User-defined Material Subroutine Research Articles

Trans-scale analysis of 3D braided composites with voids based on micro-CT imaging and unsupervised machine learning

Voids are unavoidable during the manufacturing of 3D braided composites. This study proposes an unsupervised machine learning method combined with micro-computed tomography (micro-CT) scanning and a progressive damage analysis to analyze defects in these composites at a trans-scale level. The method enables the creation of real multiscale models and the determination of the porosity in both the intra-yarn (1.52 %) and inter-yarn (5.04 %) planes. Here, the unsupervised machine learning method is introduced in a trans-scale damage analysis to reduce calculation dimensions and to visualize the clustering data. A user-defined material subroutine (UMAT) is also developed to implement the trans-scale damage model. The experimental validation of the simulation results demonstrates the effective trans-scale damage analysis, showing the predominant pull-shear damage in the yarns, which is primarily located at the interfaces both between the yarns and between the yarns and the matrix. Finally, based on the scanned geometric data the degradation in modulus and strength of 3D braided composites with porosity is studied.

Effect of temperature on post-yield behavior of PVC foams

Experiments were conducted on Divinycell HCP30 foam to develop equations predicting its elastic and post-yield behavior from − 40 to + 60 °C. In these experiments, the foam was subjected to post-yield cyclic tension, compression and shear and monotonic biaxial tension and compression loading in the environmental chamber of an MTS servo-hydraulic machine. Elastic modulus and yield strength of the foam were found to decrease linearly with increasing temperature and could be expressed by a single equation in terms of room temperature properties. Post-yield behavior involved plasticity, viscoelasticity, and damage. An elastic–plastic viscoelastic damage model was used to predict post-yield behavior of the foam at different temperatures. Temperature dependent plastic hardening and viscoelastic damage functions were extracted from the experimental results and used to simulate elastic and post-yield stress–strain behavior in ABAQUS Explicit using a user-defined material subroutine. The ABAQUS user-defined material was validated with experiments on Divinycell HCP30 foam sheets at various temperatures. Good comparisons were found between ABAQUS and experimental results.

Finite Element Method of Functionally Graded Shape Memory Alloy Based on UMAT

Functionally graded shape memory alloy (FG-SMA) is widely used in practical engineering regions due to it possessing the excellent properties of both FG material and SMA material. In this paper, the incremental constitutive equation of SMA was established by using the concept of a shape memory factor. On this basis, the secondary development function of the ABAQUS software 2023 was used to write the user-defined material subroutine (UMAT). The phase transformation and mechanical behavior of transverse and axial FG NiTi SMA cantilever beams under concentrated load at free ends were numerically simulated by discrete modeling. Numerical results show that the stress and shape memory factor were distributed asymmetrically along the thickness direction of the transverse FG-SMA cantilever beam, while the stress and the shape memory factor distributed symmetrically along the thickness direction of the cross section of the axial FG-SMA cantilever beam. The bearing capacity of the axial FG-SMA cantilever beam is stronger than the SMA homogeneous cantilever beam, but weaker than the transverse FG-SMA cantilever beam. The load-bearing capacity of the transverse FG-SMA cantilever beam is twice that of the axial FG-SMA cantilever beam under the same functionally graded parameters and deflection conditions. The discrete modeling method of FG-SMA beams proposed in this paper can simulate the phase transformation and mechanical behavior of an FG-SMA beam well, which provides a reference for the practical application and numerical calculation of FG-SMA structures.

Nonlinear electromechanical responses in multi-layered fiber-reinforced dielectric elastomer composites

The capabilities of dielectric elastomer actuators (DEAs) across various applications of soft smart materials constantly expands. However, the electromechanical behavior of multi-layer anisotropic dielectric elastomer composites (DECs), has not been studied accurately despite of its great potentials. Hence, this paper proposes a comprehensive coupled electromechanical model to address this issue and effectively capture various attributes of such an actuator including the number of layers and layers’ configuration. Using a coupled nonlinear model enables it to analyze multi-layer DECs with an unlimited number of layers, and reinforcing fiber families. A new user defined material subroutine is developed to explore the actuation performance of different multi-layer DECs such as binder, diaphragm, and tubular actuators. It provides a unique insight into effects of the number and arrangement of layers on the electromechanical performance of these actuators. Experimental results have been used for validation of developed model and numerical implementation. The results propose a practical tool for designing and optimizing fiber-reinforced multi-layer DECs based on objective purposes, contributing to developing more efficient and reliable electromechanical models for these materials.

