User Subroutine Research Articles

NUMERICAL IMPLEMENTATION OF THE TSCHOEGL–CHANG–BLOCH NONLINEAR VISCOELASTIC CONSTITUTIVE LAW FOR UNVULCANIZED CARBON BLACK–FILLED RUBBERS

ABSTRACT Rubber engineering design analysis requires a fundamental understanding of the mechanical behavior of polymers, especially in their unvulcanized state. It necessitates the establishment of a three-dimensional constitutive material to account for the observed mechanical behavior. This law is required to produce realistic descriptions of the viscoelastic performance in a mathematically simple form that is easy to implement in engineering applications. This article describes the theory of the Tschoegl–Chang–Bloch time-dependent nonlinear viscoelastic constitutive law. The experimental verification of this law is provided under different deformation fields and multiple load steps. Laboratory test procedures to obtain the parameters required to describe the material under consideration are provided in detail. A recursive form of the constitutive law, suitable for finite element application, is derived and coded in the finite element commercial code Abaqus via the user subroutine UMAT. Comparisons between the experimental observations, the theoretical results, and the numerical data are drawn for simple test models examined under creep or shear relaxation conditions. The excellent agreements observed indicate the suitability of the governing law in analyzing viscoelastic problems of unvulcanized carbon black–filled rubbers.

Multiphysics Study of Thermal Profiles and Residual Stress in Welding.

One of the effects of welding is residual stress. Welding involves complex tests concerning differences in values of the mechanical parameters of its regions as an effect of residual stress. Such multiphysics characteristics of welding pose a challenge in predicting residual stress. In the present study, a thermo-mechanical constitutive model considering phase transformation and transformation plasticity is implemented in the numerical model in ABAQUS user subroutines. In order to consider phase evolution in welding, the metallurgical parameters for Leblond's phase equation were obtained from the calibration of DH36 steel with a CCT diagram. In addition, the effects of welding speed on thermal profiles and residual stress generation were investigated. Analysis has suggested that the width of the heat-affected zone (HAZ) decreases with an increase in welding speed, and the phase fraction is significantly affected by this kind of parameter. Such phase transformation has led to the generation of a compressive stress in the fusion zone (FZ) and HAZ. The volume difference between coexisting phases produces a compressive stress in cooling, and its magnitude was increased with martensite increasing.

Geometry Effects on Joint Strength and Failure Modes of Hybrid Aluminum-Composite Countersunk bolted Joints

This paper presents the effects of geometry parameters (width/hole diameter, and edge distance/hole diameter ratios) on the damage initiation and growth in the CFRP (Carbon Fiber Reinforced Polymer) composite-aluminum countersunk bolted joints. Strain gauge measurements conducted with an Instron testing machine along with a detailed 3D finite element model incorporating geometric, material, and friction-based contact nonlinearities were used to investigate the geometry parameters on the Progressive Damage Analysis (PDA) of the orthotropic material model. The PDA material model integrates the lamina nonlinear shear deformation, Hashin-type failure criteria, and strain-based continuum degradation rules, using the UMAT user subroutine in the MSC Software Corporation Patran-Nastran commercial software. The results showed that the geometry effects on damage initiation and failure modes are quite accurately predicted by the PDA material model, which proved to be computationally efficient, and therefore can predict failure propagation and damage mechanisms. Plate geometry is an important parameter in the design process of an adequate bolted joint while its effects on damage initiation and failure modes were quite accurately predicted by the analysis. The latter proved to be computationally efficient, and could successfully predict failure propagation and damage mechanism in hybrid metal-composite countersunk bolted joints.

Internal Pressure-Temperature Coupling Analysis Method for Thermal Decomposition of GFRP Composites Based on the Overlapping Elements Method.

