User Material Subroutine Research Articles

A 3D finite deformation constitutive model for anisotropic shape memory polymer composites integrating viscoelasticity and phase transition concept

The phase transition theory of shape memory polymers (SMPs) often involves a phenomenological assumption that the reference configuration of the newly transformed phase deviates from that of the initial phase. This distinction serves as a crucial mechanism in the manifestation of the shape memory effect. However, elucidating the precise definition of the reference configuration of the transformed phase poses a significant challenge in the formulation of the constitutive model. To tackle this challenge, a three-dimensional (3D) finite deformation constitutive model incorporating effective phase evolution for SMPs has been developed. This model merges insights from the classical viscoelastic framework with the phase transition theory. The anisotropic thermo-viscoelastic constitutive model is further developed by introducing hyperelastic fibers, which integrate the anisotropy of the fibers into a continuous thermodynamic framework through structure tensors. Implemented within the ABAQUS software via a user material (UMAT) subroutine, the proposed model has been meticulously validated against experimental data, showcasing its prowess in simulating stress-strain responses and shape memory characteristics of SMPs and their composites (SMPCs). This innovative model stands as an invaluable instrument for the design and of sophisticated SMP and SMPC structures.

Low‐velocity impact resistance of the Z‐pin reinforced carbon fiber composite laminates

AbstractA voronoi user material subroutine (VUMAT) was developed using the three‐dimensional Hashin damage criterion and exponential nonlinear damage evolution method. An interlayer damage model based on the quadratic nominal stress (QUADS) criterion and B‐K fracture criterion was introduced, and a finite element model of Z‐pin reinforced composite laminates under low‐velocity impact was established. The low‐velocity impact behavior of Z‐pin reinforced composite laminates with different impact velocities (0.6 m/s, 0.4 m/s, and 0.3 m/s), different layup forms ([0°/90°]4 and [0°/45°/90°/−45°]2), and different Z‐pin spacing (4 mm, 8 mm, and 16 mm) was studied using ABAQUS. The results indicate that different layup forms have little effect on the low‐velocity impact behavior of Z‐pin reinforced composite laminates. The Z‐pin spacing has a significant influence on the low‐velocity impact behavior of Z‐pin reinforced composite laminates. When the impact velocity is 0.4 m/s, the specific energy absorption of composite laminates with Z‐pin spacing of 16 mm is 85.93% and 87.7% lower than that of composite laminates with Z‐pin spacing of 4 mm and 8 mm. As the Z‐pin spacing decreases (Z‐pin density increases), the impact resistance of Z‐pin reinforced composite laminates first increases and then decreases.Highlights• The low‐velocity impact of Z‐pin reinforced composite laminates was studied.• Analyzed the effect of layup forms of laminates on their impact behavior.• Explored the influence mechanism of Z‐pin spacing on the impact behavior.• Studied the energy absorption of different Z‐pin spacing under impact velocity.

Mechanical evaluation of multi-continuous interpenetrating phase composites based on Schwarz Primitive cellular structure

Interpenetrating phase composites (IPCs) have been extensively promoted due to their robust mechanical properties. To further obtain the enhanced properties and elucidate the underlying mechanical mechanism, we designed and manufactured the tri-continuous IPCs by filling hyperelastic PDMS into a 3D-printed Schwarz Primitive (P) cellular skeleton based on the viscoplastic polymer. Subsequently, the compressive properties, cyclic properties, and relaxation properties of the IPCs were experimentally investigated. Results demonstrated that interpenetrating can improve the compressive properties, reduce the relaxation behavior, and weaken the cyclic softening effect. By incorporating a user material subroutine in simulations, we analyzed the deformation behaviors of P cellular material and IPCs. Through a combination of experimental observations and simulated outcomes, we refined our understanding of the deformation mechanism of IPCs. Our analysis revealed that filled PDMS played a positive role in enhancing the mechanical performance of TC-IPCs through three key mechanisms: Firstly, it shears part of the external load of TC-IPCs. Secondly, it astricts the bending deformation in the skeleton, thereby preventing the stress drop induced by buckling. Thirdly, the interaction between PDMS and P cellular skeleton puts them in compressive stress in tri-direction, enhancing the overall mechanical properties. These findings contribute to advancing the development and application of IPCs.