Thermal-mechanical coupling in drilling high-performance CFRP: Scale-span modeling and experimental validation

The focus of this study is to explore a scale-span thermal–mechanical coupling method for predicting the dynamic mechanical progressive failure behaviors and predicting thermal damage during the drilling process of Carbon Fiber Reinforced Plastic (CFRP). Initially, a thermal conduction constitutive model of drilling CFRP was developed based on the proposed thermal distribution ratio calculation method. Meanwhile, a dynamic span-scale progressive damage constitutive model for CFRP, incorporating modified micromechanics failure criterion with bilinear damage evolution laws, was proposed, and a bilinear cohesive model, including three damage modes, is employed to simulate interlaminar delamination. Subsequently, a user-defined material subroutine VUMAT was implemented on the ABAQUS/Explicit platform to simulate the thermal–mechanical coupling behaviors of drilling T700S-12K/YPH-23 CFRP using a twist drill bit. Finally, a comprehensive information monitoring platform for CFRP drilling experiments was established to validate the accuracy of the simulation results by considering drilling temperature, thrust force, and hole-wall morphology. The results demonstrate excellent agreement between the established thermal–mechanical coupling span-scale model and the experimental data. Furthermore, the simulation effectively captures the various damage behaviors and thermal conduction phenomenon, that occur during the intact drilling process.

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

Micromechanical modeling for analyzing non-linear behavior of flexible pavements under truck loading

This research paper presents a precise three-dimensional (3D) pavement model designed to accurately account for the detrimental effects of the asphalt layer while representing various layers within a pavement structure. The primary objectives of this study include the development of an accurate 3D pavement model, the integration of asphalt concrete's viscoelastic properties into the analysis, and the improvement of pavement distress prediction accuracy. To achieve these goals, a comprehensive approach was undertaken, involving a stress relaxation test to assess the viscoelastic properties of asphalt concrete. The study incorporates Prony series coefficients into the analysis, employing Finite Element Modeling Software Abaqus for an accurate representation of asphalt concrete behavior. The realistic geometry of asphalt concrete is captured using the Simpleware application, enhancing precision compared to Abaqus mesh geometry. Additionally, a user-defined material subroutine (UMAT) based on the Kelvin viscoelastic model is integrated into the finite element analysis within Abaqus. This approach significantly enhances predictions of vertical displacements and horizontal strains associated with common pavement distresses, surpassing conventional linear pavement modeling methods. Moreover, it offers improved accuracy in representing the actual geometry of asphalt concrete and enhances the prediction of wearing course performance, especially in high-temperature regions. By customizing the UMAT subroutine to simulate flexible pavement behavior, this research contributes to the advancement of pavement analysis and design.

Study on High-Velocity Impact Perforation Performance of CFRP Laminates for Rail Vehicles: Experiment and Simulation.

To study the perforation performance of CFRP laminates for rail vehicles under high-velocity impact from foreign objects, impact tests on CFRP laminates at a velocity of 163 m/s were carried out, and a corresponding finite element model was established using ABAQUS and verified. The user-defined material subroutine combined the material strain rate hardening effect and the 3D-Hashin damage criterion. The effects of impact velocity, impact object shape, and oblique angle on the perforation performance of CFRP laminates are discussed. Results show that impact velocity positively correlates with impact peak force and residual velocity. Laminates can be perforated by projectiles with a velocity above 120 m/s, and impact velocity greatly influences delamination below 140 m/s. Three shapes of projectile impacting laminates are considered: spherical, cylindrical, and conical. The conical projectile penetrates the laminate most easily, with the largest delamination area. The cylindrical projectile with a flat end suffers the most resistance, and the delaminated area is between the impact conditions of the conical and spherical projectiles. Increasing the angle of inclination increases the impacted area of the laminate and the extent of damage, thus dissipating more energy. The projectile fails to penetrate the laminate when the oblique angle reaches 60°. CFRP composite structures penetrated by high-speed impacts pose a significant threat to the safety of train operations, providing an opportunity for the application of bio-inspired composite structures.

Establishment and engineering application of viscoelastic-plastic constitutive laws for creep modeling in interbedded rock masses

