User-defined Element Subroutine Research Articles

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.

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

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.

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.

Prediction of a complex delamination front using a general cohesive model

The influence of the delamination direction with respect to the fiber orientation in adjacent plies on the apparent interlaminar toughness is considered by proposing a general cohesive model. A local delamination-direction definition method is adopted. Based on the mismatch between the fiber orientation and delamination direction, the linear evolution of the apparent toughness is developed. The general cohesive model is implemented in a user-defined element subroutine in ABAQUS and is validated on a case study with a single cohesive element. Second, a square sample under Mode I fractures is designed, where multiple delamination directions, ranging from 0° to 90°, form a complex delamination front. Nonlocal crack branching can be observed where high-delamination direction angles exist. Using the segmented linear evolution of toughness can significantly improve the accuracy of predicting the delamination fronts and the reaction-force-opening curve. This work provides a framework to assess the intra/interlaminar damage coupling during the multidirectional delamination propagation.

Improved Staggered Algorithm for Phase-Field Brittle Fracture with the Local Arc-Length Method

The local arc-length method is employed to control the incremental loading procedure for phase-field brittle fracture modeling. An improved staggered algorithm with energy and damage iterative tolerance convergence criteria is developed based on the residuals of displacement and phase-field. The improved staggered solution scheme is implemented in the commercial software ABAQUS with user-defined element subroutines. The layered system of finite elements is utilized to solve the coupled elastic displacement and phase-field fracture problem. A one-element benchmark test compared with the analytical solution was conducted to validate the feasibility and accuracy of the developed method. Our study shows that the result calculated with the developed method does not depend on the selected size of loading increments. The results of several numerical experiments show that the improved staggered algorithm is efficient for solving the more complex brittle fracture problems.

A viscoelastic cohesive zone model for starch-gluten interface to simulate dough deformation

A viscoelastic cohesive zone model was proposed to simulate rate-dependent starch-gluten interface debonding. The debonding was believed to influence stress-strain curves of tensile and shear tests at different strain rates. The model was written as a user-defined finite element subroutine codes, which was then included into an interface element geometry between starch filler and gluten matrix. The finite element modelling results showed agreement with experimental data under uniaxial tension and simple shear at different strain rates (5/min and 0.5/min). This was due to the viscoelastic effect of the interface model, which caused difference between traction initiation at different rates for the cohesive zone model (i.e. ∼1.1kPa and ∼0.5kPa at 5/min and 0.5/min, respectively). In addition, it was shown that critical shear stress is a very important debonding parameter, where slight changes of the shear traction values caused the model stress-strain curve to deviate from the experimental results. Simulations of starch-gluten dough deformation were then conducted at different strain rates to imitate dough processes like baking, extrusion and proving (0.003/s, 1/s and 10/s, respectively). The interface model was shown to influence stress-strain curve at lower strain rate processes like baking and extrusion.

Computation of two dimensional mixed-mode stress intensity factor rates using a complex-variable interaction integral

The well-known interaction integral, also known as the M-integral or I-integral, is a method to compute the mixed-mode stress intensity factors (SIFs) for fracture mechanics problems. The capabilities of the M-integral are extended here to compute derivatives of the SIFs with respect to the crack extensions for an isotropic linear elastic material under static loading. These derivatives were calculated using the complex Taylor series expansion (CTSE) numerical differentiation method. The derivatives of the auxiliary fields are calculated by applying CTSE directly to the M-integral formulation. The derivatives of the actual displacement fields are computed using a hypercomplex-variable finite element method (ZFEM) that also employs CTSE. SIF rates with respect to all crack tips are computed in a single analysis. The method is general and can be easily extended to other two-dimensional loading scenarios and different material models in a straightforward manner through the use of the appropriate auxiliary fields. The complex-variable M-integral was implemented within the commercial finite element software Abaqus through a user-defined element subroutine (UEL). Numerical examples demonstrate the high accuracy of the method.

Dynamic Versus Quasi-Static Analysis of Crack Propagation in Soft Materials

Abstract Cracks usually propagate dynamically that makes them so dangerous. However, most crack simulations are based on quasi-static analyses because they are simpler than the dynamic ones. Is it correct to use quasi-static analyses instead of the dynamic ones? Will the quasi-static and dynamic simulations provide similar results? We try to answer these questions in the present work. We compare results of quasi-static and dynamic simulations of crack propagation in aneurysm material. We use the material-sink (MS) approach, which is based on the notion of the diffused bond breakage. The latter feature implies a local loss of material and, consequently, decrease of mass density, which, in its turn, means that both stiffness and inertia go down in the damaged zone. The cancellation of inertia is an important feature of the MS approach in contrast to more formal regularization theories as phase field, gradient damage, and other nonlocal formulations. The MS approach is implemented within commercial finite-element software abaqus. A reduced mixed finite-element formulation is adopted to circumvent the volumetric locking and an implicit staggered solution algorithm is developed via the user-defined element subroutine UEL. Considered examples show that the onset of crack instability under static loads is followed by the dynamic rather than quasi-static crack propagation. Moreover, dynamic and quasi-static simulations, generally, provide different results.