Modelling and Characterisation of Orthotropic Damage in Aluminium Alloy 2024.

The aim of the work presented in this paper was development of a thermodynamically consistent constitutive model for orthotopic metals and determination of its parameters based on standard characterisation methods used in the aerospace industry. The model was derived with additive decomposition of the strain tensor and consisted of an elastic part, derived from Helmholtz free energy, Hill's thermodynamic potential, which controls evolution of plastic deformation, and damage orthotopic potential, which controls evolution of damage in material. Damage effects were incorporated using the continuum damage mechanics approach, with the effective stress and energy equivalence principle. Material characterisation and derivation of model parameters was conducted with standard specimens with a uniform cross-section, although a number of tests with non-uniform cross-sections were also conducted here. The tests were designed to assess the extent of damage in material over a range of plastic deformation values, where displacement was measured locally using digital image correlation. The new model was implemented as a user material subroutine in Abaqus and verified and validated against the experimental results for aerospace-grade aluminium alloy 2024-T3. Verification was conducted in a series of single element tests, designed to separately validate elasticity, plasticity and damage-related parts of the model. Validation at this stage of the development was based on comparison of the numerical results with experimental data obtained in the quasistatic characterisation tests, which illustrated the ability of the modelling approach to predict experimentally observed behaviour. A validated user material subroutine allows for efficient simulation-led design improvements of aluminium components, such as stiffened panels and the other thin-wall structures used in the aerospace industry.

Direct application of elasto-visco-plastic self-consistent crystal plasticity model to U-draw bending and springback of dual-phase high strength steel

The incremental elasto-visco-plastic self-consistent polycrystal model (ΔEVPSC) was utilized to describe the constitutive behavior of dual-phase 980 (DP980) steel. A simple baseline modeling approach was chosen: the hardening behavior of each constituent phase in the DP980 steel was described by a simple Voce hardening law without explicitly considering the back stress; and it was assumed that using the same single crystal elastic modulus for ferrite and martensite is sufficiently representative. The adequacy of this baseline modeling approach was evaluated by comparing various mechanical experimental data with model predictions in terms of the stress vs. strain curves obtained from uniaxial tension, tension-compression, and loading-unloading-loading (LUL) tests. Additionally, the evolution of experimental lattice strain data reported in literature was used to validate the phase-specific Voce hardening parameters. Despite its minimalistic modeling description, the baseline ΔEVPSC model successfully captured key features: 1) the Bauschinger effect, 2) the decrease in chord modulus, and 3) the non-linearity in the stress vs. strain curves resulting from the LUL test. All three mentioned characteristics are crucial for accurate prediction of springback in sheet metals. The ΔEVPSC model, interfaced with a finite element solver (Abaqus/standard) as the user material subroutine, was employed to simulate the Numisheet93 benchmark problem. The strip of DP980 was first U-drawn followed by springback. The model-predicted springback profile aligned well with the experimental results only when stress relaxation was properly considered, resulting in improved predictive accuracy compared to predictions based on a distortional plasticity model.

Analysis on shear band development under large strain torsion of amorphous glassy polymers

Unlike the shear band development of metals generally regarded as the precursor to failure, the shear banding process in amorphous glassy polymers is known to influence both the strengthening and fracturing behaviors. Complementary to the previous experimental work in the literature on the shear band development under torsion under limited cases, the finite element (FE) analysis has been conducted to investigate the general shear banding behaviors in terms of the initiation and propagation in more detail. The FE model has been established by incorporating the Boyce-Parks-Argon (BPA) constitutive model with the full-network modification via a user material subroutine in ABAQUS. A series of nondimensional quantities were used to discuss the mesh sensitivity and the effects of predefined imperfections, specimen geometry, and torsion mode. Besides, by altering the extents of the intrinsic material softening and the strain hardening, the shear banding behaviors of typical materials under typical temperature and strain rate conditions are equivalently investigated. The validity of the simulation has been qualitatively validated by directly comparing with the experimental results from the literature.