A method of internal pressure-temperature coupling analysis for the thermal decomposition of GFRP composites under high-temperature conditions was established, which incorporates coupled calculations of heat transfer equations, the Arrhenius equation, Darcy's law, and the ideal gas state equation. Using the overlapping mesh method, the coupling calculation of temperature and internal pressure is realized based on the UMATHT and USDFLD user subroutines developed. Specifically, two user subroutines, UMATHT-1 and UMATHT-2, are used to define the heat transfer equation and gas diffusion equation separately. Numerical simulations are conducted to simulate the polymers' thermal decomposition in high-temperature environments. For glass fiber/vinyl ester composites and glass fiber/phenolic composites, the predicted temperature and pressure values are in good agreement with experimental measurements, and porosity and permeability are then analyzed. Due to the accumulation of thermal decomposition gases, inter-pressure within the material surged and reached a peak value. After that, it began to decrease, but the factors affecting the pressure decrease vary at different positions. Specifically, the pressure closest to the heating surface is influenced by the combined effects of decomposition rate, permeability, and porosity, while the pressure far away from the heating surface is only affected by the initial permeability. The pressure in the intermediate region may be influenced by both increased porosity and initial permeability.

On crashworthiness and energy-absorbing mechanisms of hygrothermal-aged CFRP structures subjected to quasi-static loads

Understanding the gradual performance degradation of carbon fiber reinforced polymers (CFRP) is critical for the design of engineering structures that are expected to be affected by hygrothermal environments. This study aims to investigate the effects of hygrothermal aging on the degradation mechanisms of the mechanical properties and energy absorption of CFRP structures. An experimental database comprising tensile, compressive, and shear tests for CFRP composite laminates (in this study) and axial crushing tests for energy-absorbing structures (from the literature) was constructed, in which all CFRP samples were immersed in deionized water to achieve a saturated water-absorption state. A material constitutive model considering the effects of water absorption and temperature was developed and implemented via the user subroutine VUMAT of the ABAQUS software. The simulated results correlated well with the experimental measurements. Simulation results of axial crushing indicated that the degradation of the inter-layer properties tends to worsen the mismatch between the intra-layer and inter-layer properties, thus significantly degrading the load-carrying capability. Owing to degradation in compressive fracture toughness, the simulated results showed reduced post-crushing integrity, thus indicating a favorable effect on the load-carrying capability.

Study on the performance of reciprocating seals under the coupling effect of elastohydrodynamic lubrication and rubber wear

Due to the lack of research on the sealing performance of reciprocating combined seals under the coupling of elastohydrodynamic lubrication and rubber wear, this paper uses the UMESHMOTION user subroutine and the improved Archard model to realize the dynamic wear process of the combined seals and the adaptive meshing of the local area to simulate the wear of the seals. At the same time, combined with the elastohydrodynamic lubrication model of the toothed slip ring combined seal ring, the sealing performance of the reciprocating combination under mixed lubrication conditions is studied. Finally, the accuracy of the model is verified by building a two-cylinder reciprocating seal test bench with more accurate measurement. The results show that the influence of the change of fluid pressure on the wear of the seal lip is greater in the fast wear stage than in the stable wear stage. The influence of the change of interference on the wear of the sealing lip is small at different wear stages. The wear of the sealing lip has a significant effect on the sealing performance of the instroke, but has little effect on the sealing performance of the outstroke.

Experimental and theoretical study of stress relaxation in high-density polyethylene

Stress relaxation of high-density polyethylene is addressed both experimentally and theoretically. Two types of stress relaxation testing are carried out: uniaxial tensile testing at constant test specimen length and compression testing of a 3D structure producing inhomogeneous deformation fields and relaxation. A constitutive model for isotropic, semi-crystalline polymers is also proposed. The model has the ability to model stress relaxation at different time scales. The developed model was implemented as a user subroutine in Abaqus (UMAT). The implicit integration scheme including an algorithmic tangent modulus is described in detail. The material model is calibrated by use of the uniaxial tensile tests, and the model is then validated by simulating the compression tests of the 3D structure. The model is able to describe the uniaxial tension tests well, and the comparison between the simulations and experimental testing of the 3D structure shows very good agreement.