Efficient quasi-brittle fracture simulations of concrete at mesoscale using micro CT images and a localizing gradient damage model

In this work, a localizing gradient damage model (LGDM) based on the generalized micromorphic theory is adopted to investigate the quasi-brittle fracture behaviour of concrete at mesoscale for the first time. Micro Computed Tomography (CT) image-based realistic concrete models are generated including aggregates, mortar, pores, and aggregate-mortar interfacial transition zones (ITZs). In the LGDM, an additional micro-force equilibrium equation is formulated with a damage-dependent interaction function to prevent spurious energetic interactions during the softening stage. The damage driving forces are evaluated as history variables through the maximum nonlocal equivalent strains at the integration points. The stiffness matrices and residual vectors for displacement and nonlocal equivalent strain fields are formulated through the conventional shape function and strain matrices of finite elements, by using the user-defined element (UEL) subroutine implemented with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm to improve numerical performance. Typical nonlinear fracture benchmarks are presented to investigate the variability of mesoscale fracture evolution, crack trajectories, and load–displacement curves as well as numerical performance. It is found that the LGDM significantly improves the computational efficiency over the conventional phase-field cohesive zone model (PFCZM) with 60% savings of CPU time, and holds great potential for multiscale fracture evaluation of quasi-brittle composite materials, through the high-fidelity representation of real materials’ microstructures, and flexible simulation of the complicated nonlinear fracture without the need for re-meshing or mesh enrichments.

Simultaneous identification of multi-parameter for power hardening elastoplastic problems in three-dimensional geometries

PurposeThe purpose of this study is to simultaneously determine the constitutive parameters and boundary conditions by solving inverse mechanical problems of power hardening elastoplastic materials in three-dimensional geometries.Design/methodology/approachThe power hardening elastoplastic problem is solved by the complex variable finite element method in software ABAQUS, based on a three-dimensional complex stress element using user-defined element subroutine. The complex-variable-differentiation method is introduced and used to accurately calculate the sensitivity coefficients in the multiple parameters identification method, and the Levenberg–Marquardt algorithm is applied to carry out the inversion.FindingsNumerical results indicate that the complex variable finite element method has good performance for solving elastoplastic problems of three-dimensional geometries. The inversion method is effective and accurate for simultaneously identifying multi-parameters of power hardening elastoplastic problems in three-dimensional geometries, which could be employed for solving inverse elastoplastic problems in engineering applications.Originality/valueThe constitutive parameters and boundary conditions are simultaneously identified for power hardening elastoplastic problems in three-dimensional geometries, which is much challenging in practical applications. The numerical results show that the inversion method has high accuracy, good stability, and fast convergence speed.

Investigation of the effect of modular construction details on the lateral behaviour of cold-formed steel framed shear walls

This paper investigates the effect of modular construction details on laterally-loaded cold-formed steel (CFS) framed shear walls sheathed with wood- and cement-based panels by means of finite-element (FE) analyses. Shell FE-based models have been developed in ABAQUS with the aim of accurately capturing the behaviour, strength and stiffness as well as the corresponding failure modes of CFS framed shear walls subjected to monotonic lateral load (i.e., wind). User-defined element subroutines were adopted for precise modelling of sheathing-to-CFS screws shear behaviour. The proposed modelling protocol is validated using experimental test results, where an acceptable concordance (4% difference) has been achieved. Subsequently, the effect of modular construction details, which go beyond the scope of the current lateral design provisions (AISI S400), on the lateral behaviour of CFS framed shear walls is assessed. In particular, this paper investigates the impact of: (i) floor and ceiling ledger beams on the interior face of the shear wall, (ii) sheathing boards having different sizes from the overall shear wall and thus the presence of both vertical and horizontal seams, (iii) cement particle boards at the bottom stripe of the shear wall and (iv) different screw spacing in the top and bottom stripes from the middle part of the shear wall. The key parameters, which have most affected the lateral behaviour, were identified, and based on that, rules have been established for optimizing the screws pattern and sheathings layout efficacy in the above-described lateral load resisting system. The obtained results shed light on the capability of the developed modelling protocol to be used as a virtual test bench, particularly in offsite mass production and manufacture (DfMA), for the development of a new CFS framed wall system for lateral stability of lightweight modular houses.

Orchestrated neuronal migration and cortical folding: A computational and experimental study.