Seismic Response and Collapse Analysis of a Transmission Tower Structure: Assessing the Impact of the Damage Accumulation Effect

This paper delves into the impact of the damage accumulation effect, which leads to the degradation of material strength and stiffness, on the seismic resistance of transmission towers. Building upon the elastic–plastic finite element theory, a mixed hardening constitutive model is derived for circular steel tubes, standard elements in transmission towers, incorporating the damage accumulation effect. A user material subroutine, UMAT, is created within the LS–DYNA framework. The program’s validity and reliability are established through axial constant–amplitude loading tests on single steel tubes. The subroutine is employed to conduct the incremental dynamic analysis (IDA) of an individual transmission tower and to contrast it with the structure utilizing the Plastic Kinematic material model, assessing the discrepancies in tower top displacements and segment damage indices (SDIs) at both macroscopic and microscopic scales. The results shows that the Plastic Kinematic model inflates the seismic performance of the transmission tower. When considering the damage accumulation effect in structural failure, the damage index of the members increases, leading to a reduction in both the structural strength and stiffness. The dynamic response in the plastic phase becomes more pronounced, and the onset of structural failure is accelerated. Consequently, structural analysis under seismic conditions should account for the damage accumulation process. Through the delineation of member and segment damage, the extent of damage to transmission tower segments can be quantitatively assessed. Subsequently, the ultimate load–bearing capacity and the most vulnerable location of the transmission tower can be ascertained. Finally, this paper provides a detailed analysis of the transmission tower collapse process under seismic action and summarizes the mechanism of collapse for the structure.

Crash analysis of glass mat thermoplastic (GF/PA6) tubes considering splaying failure mode and energy absorption

Glass mat thermoplastic tubes are potential materials for improving crashworthiness owing to their excellent crash energy absorption capability due to their splaying failure mode of glass mat thermoplastic tubes, which must be considered in the crash analysis to accurately predict their crash performance. This study investigates the crash analysis of glass-mat thermoplastic composite tubes to realize the splaying failure mode and crash energy absorption capability. We evaluated the mechanical properties and fracture toughness of advanced glass mat thermoplastics, termed multi-layered hybrid mats, and employed the result in a 3D Hashin-type continuum damage model implemented with a user material subroutine. For the crash analysis of glass mat thermoplastic tubes, a three-dimensional finite element (FE) model, including cohesive elements in the middle layer of the tube to simulate the splaying failure mode, was constructed. In addition, in the process of the efficient FE modeling of the crash tube, the fracture toughness correction factor was proposed and optimized to calibrate the energy absorption in conjunction with crash test results, as interlaminar fracture modeling causes a difference in energy absorption between the actual test and simulation. As a result, the proposed crash analysis predicted the energy absorption capacity and a splaying failure mode of glass-mat thermoplastic tubes, demonstrating strong concordance with experimental results.

A 3D Elastoplastic Constitutive Model Considering Progressive Damage Behavior for Thermoplastic Composites of T700/PEEK.

Due to their excellent mechanical properties, the carbon fiber-reinforced polymer composites (CFRPs) of thermoplastic resins are widely used, and an accurate constitutive model plays a pivotal role in structural design and service safety. A two-parameter three-dimensional (3D) plastic potential was obtained by considering both the deviatoric deformation and the dilatation deformation associated with hydrostatic stress. The Langmuir function was first adopted to model the plastic hardening behavior of composites. The two-parameter 3D plastic potential, connected to the Langmuir function of plastic hardening, was thus proposed to model the constitutive behavior of the CFRPs of thermoplastic resins. Also, T700/PEEK specimens with different off-axis angles were subjected to tensile loading to obtain the corresponding fracture surface angles of specimens and the load-displacement curves. The two unknown plastic parameters in the proposed 3D plastic potential were obtained by using the quasi-Newton algorithm programmed in MATLAB, and the unknown hardening parameters in the Langmuir function were determined by fitting the effective stress-plastic strain curve in different off-axis angles. Meanwhile, the user material subroutine VUMAT, following the proposed constitutive model, was developed in terms of the maximum stress criterion for fiber failure and the LaRC05 criterion for matrix failure to simulate the 3D elastoplastic damage behavior of T700/PEEK. Finally, comparisons between the experimental tests and the numerical analysis were made, and a fairly good agreement was found, which validated the correctness of the proposed constitutive model in this work.