Modeling of rigidly-constrained pure shear dielectric elastomer actuators: electromechanical coupling network method

The rigidly-constrained pure shear dielectric elastomer actuator (PS-DEA) has become one of the critical configurations in linear soft actuator design due to its excellent uni-directional actuation performance and convenient preparation process. However, the theoretical analyses are primarily conducted by employing ideal models and lack consideration of the lateral necking deformation of PS-DEA, which has an essential impact on the performance evaluation and optimal design of PS-DEA. Therefore, in this paper, a user subroutine that describing the behavior of the electromechanical behavior of DE in terms of the Gent free-energy model is developed, and then a parametric model of the PS-DEA is established. Different combinations of actuator parameters are obtained by Latin hypercube sampling, and the actuator’s performance under the parameters is simulated by the finite element method. The finite element results are taken as a sample set, and a BP neural network with three hidden layers is employed to train the samples and obtain a PS-DEA network prediction model, which is experimentally analyzed to validate its accuracy and effectiveness. The prediction model explores the influence of geometric and pre-stretching parameters on the actuator’s performance and obtains the difference between the ideal theoretical and the network prediction model under various parameters. The method in this paper provides a new design methodology and theoretical basis for developing high-performance DE actuators.

Exploring Advanced Functionalities of Carbon Fiber-Graded PEEK Composites as Bone Fixation Plates Using Finite Element Analysis.

This study aims to address the challenges associated with conventional metallic bone fixation plates in biomechanical applications, such as stainless steel and titanium alloys, including stress shielding, allergic reactions, corrosion resistance, and interference with medical imaging. The use of materials with a low elastic modulus is regarded as an effective approach to overcome these problems. In this study, the impact of different types of chopped carbon fiber-reinforced polyether ether ketone (CCF/PEEK) functionally graded material (FGM) bone plates on stress shielding under static and instantaneous dynamic loading was explored using finite element analysis (FEA). The FGM bone plate models were established using ABAQUS and the user's subroutine USDFLD and VUSDFLD, and each model was established with an equivalent overall elastic modulus and distinctive distributions. The results revealed that all FGM bone plates exhibited lower stress shielding effects compared to metal bone plates. Particularly, the FGM plate with an elastic modulus gradually increased from the centre to both sides and provided maximum stress stimulation and the most uniform stress distribution within the fractured area. These findings offer crucial insights for designing implantable medical devices that possess enhanced mechanical adaptability.

Numerical modeling for shearing of unidirectional carbon fiber reinforced plastic laminates by means of near-net-shape blanking

Structural components made of carbon fiber reinforced plastics (CFRP) exhibit a high degree of lightweight suitability. In order to fulfill geometric and functional requirements, a finishing process step of outer and inner contours is necessary. Near-net-shape blanking processes show potential for economical finishing of CFRP structural components. For the knowledge-based design of a near-net-shape blanking process comparable to fine blanking an understanding of the separation mechanisms during shearing of CFRP laminates is required. Therefore, this paper deals with the development of a finite element (FE) process model for near-net-shape blanking of unidirectional (UD) CFRP laminates with different fiber volume fraction and fiber orientation. Material modeling of the UD CFRP laminates was carried out by means of experimental characterization based on tensile, compression and shear tests. The formulation of the material model was implemented using a VUMAT user subroutine. The application of the blank holder and counter force was realized using a kinematic model based on a VUAMP user subroutine. A validation based on experimental near-net-shape blanking tests will be conducted in the next step.

NUMERICAL IMPLEMENTATION OF THE TSCHOEGL–CHANG–BLOCH NONLINEAR VISCOELASTIC CONSTITUTIVE LAW FOR UNVULCANIZED CARBON BLACK–FILLED RUBBERS

ABSTRACT Rubber engineering design analysis requires a fundamental understanding of the mechanical behavior of polymers, especially in their unvulcanized state. It necessitates the establishment of a three-dimensional constitutive material to account for the observed mechanical behavior. This law is required to produce realistic descriptions of the viscoelastic performance in a mathematically simple form that is easy to implement in engineering applications. This article describes the theory of the Tschoegl–Chang–Bloch time-dependent nonlinear viscoelastic constitutive law. The experimental verification of this law is provided under different deformation fields and multiple load steps. Laboratory test procedures to obtain the parameters required to describe the material under consideration are provided in detail. A recursive form of the constitutive law, suitable for finite element application, is derived and coded in the finite element commercial code Abaqus via the user subroutine UMAT. Comparisons between the experimental observations, the theoretical results, and the numerical data are drawn for simple test models examined under creep or shear relaxation conditions. The excellent agreements observed indicate the suitability of the governing law in analyzing viscoelastic problems of unvulcanized carbon black–filled rubbers.

