Material Constitutive Relations Research Articles

Study on Flexural Capacity of UHPC-NC Composite Slab with Reinforced Truss in the Normal Section

Ultra-high-performance concrete (UHPC) exhibits significantly higher tensile strength compared to normal concrete (NC). In this paper, the application of UHPC to the precast base plate of composite slabs was proposed, leading to the development of a reinforced truss UHPC-NC composite slab. This approach effectively enhanced the crack resistance of the slab. A finite element model (FEM) for the reinforced truss UHPC-NC composite slab was developed based on the ABAQUS (2016) platform, using appropriate material constitutive relationships for UHPC, NC, and steel reinforcement. The validity of the model was verified through comparison with relevant test results. Subsequently, the effects of parameters such as the cross-sectional area of the upper and lower truss chords, the reinforcement ratio of the precast base plate, the strength grade of the UHPC base plate, and the thickness of the UHPC base plate on the flexural capacity of the UHPC-NC composite slab were investigated. Finally, the equations for calculating the flexural capacity of the UHPC-NC composite slab were proposed. It was found that increasing the cross-sectional area of the lower truss chord improved the flexural capacity and stiffness of such slabs to some extent, though ductility was slightly reduced. On the other hand, increasing the upper chord cross-sectional area had limited impact on the flexural performance. Increasing the reinforcement ratio of the longitudinal reinforcement in the precast base plate significantly enhanced the load-bearing capacity and stiffness but similarly reduced ductility. As the UHPC grade of the precast base plate increased, the cracking load, yield load, and ultimate load of the slab also increased. However, when the UHPC grade exceeded C120, the improvement in flexural capacity became less significant. With an increase in thickness of the precast UHPC base plate, cracking, yield, and ultimate loads also rose, but ductility decreased. When the thickness of UHPC exceeded 60 mm, the increase in flexural capacity became modest. The proposed equations for calculating the flexural capacity of the reinforced truss UHPC-NC composite slab in the normal section agreed well with simulation results, providing theoretical and numerical support for the design and analysis of UHPC-NC composite slabs.

Nonlinear dynamic characteristics of smart FG-GPLRC sandwich varying thickness truncated conical shell with internal resonance for first three order modes

This paper examines the 1:1:1 internal resonant nonlinear dynamic characteristic of the simply supported varying thickness functionally graded graphene platelets reinforced composite (FG-GPLRC) smart truncated sandwich conical shell subject to the combined effects of transverse load and in-plane force. The truncated smart sandwich conical shell is composed of an FG-GPLRC varying thickness core and two magneto-electro-elastic face layers, whose material properties and constitutive relations are individually identified by the rule of mixture, improved Halpin-Tsai approach and generalized Hooke's law. Utilizing the first-order shear deformation theory (FSDT), von Karman's geometrical nonlinearity, Hamilton's principle and Galerkin technique, the 3DOF dimensionless nonlinear dynamic formulations for the truncated smart FG-GPLRC conical shell are established. The multiple-scale technique is applied to developing the averaged equations for the truncated smart FG-GPLRC conical shell under combined resonance. The frequency-response and force-response curves, Poincare maps, phase portraits, time history diagrams, bifurcation and maximum Lyapunov exponent diagrams can be portrayed by the nonlinear equation solver and Runge-Kutta approach. The effects of the damping and tuning parameters, transverse and in-plane forces on the 1:1:1 internal resonant nonlinear dynamic characteristic of truncated smart varying thickness FG-GPLRC sandwich conical shell are examined.

Jacobian vs. disturbance method for UMATs in ABAQUS: An application to isotropic damage mechanics

This paper compares the computational efficiency of different methodologies to estimate the tangent stiffness applied to ABAQUS standard UMAT user-subroutine, using implicit formulation with predictor corrector methodology. It uses two new methodologies to estimate the stiffness matrix for the predictor-corrector iterative process, named Disturbance Method and Implicit to Explicit Method. With the Disturbance Method, it is enough to build UMATs using only a secant matrix, since an approximate tangential material matrix is automatically computed, promoting a faster implementation of new material constitutive relations in the ABAQUS standard. It is also studied the possibility of the use of a new algorithm that transforms the UMAT implicit formulation to an explicit formulation using a new secant predictor corrector algorithm. In this study, a new concrete damage model that considers fracture energy regularization for both tensile and compressive behaviour with Mode I Fracture is utilized. Classical and known benchmarks to test damage models in the scientific community are used to compare both methods for the calculation of the Jacobian matrix in terms of time and number of iterations.