Brain development involves precisely orchestrated genetic, biochemical, and mechanical events. At the cellular level, neuronal proliferation in the innermost zone of the brain followed by migration towards the outermost layer results in a rapid increase in brain surface area, outpacing the volumetric growth of the brain, and forming the highly folded cortex. This work aims to provide mechanistic insights into the process of brain development and cortical folding using a biomechanical model that couples cell division and migration with volumetric growth. Unlike phenomenological growth models, our model tracks the spatio-temporal development of cohorts of neurons born at different times, with each cohort modeled separately as an advection-diffusion process and the total cell density determining the extent of volume growth. We numerically implement our model in Abaqus/Standard (2020) by writing user-defined element (UEL) subroutines. For model calibration, we apply in utero electroporation (IUE) to ferret brains to visualize and track cohorts of neurons born at different stages of embryonic development. Our calibrated simulations of cortical folding align qualitatively with the ferret experiments. We have made our experimental data and finite-element implementation available online to offer other researchers a modeling platform for future study of neurological disorders associated with atypical neurodevelopment and cortical malformations.

Fast nonlinear mechanical features decoupling to identify and predict asphalt-based composites

Nonlinear matrices employed in asphalt-based composites exhibit a prominent nonlinear elastic-viscoplastic-viscodamageable mechanical response. The constitutive model for this type of matrices requires a significant experimental effort to identify the material constants. To alleviate the characterization effort without losing reliability in the mechanical prediction, this paper presents a fast procedure decoupling the elasto-viscoplastic response from the viscodamageable one and facilitating the identification of the material constants via efficient optimization. This procedure relies on a combined experimental–numerical also applicable to other rheologically complex materials like polyurea, thermoplastics or elasto-viscoplastic polycrystals. The experimental part is deliberately designed to only conduct cost- and time-effective monotonic loads at different strain rates in tension and compression. These pure monotonic results are used in the constitutive model to predict more complex loading conditions such as multiple load–unload–reload (LUR) cycles. To do this, an elasto-viscoplastic constitutive model suitable to describe creep-like phenomena and large irreversible deformations is proposed. This model incorporates pressure and strain rate sensitivity, which is essential to capture the compression–tension asymmetry in asphalt-based composites. A rate-dependent damage model is proposed to describe the degradation rate of the elasto-viscoplastic part. The stress and the consistent tangent modulus are derived. The model implementation for user-defined finite element subroutines are given for explicit or implicit solvers. The proposed decoupling facilitates an efficient identification of the constant parameters via an in-house Nelder–Mead-based optimization method. To accelerate the identification, all the stress–strain curves, either in tension or compression, are simultaneously used with applying physically-based constrains. The framework is validated with asphalt matrix at room temperature (24 °C) and verified under LUR conditions at different rates. The identified model predicts correctly the experimental observations, proving its applicability to investigate particle-based composites with highly nonlinear matrices.

On realizing specific failure initiation criteria in the phase field model

In the phase field model (PFM), fracture timing and direction are determined automatically by the stationary condition of the system’s potential, it is normally considered an advantage since not a failure initiation criterion is required to be appointed. However, it may become an obstacle when a specific failure criterion is required to calculate the fracture timing and direction. In order to solve this issue, we propose a simple way to embed different failure criteria into the PFM in this work. On one hand, an activation parameter is introduced into the PFM’s driving force to control the fracture timing, and the parameter’s value is one if the specified criterion is satisfied and is zero otherwise. On the other hand, a structural tensor is introduced into the PFM’s surface density function to reflect the fracture direction predicted by the specified criterion. The fracture evolution direction is enforced in line with the criterion through a penalty parameter. The proposed PFM is implemented into ABAQUS through using the user-defined element (UEL) subroutine, and comparisons with the extended finite element method (XFEM) and experiments are provided for verification and validation.

A coupled adhesive-frictional model tailored for interfacial behaviors between UHPC and NC materials

In this paper, a coupled adhesive-frictional is proposed and implemented within an implicit finite element (FE) solver, targeting interfacial behaviors between ultrahigh-performance concrete (UHPC) and normal concrete (NC) materials. The model couples the adhesive force and frictional force, which is consistent with the mainstream shear-friction theory. The proposed model is realized by the zero-thickness cohesive element, thorough user-defined element (UEL) subroutine provided by the general FE software Abaqus/Standard. The model satisfactorily predicts the bond strength between UHPC and NC materials subject to various statuses, i.e., the tensile force (direct-tensile test), and combined compressive and shear forces (slant shear test). In addition, the interfacial model works fully compatible with the concrete damaged plasticity model, which is adopted for the UHPC and NC materials. The combination of these two models yields agreed with simulation results, which effectively predicts various cracking propagation and failure patterns of UHPC-NC composite specimens. The specimens in literatures are selected for comparisons and the numerical simulations clearly illustrate the complex interactions between the matrix cracking and interfacial debonding.