In order to study the creep behavior of the surrounding rock of the interbedded rock mass tunnel considering the time-dependent deformation, this paper proposes a viscoelastic-plastic seven-element model considering the stress threshold, and derives and establishes its creep equation under three-dimensional stress state. At the same time, the UMAT (User-defined Material) subroutine of the model is developed based on the ABAQUS software. The rationality of the seven-element model and the effectiveness of the subprogram are verified by rheological test results. Finally, the UMAT subroutine is applied to the numerical simulation of the creep behavior of soft and hard interbedded rock tunnels with different rock inclinations (α). The results show that the different rock inclination angles have different effects on the horizontal displacement of the ground above the tunnel, settlement deformation, and the convergence of the tunnel section. With the increase of the rock inclination (0 ≤ α ≤ 90°), the horizontal displacement of the surface on both sides is antisymmetric. When α is 0°, 45° and 90°, the horizontal displacement on both sides is equivalent. Surface subsidence decreases and then increases slowly. When α is 0° and 45°, the surface subsidence is the largest (12.4 mm) and the smallest (11.1 mm), respectively. The convergence values of the tunnel section change according to different parts of the tunnel. The convergence values of the arch top and arch bottom decrease continuously, and their maximum convergence values are 23.4 mm and 17.3 mm, respectively. The change trend of the arch waist and arch shoulder convergence values is the opposite. When α is 0°, the convergence value of the arch waist is maximum (3.5 mm). When α is 15°, the convergence value of the arch shoulder is the maximum (2.0 mm).

Numerical Investigation of the Evolving Inelastic Deformation Path of a Solder Ball Joint under Various Loading Conditions

Solder joints of ball grid arrays (BGA) have been widely used to connect electronic components to printed circuit boards (PCBs) and are often subjected to mechanical stress. Several studies have been conducted on the mechanical reliability of solder joints. While these studies have been useful in the industry, detailed studies on how the inelastic deformation path of the solder ball joints evolves under specific loading conditions have not been sufficiently reported. This study aims to understand how the inelastic deformation path evolves when a solder joint is subjected to a constant external force by utilizing the theory of mechanics. It has also been found that the mechanical failure is strongly influenced by the evolution history of the deformation modes in materials. For this study, an elastoplastic constitutive model and a ductile fracture criterion were implemented into the vectorized user-defined material (VUMAT) subroutine of the ABAQUS program for finite element (FE) analysis. With the model, the evolution of the inelastic deformation path of a single solder ball under different loading conditions was numerically analyzed. Three loadings (shear, compression, and bending) were chosen as the basic loading conditions. In addition, combinations of the basic loadings resulted in three dual loadings and one complex loading. The simulation results showed that the shear and bending caused the fracture for both single and dual loadings, but when combined with compression, the fracture was suppressed. The results indicate that fracture is not solely determined by the magnitude of equivalent plastic strain but also by the evolution of inelastic deformation mode. This research offers an improved understanding of the significance of the inelastic deformation path and fracture.

Implicit integration with a substepping scheme of the zero-elastic range SANISAND-Z model for sand

The SANISAND-Z model is a zero-elastic range boundary surface model. The zero-elastic range makes the model incrementally nonlinear, and consequently, the system of ordinary differential equations of the model formulation is intrinsically implicit. Considering that the calculation results are heavily dependent on the integration step size when the backward Euler method is used to integrate the model, a two-stage diagonally implicit Runge-Kutta algorithm with a substepping scheme is proposed in this study. The substepping scheme is achieved by an embedded local integration error estimate. Based on the user-defined material subroutine interface UMAT of ABAQUS software, the SANISAND-Z model is numerically implemented with the proposed numerical integration algorithm. By monotonic and cyclic element tests and the case of strip footing loading, the performance of the proposed numerical integration algorithm is thoroughly investigated. The results show that the proposed algorithm is more accurate and efficient than the backward Euler method.

Simulation-based investigation on ultra-precision machining of additively manufactured Ti-6Al-4V ELI alloy and the associated experimental study

Additive Manufacturing (AM) has shown excellent research potential for biomedical implants, complex aerofoil structures, military applications, high-pressure cryogenic vessels, and automobile components. The mechanical properties exhibited by the additively manufactured Ti6Al4V ELI alloy components are significantly different from traditionally manufactured Ti6Al4V alloy due to the material anisotropy, orientation of the microstructure, and variation in heat treatments. Among AM techniques, SLM (Selective laser melting) offers unparalleled design flexibility with minimum impurities and high reproducibility. However, post-processing of additive manufactured components is essential due to their poor surface finish and lack of dimensional accuracy. Ti6Al4V ELI (Extra Low Interstitials) alloy is a difficult-to-cut material in Ultra-Precision Machining (UPM) due to its excessive tool wear, hardness, and chemical reactivity. Optimizing machining parameters for better surface finish by UPM is time-consuming and often not economical. Modeling and simulation provide a low-cost approach for the investigation of machining. In this work, a series of cutting experiments have been carried out on additively manufactured Ti6Al4V ELI alloy to study the cutting mechanism during UPM. In addition, Finite Element Model (FEM) is employed to understand the chip formation and cutting forces in UPM with a built-in Johnson-Cook (JC) model and a Johnson-Cook-TANH (JC-TANH) vectorized user-defined material subroutine (VUMAT) model. Cutting forces corresponding to the JC model and JC-TANH are examined with the experimental forces in literature, and the results are found to be fairly close.