Small Punch Testing of a Ti6Al4V Titanium Alloy and Simulations under Different Stress Triaxialities.

The mechanical properties of local materials subjected to various stress triaxialities were investigated via self-designed small punch tests and corresponding simulations, which were tailored to the geometry and notch forms of the samples. The finite element model was developed on the basis of the actual test method. After verifying the accuracy of the simulation, the stress, strain, and void volume fraction distributions of the Ti6Al4V titanium alloy under different stress states were compared and analyzed. The results indicate that the mechanical properties of the local material significantly differ during downward pressing depending on the geometric shape. A three-dimensional tensile stress state was observed in the center area, where the void volume fraction was greater than the fracture void volume fraction. The fracture morphology of the samples further confirmed the presence of different stress states. Specifically, the fracture morphology of the globular head samples (with or without U-shaped notches) predominantly featured dimples. Modifying the specimen's geometry effectively increased stress triaxiality, facilitating the determination of the material's constitutive relationship under varying stress states.

Study on the effects of ultrasonic impact treatment on the local mechanical properties of welded joints based on the digital image correlation

In this study, UIT was used to strengthen the local mechanical properties of welded joints, and the influence of UIT on the local mechanical properties of welded joints was analyzed by 3D-DIC technology. At the same time, the mechanism of UIT on the microstructure and properties of welded joints was revealed by microstructure observation. By measuring the full-field strain process of the welded joint after UIT under uniaxial tensile load, the curve of the strain in the local area with time is obtained. At the same time, the Ramberg-Osgood equation and Considère criterion are used to fit the material constitutive relationship at each point in the local area. The results show that UIT significantly improves the yield strength of the WM and the tensile strength of the BM. This study provides technical and theoretical support for the preparation of high-quality welded joints by UIT technology.

Finite element method based modeling of cutting forces and cutting temperature in micro-milling LF21

The demands for aluminum alloy LF21 micro precision parts are increasing in the fields of aerospace, high-tech electronic products, and the other fields. Micro-milling is an effective technology for machining small LF21 precision parts. Cutting forces and temperature are crucial factors in micro-milling process, directly affect tool vibration, tool wear, and surface quality of the workpiece, and even result in large deformation of the tool and workpiece. Direct measurement of cutting forces during micro-milling requires high-precision and expensive instruments. Moreover, due to the small cutting area in micro-milling, it is challenging to achieve accurate measurements of cutting area temperature. Therefore, accurate prediction of cutting forces and temperature in micro-milling is urgent and challenging. Nowadays, there are few studies on prediction of cutting forces in micro-milling LF21. The study on prediction of temperature in micro-milling LF21 is still blank. To solve the above problems, this paper proposes a finite element method based on modeling for prediction of cutting forces and temperature in micro-milling LF21. ABAQUS software is adopted. First, the geometry models of the micro-milling tool and workpiece are established. Then, the assembly and mesh division of the established models are completed. Johnson-Cook constitutive model and Johnson-Cook damage criteria are used to describe the material constitutive relationship and chip separation criteria, respectively. The suitable tool-workpiece friction models are determined. Finally, the simulation of the micro-milling LF21 process is achieved. Experiments of micro-milling LF21 are conducted and the cutting forces are measured using the dynamometer. The validity of the built process simulation model and the correctness of the cutting force prediction results are verified by the comparison of experiment and simulation cutting forces. Then, the prediction of temperature is achieved based on the verified process simulation model of micro-milling LF21.