Artificial neural network enhanced plasticity modeling and ductile fracture characterization of grade-1 commercial pure titanium

This study primarily aims to develop a robust modeling approach to capture the complex material behavior of CP-Ti, appeared by high anisotropy, differential hardening due to anisotropy evolution, and flow behavior sensitive to strain rate and temperature, using artificial neural networks (ANNs). Plasticity is characterized by uniaxial tension and in-plane biaxial tension tests at temperatures of 0 °C and 20 °C with strain rates of 0.001 /s and 0.01 /s, and the results are used to calibrate the non-quadratic anisotropic Yld2000–3d yield function with respect to the plastic work. In order to predict the intricate plastic deformation with the temperature and strain rate effects, two distinct ANN models are developed; one to capture the strain hardening behavior and the other to predict the anisotropic parameters in the chosen yield function. The developed ANN models predict an unseen dataset well, which is intermediate testing conditions at a temperature of 10 °C and strain rate of 0.005 /s. The ANN models, being computationally stable and adhering to conventional constitutive equations, are implemented into a user material subroutine for the ductile fracture characterization of CP-Ti sheet using the hybrid experimental-numerical analysis. The favorable agreement between experimental data and numerical predictions, particularly using the ANN models with evolving anisotropic material parameters for the Yld2000–3d yield function, underscores the significance of the differential hardening effect on the ductile fracture behavior and highlights the capabilities of ANN models to capture the complex plastic behavior of CP-Ti. The key parameters including stress triaxiality, Lode angle parameter, and equivalent plastic strain at the fracture location are extracted from the simulations, enabling the calibration of ductile fracture models, namely Johnson-Cook, Hosford-Coulomb, and Lou-2014, and construction of fracture envelopes.

Statistically based mechanical model of shape memory hydrogels

The constitutive models of shape memory hydrogels (SMHs) are gaining increasing interest due to their important applications in human tissue, artificial skin, and drug release because these models can elucidate the interaction between water molecule diffusion and transient network deformation, and clarify the mechanism of shape memory effect. Herein, based on the chain statistic theory, a micro-macroscopic SMH constitutive model is developed, which simultaneously considers solvent diffusion and network evolution. Compared with existing models, our model considers the coupling effect of water molecule diffusion and dynamic network deformation, kinetics of dynamic bond controlled by temperature, chemical potential and chain force, and can capture the location-dependent shape memory effect of SMHs. In addition, this model is implemented into ABAQUS through a user material subroutine (UMAT) and the simulation results are in reasonable agreement with experimental measurements. Three simulation examples, the constrained swelling of a strip, deformation of a flat plate with a hole and SMH indentation, are presented and simulation results indicate that our model can capture the location-dependent shape memory behaviors. This work provides a powerful tool to elucidate complex mechanical behaviors of SMHs and may guide their structure designs and applications.

Welding residual stress analysis of the X80 pipeline: simulation and validation

Abstract. In this work, a finite-element welding model of the X80 pipeline is established, and the residual stress is calculated using a direct thermal–mechanical coupling method through the User Material (UMAT) subroutine of the double-ellipsoid moving heat source. The effects of process parameters on the welding residual stress of the X80 pipelines are discussed. The ultrasonic longitudinal critical refraction (LCR) wave-detecting method is adopted to verify the simulation results. The results show that the residual stress at the inner surface is higher than that at the outer surface, and the peak Mises stress at the welding seam approaches the yield stress. With the increase in welding groove angle and heat input, the peak Mises stress increases at the inner surface and decreases at the outer surface, but the high-stress zone at the outer surface broadens. The residual stresses at the outer surface are more sensitive to the welding parameters. The comparison between the simulated results and ultrasonic LCR detection indicates that the finite-element method is feasible, and the simulation results are credible.