Offshore foundations in low-plasticity cohesive soils: Cyclic degradation experimental evidence and simplified numerical analysis

The paper studies the effect of soil strength and stiffness degradation on the undrained cyclic performance of offshore foundations in low-plasticity cohesive soil using 3D finite element modelling. Cyclic triaxial tests on reconstituted kaolin are conducted at the ETH Zurich laboratory, providing insights into key parameters affecting the degradation process. A simplified soil constitutive model accounting for cyclic degradation is developed and encoded in Abaqus via a user subroutine. The model is calibrated against experimental results and validated with published centrifuge model tests of monopiles under cyclic lateral loading. It is subsequently used to evaluate the performance of suction caisson foundations with different aspect ratios (L/D = 0.5 and 2) under short-term cyclic and seismic loading. Due to its ductile resistance mechanism, the L/D = 0.5 caisson exhibits superior performance under vertical cyclic loading in fast-degrading soil. Under inclined cyclic loading, the slower degradation rate of the L/D = 2 caisson governs response, reversing the trend. Under seismic shaking, the degradation-induced resistance imbalance amplifies the irrecoverable settlements produced by kinematic shearing at the caisson sidewalls. For the fast-degrading soil examined, degradation is shown to increase settlements by up to 50%.

Strain rate-dependent failure modelling of impact damage in laminated CFRP structures

This work focuses on the development, implementation, and validation of a constitutive model for unidirectional composites, aiming to numerically simulate impact damage in laminated structures. The model incorporates a failure criterion that accounts for the influence of strain rate on failure initiation and distinguishes between four failure modes. Failure initiation criteria are 3D phenomenological-based criteria according to the previous work of Puck and Schürmann (1998) and Pinho (2006). Additionally, a mesh-objective damage propagation model is implemented to simulate the impact damage. The impact simulations are performed using Abaqus/Explicit, with the constitutive model implemented through the user subroutine VUMAT. Validation of the strain rate effects on failure initiation is performed using strain rate-dependent bi-axial failure curves for IM7/8552 and AS-4/3506. The analyses indicate that the properties governing the strain rate dependence of failure initiation are consistent. Therefore, the hypothesis was tested in which the same strain rate scaling approach could be used for CFRP materials for which only static properties are available. This hypothesis was tested in high and low-velocity impact simulations at laminated IMS60/977–2 CFRP plates. The results demonstrate that the model accurately replicates the experimentally observed impact-induced contact forces and effectively captures the damaged state in the impacted plate.

Research on dynamic deformation behavior and constitutive relationship of hot forming high strength steel

To accurately characterize the dynamic deformation mechanical properties of hot forming steels 6Mn6 and 22MnB5 under collision conditions, quasi-static tensile tests (0.001s−1) and Hopkinson compression bar tests (∼2000s−1, ∼3000s−1, ∼4000s−1) were conducted to analyze the influence of strain rate on the material mechanical properties. Based on the experimental results, four constitutive models including Johnson-Cook (JC), modified JC (m-JC), Cowper-Symond (CS), and Khan-Huang (KH) models were established for both 6Mn6 and 22MnB5. Additionally, a modified model based on the Swift-Voce strain hardening model coupled with the Cowper-Symond model was proposed. A numerical simulation model for compression bar tests was developed using JC and m-JC models. The experimental results indicate that both hot forming steels exhibit strain rate sensitivity, with 6Mn6 performed a more pronounced effect than 22MnB5. The average absolute error (AARE) and correlation coefficient (R) of the m-JC and CS models were 0.99 and 0.29 %, 0.95 and 0.4 %, respectively. The dynamic deformation behavior of 6Mn6 and 22MnB5 at high strain rates was accurately predicted. Comparing with the JC model, the utilization of the m-JC user subroutine has resulted in a significant improvement in simulation accuracy by 58 % and 84 % for these two materials, which laying a solid foundation for high-precision vehicle collision simulation.