Machine-Learning Metacomputing for Materials Science Data

Abstract Materials science requires the collection and analysis of great quantities of data. These data almost invariably require various post-acquisition computation to remove noise, classify observations, fit parametric models, or perform other operations. Recently developed machine-learning (ML) algorithms have demonstrated great capability for performing many of these operations, and often produce higher quality output than traditional methods. However, it has been widely observed that such algorithms often suffer from issues such as limited generalizability and the tendency to “over fit” to the input data. In order to address such issues, this work introduces a metacomputing framework capable of systematically selecting, tuning, and training the best available machine-learning model in order to process an input dataset. In addition, a unique “cross-training” methodology is used to incorporate underlying physics or multiphysics relationships into the structure of the resultant ML model. This metacomputing approach is demonstrated on four example problems: repairing “gaps” in a multiphysics dataset, improving the output of electron back-scatter detection crystallographic measurements, removing spurious artifacts from X-ray microtomography data, and identifying material constitutive relationships from tensile test data. The performance of the metacomputing framework on these disparate problems is discussed, as are future plans for further deploying metacomputing technologies in the context of materials science and mechanical engineering.

On the elastic–plastic behaviors of centrifugal steam compressor impeller under cyclic thermomechanical loading

AbstractIn this paper, the cyclic elastic–plastic behaviors of the centrifugal steam compressor impeller (CSCI) structure under practical operating conditions are discussed employing the linear matching method (LMM). The three‐stage strategy of the LMM is employed to determine the shakedown and ratchet boundaries by conducting a series of iterative direct steady cyclic analysis, and based on this, the load regions corresponding to different types of damage behavior that may occur during the operation are identified. Computational results reveal slight contraction in the structural response diagram when considering actual material constitutive relationships, compared to ideal elastic–plastic models. Meanwhile, by integrating the unified ratchet and fatigue program with fatigue experimental data, a series of constant low‐cycle fatigue life curves has been presented for different service conditions. Furthermore, a comparison with detailed step‐by‐step inelastic analyses confirms the applicability and great efficiency of the LMM in practical engineering problems.

A time-domain integration method with equivalent complex damping model based on viscoelastic material constitutive relation

The complex damping model is only applied in frequency-domain. Based on the constitutive relation of viscoelastic materials, a vibration equation is equivalent to the constitutive relation of complex damping theory and the frequency response function satisfying the causality constraint. Compared with the existing equivalent complex damping model, the proposed equivalent damping model can consider more natural frequencies. The calculation formulas of Gauss precise integral method and improvement constant average acceleration method are derived. By the equivalent complex damping, the seismic time-history response of the typical example could carry on the numerical calculation. Compared with the Gauss precise integral calculation results of complex damping vibration equation, some conclusions can be analyzed. The proposed two methods could avoid divergent phenomenon in the time-domain numerical solution of complex damping vibration equation. The time-domain integral method of equivalent complex damping theory is stable and convergent. The Gauss precise integral method has strong equivalence and big computational complexity. The improvement constant average acceleration method has weak equivalence and small computational complexity.

Modified plastic damage model for steel fiber reinforced concrete

AbstractSteel fiber reinforced concrete (SFRC) structures have been widely adopted and attracted great research attention due to their excellent performance in resisting tension and flexure bending. However, the existing analytical and numerical analyses of SFRC structures rely mainly on the experimental data of material tests, thereby being suitable for a case‐by‐case basis. This is due to the lack of a general and reliable constitutive material model for SFRC, which analytically considers the fiber‐dependent parameters such as fiber geometry, fiber stiffness, and interface properties of fibers and concrete matrix. This study presents an approach to modify the concrete plastic damage model to represent the SFRC material constitutive relations for simulating the structural behavior of SFRC. In this approach, the general procedure to integrate the bridging effect of fibers through the pull‐out mechanism into the constitutive relation of SFRC was proposed. The comparison between the numerical and experimental results was conducted to verify the reliability of the proposed model. The results demonstrated the proposed model could well represent the material performance of SFRC and the numerical simulations could capture reasonably the effect of the volume fraction, geometry, and properties of fibers on the structural response of SFRC.