The strength prediction model of unidirectional fiber reinforced composites based on the renormalization group method

When unidirectional fiber reinforced composites are subjected to longitudinal tensile loading and reach a critical failure state, they experience a sudden transition from local damage to catastrophic failure, commonly termed as an avalanche event. This paper integrates the self-organized criticality theory (SOC) concepts into the prediction of longitudinal tensile strength of composites and establishes a strength prediction model of composites based on the renormalization group method (RGM). The predictions of the RGM model are successfully validated against experimental results in the literatures, and it demonstrates relatively acceptable predictive accuracy compared to classical strength criteria. Compared to other state-of-the-art prediction models considering stochastic fiber strength distribution, the RGM model effectively provides strength statistics for fiber bundles of any size and describes the occurrence of composites avalanche failure induced by local stress concentration. This present model can be very conveniently implemented as a User Material Subroutine (UMAT) for finite simulations, facilitating practical prediction of the strength of composites structures.

Experiments and modeling of the coupled viscoelasticity and Mullins effect in filled rubber materials

Filled rubber-like materials are widely used in engineering applications, and are known to exhibit a rate-dependent non-linear inelastic behavior, and stress-softening, also known as the Mullins effect is frequently encountered. In this work, we characterized and modeled the constitutive response of a handful of commercially available filled rubber-like materials. We first perform a set of large-deformation uniaxial experiments at room temperature and at multiple rates. Those experimental findings are used to develop and calibrate a thermodynamically consistent constitutive model, which is then numerically implemented in a finite element package by writing a user material subroutine. The constitutive model is validated by comparing the results of an inhomogeneous experiment and simulation. A key finding of this work is that the mechanisms that cause the Mullins effect appear to be the main drivers of viscoelasticity in the materials used here.

The Development of a Continuous Constitutive Model for Thin-Shell Components with A Sharp Change in the Property at Welded Joints.

Large-dimension complex integral thin-shell components are widely used in advanced transportation equipment. However, with the dimensional limitations of raw blanks and the manufacturing process, there are inhomogeneous geometric and mechanical properties at welded joints after welding, which have a significant effect on the subsequent forming process. Therefore, in this paper, the microstructure of welded joints with a sharp property change was accurately characterized by the proposed isothermal treatment method using the BR1500HS welded tube as an example. In addition, an accurate constitutive model of welded tubes was established to predict the deformation behavior. Firstly, the heat-treated specimens were subjected to uniaxial tensile tests and the stress-strain curves under different heat treatment conditions were obtained. Then, the continuous change in flow stress in the direction of the base metal zone, the heat-affected zone and the weld zone was described by the relationship between the microhardness, flow stress and center angle of the welded tube. Using such a method, a continuous constitutive model of welded tubes has been established. Finally, the constitutive model was compiled into finite-element software as a user material subroutine (VUHARD). The reliability of the established constitutive model was verified by simulating the free hydro-bulging process of welded tubes. The results indicated that the continuous constitutive model can well describe the deformation response during the free hydro-bulging process, and accurately predicted the equivalent strain distribution and thickness thinning rate. This study provides guidance in accurately predicting the plastic deformation behavior of welded tubes and its application in practice in hydroforming industries.

Modelling time-dependent relaxation behaviour using physically based constitutive framework

The application of interrupted die motion during the deformation process in a servo press cycle is known to enhance the forming limit of metallic materials. This observation is generally attributed to the transient effects associated with stress relaxation phenomenon. However, attempts to model stress relaxation behaviour using physically based constitutive formulations in the finite element method are scarce. In this work, a modified version of the Kocks–Mecking–Estrin (KME) dislocation density model is used to evaluate the substructural changes during relaxation. An ‘uncoupled’ elasto-viscoplastic approach is employed to accommodate the plastic strain rate effect. This modelling approach is implemented in the commercial finite element software via a user material subroutine. The model is validated through simulations of interrupted uniaxial tensile tests for aluminium alloy AA7075 under two different aging conditions. The implemented model is shown to closely capture the experimental results and account for changes in dislocation density and the athermal component of flow stress during relaxation. Subsequently, the model is applied to simulate monotonic and interrupted hole expansion tests (HET), and the results are discussed qualitatively.