Numerical and analytical investigations on tensile behavior of thick rubber bearings

Thick rubber bearings (TRBs) are used for the mitigation of subway-induced vibrations in over-track buildings. TRBs might be loaded in tension in tall buildings, thus their tensile behavior needs to be explored. This paper performs numerical and analytical investigations on the tensile properties of TRBs. First, constitutive laws describing the rubber material under tension beyond cavitation were developed via a two-phase softening model, using the UHYPER user subroutine in ABAQUS. Then, parametric FE analyses were carried out to explore the effects of the shape factors, the thickness of the steel shims and the offset displacement on the tensile properties of TRBs. The numerical results showed that decreasing the first and second shape factors reduced the tensile stiffness of bearings, although the influence of the first shape factor seems marginal, when it is larger than 10. The code specified steel shim thickness (2 mm) seemed adequate, while reducing it to 0.5 mm or 0.2 mm could lead to local buckling of the shims, especially for bearings of lower first shape factors. The reduction of the tensile stiffness and yield force due to shear displacement was quantified. Finally, an analytical model that captures the tensile behavior of the bearings under cyclic loading was proposed and validated on published experimental tests.

Numerical Simulation of a Masonry Arch Bridge with Initial Defects Based on Cohesive Elements

Most of the existing masonry bridges have been in service for a significant duration, and as a result of construction limitations, these structures often exhibit intricate geometric defects. Furthermore, under prolonged loading conditions, the rheological behavior of rock can induce deformation in masonry bridges, leading to a continuously evolving stress state. Employing an idealized model for safety assessment frequently results in an overestimation of their load-bearing capacity. To accurately evaluate the load-bearing performance and remaining service life of masonry bridges, as well as to prevent safety incidents, this study employs a parametric approach to establish a two-phase numerical model of masonry bridges. In this model, cohesive elements are introduced to simulate the bonding relationship, while the distribution pattern of geometric initial defects is determined based on the theory of conditional random fields. Additionally, the rheological behavior of rock is incorporated through a custom-written Abaqus user subroutine. Building upon this foundation, the probability distribution of the load-bearing capacity of masonry bridges is reconstructed using the maximum entropy method with fractional moment constraints. The resulting outcomes are compared and validated against those obtained using the decomposition conditional correlation matrix. Finally, the effectiveness and applicability of the proposed method are demonstrated through numerical simulations and field measurements conducted on an actual bridge. The findings reveal that the method introduced in this paper adequately accounts for the stochastic nature of geometric initial defects, objectively reflects the operational performance of masonry bridges, and effectively simulates the complete failure process of such structures. Consequently, this method provides a solid basis for the safety assessment of masonry bridges.

Modeling strain-induced martensitic transformation in austenitic stainless steels subjected to cryogenic temperatures using incremental mean-field homogenization schemes

Austenitic stainless steels are commonly used as structural materials in high-field superconducting magnet systems because they retain high strength, ductility, and toughness at very low temperatures, and they are paramagnetic or antiferromagnetic under the Néel temperature in their fully austenitic state. However, they are susceptible to strain-induced martensitic transformation, especially at cryogenic temperatures, which modifies the material properties, induces volume changes and additional strain hardening, and leads to ferromagnetic behavior. Thus, accurate predictions of the structural performance of these materials at very low temperatures are of great interest for the conception and design of these cryo-magnetic systems. In this paper, we propose an adequate constitutive model for the evolving bi-phase material—austenite and martensite—based on a Hill-type incremental formulation. Two different versions of the model are proposed based on the linear mean-field homogenization scheme: Mori-Tanaka and Self-Consistent. Moreover, a rate-independent nonlinear mixed kinematic-isotropic hardening law is used for each phase, and the martensitic transformation is described by the nonlinear kinetic law proposed by Olson and Cohen (1975). The constitutive model is implemented in ABAQUS/Standard through a UMAT user subroutine, for which a return mapping algorithm based on the implicit backward Euler integration scheme is used and a closed-form expression of the consistent Jacobian tensor is provided. The Mori-Tanaka and Self-Consistent approaches are evaluated in terms of their ability to describe the mechanical behavior of the bi-phase aggregate by comparing the predictions of the homogenization schemes with unit-cell finite element calculations with an explicit description of the martensite inclusions and the austenite matrix. The comparison is carried out for different stress states with controlled triaxiality and Lode parameter under monotonic and cycling loading, paying special attention to the evolution of the mechanical fields in each phase. The unit-cell calculations are performed for both constant and evolving martensite volume fractions. In addition, numerical simulations of tensile tests on samples subjected to different initial temperatures are carried out for the transforming bi-phase material and the results are compared to experimental data for AISI 304L and AISI 316LN steels.