Static analysis of functionally graded porous beam-column frames by the complementary functions method

In this paper, an efficient and accurate numerical approach is implemented to examine the static behavior of Functionally Graded Porous (FGP) planar frames for the first time. The symmetric material constitutive relationship (SMCR), monotonic material constitutive relationships (MMCR), and uniform material constitutive relationship (UMCR) models are used to define the gradation of porosity along the thickness direction. The effects of porosity coefficient and material porosity distribution type on the static behavior of the FGP frames are investigated in detail. A direct relation between porosity coefficient and nodal deformations is observed.The effect of shear deformation is considered in the governing equations based on the Timoshenko Beam Theory (TBT). Within the scope of the presented procedure, fifth-order Runge-Kutta (RK5) algorithm is applied in the solution of the initial value problems. Imposing the rigidity matrix-based Complementary Functions Method (CFM) on the static analysis of the FGP planar frames is the novelty of this research. The results of the suggested approach are verified with the those of the finite element method (FEM), and those of the available literature. It has been carried out that type of the porosity distribution and porosity gradient index have an important impact on the response of FGP planar frames. By increasing the porosity coefficient, the displacement values of the frames made of UMCR and MMCR porosity distribution are affected more than those of the UMCR distributions. It can be noted that the SMCR can be preferred for designing the FGP beam-column structure as the minimum deformation values are obtained.

Lagrangian operator inference enhanced with structure-preserving machine learning for nonintrusive model reduction of mechanical systems

Complex mechanical systems often exhibit strongly nonlinear behavior due to the presence of nonlinearities in the energy dissipation mechanisms, material constitutive relationships, or geometric/connectivity mechanics. Numerical modeling of these systems leads to nonlinear full-order models that possess an underlying Lagrangian structure. This work proposes a Lagrangian operator inference method enhanced with structure-preserving machine learning to learn nonlinear reduced-order models (ROMs) of nonlinear mechanical systems. This two-step approach first learns the best-fit linear Lagrangian ROM via Lagrangian operator inference and then presents a structure-preserving machine learning method to learn nonlinearities in the reduced space. The proposed approach can learn a structure-preserving nonlinear ROM purely from data, unlike the existing operator inference approaches that require knowledge about the mathematical form of nonlinear terms. From a machine learning perspective, it accelerates the training of the structure-preserving neural network by providing an informed prior (i.e., the linear Lagrangian ROM structure), and it reduces the computational cost of the network training by operating on the reduced space. The method is first demonstrated on two simulated examples: a conservative nonlinear rod model and a two-dimensional nonlinear membrane with nonlinear internal damping. Finally, the method is demonstrated on an experimental dataset consisting of digital image correlation measurements taken from a lap-joint beam structure from which a predictive model is learned that captures amplitude-dependent frequency and damping characteristics accurately. The numerical results demonstrate that the proposed approach yields generalizable nonlinear ROMs that exhibit bounded energy error, capture the nonlinear characteristics reliably, and provide accurate long-time predictions outside the training data regime.

Meso-damage behaviour of cement-stabilised macadam after long-time immersion based on particle flow theory

Water can cause a certain degree of damage to cement-stabilised macadam (CSM), and the degree of damage is greater if CSM is immersed in water for a long time. In order to study CSM damage after lengthy water immersion, a discrete-element model of CSM was established. The Weibull distribution function was used to simulate the heterogeneous contacts between particles. The parallel bond model was used to simulate the material constitutive relationship. The microscopic parameters of CSM were obtained by trial-and-error method. The stress–strain curve was obtained from immersion tests. The micromechanical behaviour of the CSM after immersion was analysed. The results showed that the contact area and strength of the CSM immersed for 30 days were, respectively, 31.4% and 46% less than those of the non-immersed macadam. The force chains between particles were evenly distributed. At peak loading, the normal contact force between particles was much larger than the tangential contact force, and the vertical force chain was much larger than the transverse force chain. The distributions of cementation energy, friction energy and impact energy were not uniform in the middle/peak loading stage.