An elastoplastic model with egg-shaped yield surface for coastal soft clay

A novel elastoplastic constitutive model with an egg-shaped yield surface (ESE model) is proposed herein to elucidate the strength-deformation characteristics of marine soft clay. One of the key improvements offered by this model is its ability to address the singularity associated with plastic strain increments at yield surface corners—a limitation commonly encountered in traditional elastoplastic models. Additionally, the proposed model demonstrates flexibility, as it can transform into various forms under different conditions. Subsequently, to evaluate the efficacy of this egg-shaped elastoplastic model, numerical simulations are performed within the finite element software ABAQUS using an implicit integration algorithm through the user material subroutine interface (UMAT). The simulations encompass standard triaxial consolidation tests involving saturated soft clay sourced from the Itsukaichi marine clay as well as two types of saturated kaolin clays. The outcomes derived from these simulations by the ESE model are compared with both empirical data and numerical simulations originating from the widely employed Modified Cam-Clay (MCC) model. The simulations of the ESE model for three conventional triaxial tests on clay demonstrate superior concordance with experimental measurements in comparison to the MCC model. This underscores the efficacy of the proposed ESE model in predicting the strength and deformation characteristics manifested by coastal soft clays under undrained conditions. Finally, the predictions for deformation in an adjacent tunnel according to the ESE model closely align with experimental measurements and prior to the simulations conducted using the MCC model and advanced models such as the bounding surface model and the unified model, thereby affirming its practical utility in engineering applications.

Pseudograin decomposition of short fiber-reinforced plastics for two-step homogenization using machine learning approach

Decomposing the representative volume element (RVE) of short fiber-reinforced plastics (SFRPs) into several pseudograins (PGs) is essential for understanding its effective mechanical behavior. However, conventional PG decomposition methodologies are limited by their high computational costs due to iteration-based algorithms. To address this, we propose a machine learning-assisted PG decomposition procedure that utilizes a series–parallel artificial neural network (ANN) system to facilitate the time-consuming decomposition process. To validate the effectiveness of our proposal, we implemented a two-step homogenization framework of SFRP that consists of the series–parallel ANN system, Mori-Tanaka model, and Voigt model into ABAQUS user material subroutine (UMAT). The elastic modulus values predicted by the UMAT are found to be in good agreement with both DIGIMAT-MF and experimental values, while also maintaining low computational time.

Effect of damage evolution on the auxetic behavior of 2D and 3D re-entrant type geometries

In this work, a mathematical formulation based on variational asymptotic method (VAM) has been proposed to determine the effect of damage on the auxetic properties of two-dimensional (2D) and three-dimensional (3D) re-entrant geometries. The influence of damage progression on the auxetic behavior was captured using a geometrically exact one-dimensional beam theory and an isotropic damage law, implemented in a nonlinear finite element framework. The effect of material degradation on the macroscale effective elastic properties such as the elastic modulus and Poisson’s ratio for the two-dimensional and three-dimensional re-entrant auxetic geometries was quantified. The mechanical behavior as predicted by the in-house Python-based implementation of the proposed VAM-based formulation is verified with the results from the commercial finite element solver Abaqus, wherein the user material subroutine was used to capture damage evolution. The numerical examples presented in this paper reveal that the macroscale auxetic behavior of the geometries was affected significantly by damage progression. The results of this research will provide insights into the design and analysis of auxetic materials for applications that warrant consideration of damage evolution.

Study on predicting rolling contact fatigue of pitch bearing raceway in offshore wind turbine

Pitch bearing is the critical component that are widely used to ensure the operation of offshore wind turbine blades and enable efficient capture of wind energy. Uncertain environmental factors and extreme load conditions can induce early fatigue failure in pitch bearings, and lead to major accidents such as blade detachment. In this study, a damage coupling fatigue simulation model, considering residual stress (RS) and surface hardness effect, was constructed following the continuum damage mechanics (CDM) to investigate the rolling contact fatigue (RCF) of pitch bearing under ultimate loading conditions. Different ultimate loading conditions were calculated on an integrated load simulation platform established using Python script. The damage-coupled elastoplastic constitutive equation and damage-controlling equations considering RS and surface hardness were derived and programmed in the material user subroutine UMAT. The effects of ultimate loading conditions, RS, and surface hardness on RCF were studied. Results show that increasing the surface hardness or increasing the compressive RS enhances the anti-fatigue performance of pitch bearing.