Fully coupled thermo-hydro-mechanical model with strain-dependent properties for numerical simulation of heavy oil production

Strain-dependency of permeability is a key feature for coupled multiphysics phenomena during heavy oil production under steam stimulation. This feature is also the basis for accurate estimation of steam needed to properly stimulate a given target heavy oil block. In this study, a fully coupled thermal-hydro-mechanical model is established and applied to the numerical simulation of steam injection in a block of western China Xinjiang region's heavy oil field. Strain-dependent relationships have been established for hydraulic conductivity as well as Young's modulus of reservoir formations. The distribution of reservoir temperature field and pore pressure field is obtained, and a quantitative evaluation of steam injection effectiveness is provided. The principal contents include: 1) A simplified fully coupled thermal-hydro-mechanical model for heavy oil reservoir under steam injection is presented. The model incorporates strain-dependent characteristics for rock's permeability/hydraulic conductivity and elastic modulus. 2) The simplified fully coupled model is implemented via the user subroutines of Abaqus software, and 3D finite element simulations are conducted for the steam stimulation operation and oil production processes in the heavy oil block. The temperature field and pore pressure field of the reservoir are obtained under given production history and steam injection conditions. These numerical results have provided an accurate evaluation of steam injection effectiveness. These numerical results indicate that: 1) The original design of steam injection volume and soak time is insufficient to connect the temperature rise regions around wells A1 and A2 in the block in order to get ideal production rate. The temperature rise data obtained from monitoring wells verify the accuracy of the calculation results, demonstrating the accuracy and practicality of the proposed theoretical model. 2) It is found that the maximum local pore pressure induced by steam injection may exceed the bottomhole pressure of injection wells. This is due to the thermal expansion of both solids and pore fluids caused by rapid temperature rise. 3) For the target reservoir, numerical results indicate that further steam injection for 17 days on top of the original design will connect the temperature rise regions around wells A1 and A2, and the minimum temperature at various points between wells will exceed 40 °C.

Room-to-low temperature thermo-mechanical behavior and corresponding constitutive model of liquid oxygen compatible epoxy composites

The room-to-low temperature (RT-LT) mechanical behavior of liquid oxygen-compatible epoxy composites (LOC-EP) is of great importance in the strength analysis of lightweight liquid oxygen tanks. This article first explores the tensile-compressive mechanical behaviors of LOC-EP from RT down to −183 °C. The results show that compared with RT, the tensile strength, compressive strength, and elastic modulus at −183 °C increase by 44%, 109%, and 160% respectively. Secondly, based on the theories of molecular chain freezing degree and yield surface extension, a ductile-brittle transition T of −60 °C and a completely brittle T of −90 °C are obtained sequentially. Moreover, a universal thermal-mechanical constitutive model for EP is derived, and the constitutive model parameters of LOC-EP from RT to −183 °C are fitted and calibrated using Matlab. Finally, the proposed constitutive model is introduced into Abaqus through a user subroutine. On the one hand, three-dimensional one-element analyses demonstrate that the simulation curves are highly consistent with the experimental and Matlab-fitted curves (errors less than 3%) with good convergence/accuracy. On the other hand, the fracture modes obtained from macroscopic simulations of tensile and compressive specimens are also coherent with the experimental fracture modes.

Wire Arc Additive Manufacturing: A Study of Process Parameters Using Multiphysics Simulations

In this work, analyses focus on understanding the effects of the scanning pattern and speed on the thermal profile, phase transformation, and residual stress generation in the WAAM deposition. An FE numerical model is constructed that takes into account the phase evolution and transformation plasticity using the ABAQUS user subroutine, UMAT. The results show that the scanning pattern significantly affects the heat accumulation and the cooling rate during the AM deposition, and, eventually, the generation of residual stresses. According to the simulation results, the highest residual stress is generated in the case of the out–in scanning, while the alternate pattern leads to the lowest residual stress. The influence of the scanning speed on the thermal profiles and residual stress are also examined. The analyses show that an increase in the scan speed leads to a decrease in the peak temperature and an increase in the cooling rate, which result in an increase in the martensite volume fraction of the deposition.