Mechanical properties of cement mortar with gamma-irradiated recycled plastic powder, pellet, and fiber

This study aimed to investigate the impact of gamma irradiated recycled polyethylene terephthalate (PET) pellets, powder, and fibers on the mechanical performance and ductility of cementitious mortar. The sensitivity to gamma irradiation was explored by varying the irradiation rate and total dose. The recycled PET additives employed in this experiment consisted of pellets and their different application forms: powder and fiber, containing 30 % recycled raw materials polymerized through a chemically recycled method. For comparison, plain mortar composite and virgin PET mortar composite were used as controls. When PET pellets partially replaced the aggregate, the compressive strength of the composite decreased significantly as the volume fraction of pellets increased. Conversely, specimens partially replaced by PET powder showed an overall increase in compressive strength compared to the control specimens, regardless of the volume fraction of powder, gamma irradiation rate, or total dose, with no change in ductility. To assess changes in tensile strength and ductility of the recycled PET fibers under different gamma irradiation rates and total doses, direct fiber tensile tests were conducted. The gamma-irradiated fiber specimens exhibited a slight increase in strength and ductility. This information allowed for the calibration of the tensile material constitutive relationship of PET fibers, which was subsequently used in nonlinear finite element analysis. The study also investigated the variation in direct tensile, compressive, and flexural strengths with different volume fractions of fiber. The results indicated that the strength enhancement was minimal, but the direct tensile and flexural tensile analyses predicted an enhancement.

Quantification of variability in simulated seismic performance of RC wall buildings

This paper quantifies the variability in the seismic performance of slender reinforced concrete (RC) wall buildings simulated using different fiber based nonlinear models. The models use the same material constitutive relationships and other analysis inputs (e.g., damping) so that the quantified variability in the building performance is caused by the numerical modeling approach rather than user-selected parameters. These models were first validated against the measured shake-table test behavior of a 7-story RC wall building. Then, nonlinear dynamic analyses of the 7-story wall test specimen and three RC wall archetype buildings of 4-, 8-, and 12-stories were conducted to quantify the variability in the resulting seismic performance assessment parameters and damage fragility curves. The variability in the numerical model responses was evaluated using ground motion suites corresponding to three hazard levels with 50%, 10%, and 2% probability of exceedance in 50 years, while the damage fragility curves were obtained following the FEMA P695 methodology. The variability was quantified based on global response parameters (interstory drift ratio and roof drift ratio) and local response parameters (plastic hinge rotation and curvature at the critical length), since these parameters are commonly used in seismic performance assessment of RC buildings. Based on the results, it is strongly recommended that the performance assessment of slender RC wall buildings be done using global response parameters rather than local response parameters, since the variability of the predicted response among the nonlinear models was significantly smaller for global response parameters.

Study on the evolution of material microstructure and constitutive relation during rail corrugation development

The difference between the evolution of wear mechanism, microstructure and constitutive relation of the near-surface material at the corrugation peaks and those at the troughs were studied using a twin-disc roller type set-up. The results show that the depths of corrugation increase gradually and tend to slow down at high running cycle numbers. Significant plastic deformation can be observed near the rail surface and subsurface. When the corrugation changes from uniform stage to steady stage, the thickness of the plastic deformation layer increases gradually and slows down and the wear mechanisms changes from adhesion to fatigue. The elastic modulus and hardness of material near rail surface were obtained at different wear stages during the development of corrugation and the material constitutive relations were established with the aid of finite element method. It is found that the yield stress at the peak is higher than the trough surface at the initiation and developing stages of corrugation, however, it is higher at the trough on the steady stage. The yield stresses of surface material was found to have a good correlation with the thickness of plastic deformation.

Hyperelastic constitutive model parameters identification using optical-based techniques and hybrid optimisation