Crash Performance of Inward-Inverting Composite Tubes Filled with Foam: Experimentation and Simulation.

This study presents a novel shock absorber with an inward-inverting composite foam-filled tube. Under the compression of a pressing cap and the action of an internal inversion cap, the composite tube inverted inward. During the crushing, the fronds of the composite tube compacted the foam, thereby enhancing the energy absorption. Three types of foams were applied to the absorber, and a drop-weight impact test was performed to obtain the assessment parameters. The foam increased the specific energy absorption (SEA) of the composite tube to 103 kJ/kg. Finite-element simulation based on the user-defined material subroutine was performed for the initial failure and stable stages of the crushing, and a foam model was identified through the experimental data. The mean crush force from the simulation agreed with the experimental data, and the SEA maximum error was <7%, thus validating the crush simulation of the proposed shock absorber. The development of the damage modes of the plies was analyzed based on the simulation results, showing a good energy absorption mechanism of this shock absorber.

Effect of evolutionary anisotropic hardening on the prediction of deformation and forming load in incremental sheet forming simulation

The incremental sheet forming (ISF) process typically accompanies large plastic strain without fracture exceeding uniform elongation or ultimate tensile strength (UTS) in the uniaxial tensile test. Therefore, ISF features improved formability compared to the conventional stamping process. Meanwhile, numerous studies have focused on modeling and simulation of formability in ISF where anisotropic yield function is one of the key constitutive laws for predicting sheet deformation. However, the conventional yield function is defined based on anisotropy of initial yielding, while the ISF modeling requires the deformation behavior at large strains beyond the UTS. In this study, an evolutionary anisotropic plasticity model is investigated based on Hill's 48 yield function combined with the non-associated flow rule; i.e., e-NAFR Hill's 48. The e-NAFR Hill's 48 model is implemented to the vectorized user-defined material subroutine in the commercial finite element software ABAQUS/Explicit. Then, the proposed FE model is applied to the forming of truncated cone, pyramid, and clover shaped single point incremental forming (SPIF) of an aluminum alloy 6014-T4 sheet. The simulated part profile, thickness variation, and forming force are compared with those of experiments. The evolutionary constitutive model shows an average accuracy of 99.15% in thickness prediction and 94.22% accuracy in forming force, demonstrating the importance of evolutionary sheet anisotropy in the SPIF process.

Effect of incorporating Lode angle into fracture criterion on predicting ballistic resistance of 6061-T651 aluminum alloy plates with different thicknesses struck by blunt projectiles

According to existing research, in addition to the second deviatoric stress invariant, Lode angle parameter (hereinafter abbreviated as Lode angle), which is related to the third deviatoric stress invariant, is also required to be taken into account when studying plastic flow and failure of metal materials. In order to study the effect of incorporating Lode angle into fracture criterion on predicting ballistic resistance of 6061-T651 aluminum alloy plates, a one-stage gas gun system was used to conduct ballistic tests of 6061-T651 aluminum alloy plates with different thicknesses when struck by the blunt projectile with a diameter of 12.66 mm and a mass of 34.0 g. Meanwhile, Abaqus/Explicit finite element software with user-defined material subroutine (VUMAT) was used to establish corresponding finite element models. Under the same constitutive model, numerical simulations were carried out by using Lode independent MJC fracture criterion and Lode dependent WMJC fracture criterion. It is found that when using MJC fracture criterion, not only the ductility of material is overestimated in low stress triaxiality state, resulting in significantly higher predicted ballistic limits; but also the predicted material fracture strain in high stress triaxiality state is negative, sometimes causing irrational predictions. Therefore, some modifications to MJC fracture criterion are needed to reasonably predict the impact process. By contrast, the predicted results of Lode dependent WMJC fracture criterion are more consistent with experiments. Besides, as the thickness of the target increases, the ballistic limit shows an “S” shaped growth trend. Overall, for ballistic tests of targets with different thicknesses, WMJC criterion has a better predictive effect than MJC criterion, indicating the importance of incorporating Lode angle into fracture criteria.

