under different loading conditions, and simulation results agreed with the test results. The responses of a steel structure equipped with the 3D-VIB, while subjected to earthquake ground motions and rail-induced vibrations, respectively, were analyzed and compared with the non-isolated one. The analysis results suggested that with the installation of the 3D-VIB, the maximum inter-story drift ratio of the structure under maximum considered earthquake was reduced by about 88%. The average maximum transient vibration value of the rail-induced vertical vibration at the typical points of the conventional model was 86.2 dB, while that in the 3D-isolated model was 78.6 dB, the vibration reduction was 7.6 dB.

Dynamic response of a steel catenary riser at touch-down zone

This paper introduces a numerical model for analysing the dynamic response and fatigue damage of a global steel catenary riser (SCR) at the touch-down zone (TDZ). The model incorporates an innovative pipe-soil interaction model based on a new effective-stress framework to evaluate the changing soil strength induced by the cyclic motion of the SCR, thereby allowing for a more accurate assessment of the effects of soil remoulding and trenching on the dynamic responses of the SCR. The global SCR model is implemented in a commercial finite element software – ABAQUS, with the pipe-soil interaction model integrated through a user-defined element subroutine. A comprehensive series of time-domain simulations is conducted to investigate the evolution of seabed and the subsequent development of trenching along the seabed pipeline. These simulations provide valuable insights into the structural performance of the SCR at the TDZ. Additionally, this research explores the effects of water entrainment, changing seabed strength & stiffness, and the heaving motion of the floater on the fatigue damage of the global SCR. Understanding these factors is essential for obtaining an extensive understanding of the SCR's behaviour in the TDZ. The findings provide significant insights that can be leveraged to optimise existing design practices and enhance the efficiency and safety of offshore infrastructure.

Stress evolution of TBCs considering the micro morphology characteristics with multi-oxides growth

Thermal Barrier Coatings (TBCs) are a fundamental technology for safeguarding aircraft engine blades from high-temperature environments. Under long-term exposure to a high-temperature environment, breakaway oxidation of multi-metallic metals occurs in TBCs. The growth of multi-metal oxides and stress evolution in the TBCs after breakaway oxidation is very complex for a real coating microscopic morphology. In this paper, we use the CT image technology to construct the TBCs model of the reflective TBCs microscopic morphology and use a user-defined element (UEL) subroutine involving the growth of the multi-oxides model to calculate the stress. We focus on the evolution of interfacial stress in the first and second oxide stages. The results show that the micro defects will cause multiple increases in the maximum stress near the defects in TBCs. Meanwhile, microscopic defects near the interface can bring a sharp increase of tensile stress in the local area during the cooling stage, which can easily cause cracking and delamination of the interface.

A Vehicle–Bridge Interaction Element: Implementation in ABAQUS and Verification

Vibration analysis of bridges induced by train loads is a crucial aspect of railway design, particularly considering the complexity of vehicle components such as bogie-suspension systems. Consequently, railway engineers have endeavored to improve the computational efficiency and applicability of train models using the finite-element method. This paper introduces a toolbox implemented in ABAQUS through a user-defined element (UEL) subroutine, which incorporates the vehicle–bridge interaction (VBI) element theory. This toolbox effectively handles diverse vehicle–bridge interaction systems. In the proposed theory, the wheel-track contact force is derived based on the bridge response, eliminating the need for an iterative process and significantly reducing computational workload compared to classical physics-based analysis. The presented approach is validated through a moving sprung mass model and a moving rigid bar model. Furthermore, a case study is conducted on a three-dimensional finite-element model of a high-speed railway bridge in China, based on a design sketch, to showcase the capabilities of the developed scheme. The study demonstrates the practical application of the proposed methodology in analyzing vehicle–bridge structures with high complexity.

Convergence Check Phase-Field Scheme for Modelling of Brittle and Ductile Fractures

The paper proposes a novel staggered phase-field framework for modelling brittle and ductile fractures in monotonic and cyclic loading regimes. The algorithm consists of two mesh layers (displacement and phase field) and a single special-purpose, user-defined finite element, which controls global convergence of the coupled problem and passing of the solution variables between mesh layers. The proposed algorithm is implemented into FE software ABAQUS. For the problem of high cyclic fatigue, a cycle-skipping scheme is also introduced. The proposed methodology is verified on the usual benchmark examples. Small-strain theory is applied, but it has been demonstrated that extension to large strains is straightforward using only the ABAQUS built-in option. The efficiency and stability of the proposed framework was proven by comparison of computational time and the number of iterations per increment in the RCTRL scheme.