AbstractIn this paper we propose a new optical-based technique to identify the constitutive relation coefficients of the hyperelastic material using a hybrid optimisation approach. This technique can be used in place of traditional mechanical testing of elastomers for applications that involve inhomogeneous deformation. The purpose of the proposed method is to identify the incompressible hyperelastic material constitutive relation coefficients using a single experiment under different loading cases. The method comprises sample surface 3D reconstruction and uses finite element simulations to replicate the experiments, and uses a hybrid optimisation technique to minimise the error between actual 3D deformations and FE simulation results. The proposed hybrid technique predicts the hyperelastic constitutive relation coefficients more accurately than other optimisation methods. This study introduces a novel approach by employing a subpixel image registration algorithm for 3D reconstruction. The method requires a single experiment with diverse loading cases to accurately determine the coefficients of hyperelastic constitutive relations. The setup is portable and can be accommodated in a small suitcase. For this purpose, an apparatus was constructed comprising a stereoscopic system with eight cameras and a six-degree-of-freedom force-torque sensor to measure the induced forces and torques during the experiments. We identified the constitutive relation coefficients of Ogden N1, Ogden N3, Yeoh, and Arruda-Boyce relations which are commonly used models for silicone materials, using a traditional uniaxial test, optical uniaxial test (experiments performed using a constructed optical system), and inhomogeneous deformations tests. The study demonstrated that the coefficients obtained from inhomogeneous deformation tests provided the most accurate FE predictions. It was also shown that hyperelastic constitutive relation coefficients obtained from traditional uniaxial tests are insufficient to describe the material behaviour when the material undergoes inhomogeneous deformations.

Expansion of consistent particle method to solve solid mechanics problems

AbstractOriginally developed for solving fluid dynamics problems, a Lagrangian particle method called the consistent particle method (CPM) is expanded to solid mechanics problems in this article. The motions of particles are governed by the mass conservation and dynamics equations which are solved by the second‐order predictor–corrector time stepping scheme. The spatial derivatives of variables required in solving the governing equations and computing strain increments are obtained by Taylor series expansion. Stress components are updated from strain components according to the material constitutive relation. The physical density of material is directly computed without using particle number density. No additional particles are needed for the simulation of boundaries. For boundary surface that is partially loaded, the inverse distance weighting method is applied to deal with the stress singularity problem due to sudden change of stresses. Numerical examples including shock wave propagation and large deformation of footing penetration are presented to demonstrate the capabilities of CPM in solving solid mechanics problems.

Eccentric compression behavior of Steel-FRP composite bars RC columns under coupling action of chloride corrosion and load

In order to investigate the eccentric compression behaviors of steel-FRP composite bar (SFCB) reinforced concrete (RC) columns subjected to chloride corrosion, the mechanical experiments of chloride corroded SFCBs and SFCBs RC eccentric compression columns were conducted. The effect of reinforcement type and ratio, eccentricity, slenderness, stress level and corrosion duration on bearing capacity, deformation, crack and failure pattern were investigated. The results showed that the strength retention ratio of reinforcement decreases with the increase of corrosion duration, the ultimate strengths of steel rebar, SFCB and FRP rebar decreased by 12.2%, 9.9% and 3.6%, respectively, when compared with those of uncorroded counterparts. With the increase of steel content of reinforcement, the load bearing capacity of eccentric compression RC column increases while the deformation decreases gradually. The load bearing capacity of corroded steel, SFCB and FRP RC columns maximally decreased by 16.6%, 12.4% and 7.2%, respectively, when compared with those of uncorroded counterparts. Based on the simplified materials constitutive relations and reasonable basic assumptions, formulae for discriminate failure mode, moment magnification factor and bearing capacity were developed. The predicted failure pattern, moment magnification factor and bearing capacity are in good agreement with the test results, confirming the validity of the proposed formulae, the results can be used as a reference for engineering application.

A Curved Plate-Flattening Method to Construct the Membrane Strain Distribution

The surface-flattening process has many applications in industries such as shipbuilding. Curved surfaces in the industry are usually formed from flat surfaces, so the target surface needs to be flattened to obtain its corresponding initial shape. In addition, the surface flattening process obtains the inherent strain distribution required in forming. Different forming methods in the plate forming process will produce different membrane deformations, such as shrinkage in the line heating and tensile in the roller forming. Therefore, different surface-flattening methods should be used to obtain the inherent strain distribution suitable for different forming methods. This paper proposes a method to perform the surface flattening using the finite element method and constrain the membrane strain generated in the flattening deformation by modifying the material constitutive relationship. Using a dual modulus material constitutive model in membrane deformation makes the surface more inclined to deform at locations with less stiffness during the flattening process. This method yields predominantly tensile or compressive membrane strain without changing the bending strain. By modifying the material model, this method can control the compressive strain region and the principal strain direction. The results of the proposed method applying to different surface shapes and its application in the surface-forming process are given in this paper.