Numerical and experimental investigation on tensile fatigue performance of reinforced thermoplastic pipes

With the rapid development of offshore drilling for harvesting oil and gas from the deep sea, the fatigue performance of offshore risers is increasingly demanding. This study investigated the tensile fatigue performance of reinforced thermoplastic pipes (RTPs). The theory of three-dimensional (3D) anisotropic elastic mechanics was combined with a strain potential-energy density function to construct the 3D constitutive relation of RTPs. The stiffness degradation law of RTPs was predicted by introducing a modified 3D Hashin failure criterion and the residual stiffness model. A user-defined material (UMAT) subroutine was developed to evaluate the progressive fatigue failure process of RTPs. A uniaxial tensile fatigue experiment of RTPs was designed to validate the numerical model's correctness. The analysis examined the damage failure modes of RTPs under cyclic loading conditions and revealed the stiffness degradation mechanism. Results suggested that the matrix fatigue damage of the reinforced layer of RTPs is the primary cause of the rapid stiffness degradation, which was observed to be faster with increasing cyclic load stress levels.

An experimentally validated anisotropic visco-hyperelastic constitutive model for knitted fabric-reinforced elastomer composites

A new anisotropic visco-hyperelastic constitutive model has been developed to predict the time-dependent deformation response of flexible, knitted fabric-reinforced elastomer composites. These composites exhibit a time-dependent response due to the viscoelastic behavior of the elastomer, while the anisotropic reinforcement effect is attributed to the knitted fabrics. The proposed modeling approach features an invariant-based strain energy density function that incorporates the architecture of knitted fabrics and the hyper-viscoelastic behavior of elastomers. In this study, the elastomer is considered as a viscous neo-Hookean material, and the knitted fabrics are modeled as cords with negligible stiffness in bending. The proposed material model is implemented in commercial Finite Element Analysis (FEA) software, Abaqus (version 2017), through a user-defined material subroutine, UMAT. This approach enables the determination of the constitutive behavior of the composite based on the constituent elastomer, fiber properties, and fabric architectures. The proposed model is verified through a discrete 3D FEA model, in which the elastomer and fabric reinforcement are modeled explicitly. The approach is further validated through physical testing including uniaxial tension, torsion, and three-point bending. Since the proposed strain energy-based constitutive model can predict the deformation response of knitted fabric-reinforced elastomer composites based on the fabric architecture, it can be employed as an efficient modeling tool to aid the design of knitting pattern for target mechanical properties.

Experimental and numerical investigation on the failure behavior of multi-spar composite box under bending and shear

Multi-spar composite boxes (MSCB) are common elements in structural design due to their high load capacity in different loading conditions. This paper presents an experimental and numerical investigation of the failure behavior of MSCB subjected to a combined bending-shearing load. Quadratic failure criteria and mixed-mode strain energy release rate criteria are used to predict the onset and propagation of damage at the inter-laminar interfaces of the MSCB, which was implemented into Abaqus/Explicit analysis via a user-defined material subroutine VUMT. At last, a good agreement between tests and numerical prediction was observed.

Flexural behaviour modelling of carbon/epoxy laminates using the puck-EWM approach

ABSTRACTTo develop continuous fibre compos laminates and fabrics in the aeronautics and aerospace industry, a thorough understanding of the behaviour of these materials under various loading conditions is required. The purpose of this work aims to assess the failure of different composite materials subjected to a bending load, using the progressive damage approach. Puck’s failure criteria and gradual degradation model have been used to simulate the initial and the successive damage, respectively. A user-defined material (UMAT) subroutine has been developed and implemented through finite element software Abaqus. Moreover, the effect of geometrical parameters is performed and identified by the experimental protocol. The predicted results obtained by this numerical modelling show a good correlation with the findings of the experimental test.

Experimental study on high temperature tensile behaviour of aluminium alloy AA5083 with oscillating load

The flow behaviour of aluminium alloy AA5083 at 450 ^circ C has been investigated under quasi-static loading conditions with and without a superimposed oscillating load. Samples were placed under tensile load at constant strain rates ranging from 0.001 to 0.3 s^{-1}. A fixture was designed to generate the required sine-wave oscillation and was attached to the MTS tensile test machine along with a secondary, highly sensitive load cell. The frequencies of the imposed oscillations ranged from 5 to 100 Hz with an amplitude ranging from 0.02 to 0.5-N. It was observed that the imposition of oscillations influences the deformation behaviour of the material. Although the yield and tensile strength remain relatively constant, the total elongation is 8–23% higher under an imposed oscillating load. In addition, the thickness distribution profiles along the gauge length of the tensile specimens were investigated and it was observed that in the presence of oscillations the thickness distribution is more uniform. It was concluded that the presence of a superimposed oscillative load will result in greater deformation capabilities before fracture and postpone the occurrence of damage compared to conventional forming. This phenomenon was further explored utilising a user-defined material subroutine developed for the finite element solver LS-DYNA to simulate the conducted constant load tensile tests.