Implementation and verification of a user‐defined element (UEL) for coupled thermal‐hydraulic‐mechanical‐chemical (THMC) processes in saturated geological media

AbstractEfficient and accurate modeling of the coupled thermal‐hydraulic‐mechanical‐chemical (THMC) processes in various rock formations is indispensable for designing energy geo‐structures such as underground repositories for high‐level nuclear wastes. This work focuses on developing and verifying an implicit finite element solver for generic coupled THMC problems in geological settings. Starting from the mass, momentum, and energy balance laws, a specialized set of governing equations and a thermoporoelastic constitutive model is derived. This system is then solved by an implicit finite element (FE) scheme. Specifically, the residuals and the Jacobians are scripted in a user‐defined element (UEL) subroutine which is then combined with the general‐purpose FE software Abaqus Standard to solve initial‐boundary value problems. Considering the complexity of the system, the UEL development follows a stepwise manner by first solving the coupled hydraulic‐mechanical (HM) and thermal‐hydraulic‐mechanical (THM) equations before moving on to the full THMC problem. Each implementation step consists of at least one verification test by comparing computed results with closed‐form analytical solutions to ensure that the various coupling effects are correctly realized. To demonstrate the robustness of the algorithm and to validate the UEL, a three‐dimensional case study is performed with reference to the in‐situ heating test of ATLAS at Belgium in 1980s. A hypothetical radionuclide leakage event is then simulated by activating the chemical‐concentration degree of freedom and prescribing a constant high concentration at the heater's surface. The model predicts a limited contaminated regime after six years considering both diffusion and advection effects on species transport.

A length scale insensitive phase field model based on geometric function for brittle materials

The commonly used phase field model has a broad application in static and dynamic scenarios with brittle materials. Following the assumption of irreversibility of fracture, monotonically increasing phase and tensile strain energy are applied in the commonly used phase field model. By doing so, a clear stiffness reduction, however, is observed in stress–strain curve before reaching fracture strength, which conflicts with the linear elastic behavior of brittle materials. The limitation has also been mentioned in publications when length scale is the only parameter to adjust fracture strength. To solve these problems, a generalized quadratic geometric function is proposed to build a length scale insensitive phase field model. Governing equations and one-dimensional analytical solutions (homogeneous and nonhomogeneous solutions) of this length scale insensitive phase field model are presented. By adjusting the extra parameter in the generalized quadratic geometric function and zeroing negative phase, different phase profile (ranged from exponential profile to linear profile) and fracture strength can be obtained, which could be more suitable to cover different types of fractures. Meanwhile, a narrower crack band and linear elastic behavior can be guaranteed. LS-DYNA user-defined element and user-defined material subroutines are used to implement the proposed length scale insensitive phase field model. A tensile test successfully verifies the properties of a narrower crack band and linear elastic behavior. Three representative numerical examples show the feasibility of this model to simulate fracture propagation, including a Mode Ⅰ failure of wedge splitting test, a mixed-mode failure of l-shaped panel test and a mixed-mode failure of notched beam test. From the crack band and force–displacement curve, the proposed model can handle fracture propagation better for brittle materials.

A Constitutive Model of Water-Triggered Shape Memory Hydrogels and Its Finite Element Implementation

AbstractShape memory hydrogel is a type of hydrogel whose shape can transform between a temporary shape and its initial shape when exposed to external stimuli, such as water, temperature, and pH. Over the last decade, shape memory hydrogels have gained increasing interest owing to their distinct properties; however, constitutive models to describe their shape memory mechanism are still lacking. In this paper, we propose a constitutive model for water-triggered shape memory hydrogels based on the transition between the sparse and dense phases. In the model, the shape memory process is identified using two internal variables: the frozen deformation gradient and dense phase volume fraction. To validate the model for describing shape memory effects, we implemented the model in the finite element method using a user-defined element (UEL) subroutine in ABAQUS. To verify the accuracy of the proposed UEL, we simulated the water-triggered shape memory effects in different recovery processes under different uniaxial loads. Furthermore, we investigated the water-triggered shape memory behavior of a self-bending bilayer structure and a four-arm gripper structure using both experiments and simulations. Good agreement was observed between the simulation and experimental results.

Ductile fracture simulation using phase field method with various damage models based on different degradation and geometric crack functions

For simulation of ductile fracture, plasticity and damage are two essential aspects. The phase field method emerged as an efficient mathematical tool to address the fracture processes involving crack initiation, merging, and branching. From the wide literature, it has been observed that the information on the suitability of the existing phase field models for simulation of ductile fracture is scanty. This paper proposes a phase field methodologies for simulation of ductile fracture considering the aspects like different degradation and crack geometric functions. The proposed formulation couples the damage model, constitutive behaviour of elasto-plastic solid and J2 plasticity. Numerical simulations are carried out using ABAQUS with user-defined element (UEL) subroutine codes, defining the displacement field and phase field variable. Several benchmark problems were analysed to investigate the (i) behaviour of the specimen (ii) the performance of various phase field damage models (PFDM) and (iii) the effect of non-dimensional parameters considered in the damage models. The maximum percentage difference between the numerically predicted maximum load and its corresponding displacement is in good agreement w.r.t experimental value under PFDM4 (±10% range). The output of the study provides an insight on the use of various damage models and other parameters for the simulation of ductile crack propagation. This proposed model can be further extended to the prediction of remaining life or residual strength of the structural component.