Viscoelastic Constitutive Model Research Articles

Dynamic constitutive modeling of steel fiber reinforced concrete considering damage evolution under high strain rate

This study conducted quasi-static compression and splitting tensile tests on steel fiber reinforced concrete (SFRC), as well as dynamic compression tests using the split Hopkinson pressure bar (SHPB). The mechanical properties of SFRC with varying fiber contents and under different loading strain rates were examined separately. Experimental results indicate that the addition of steel fibers effectively enhances the properties of concrete. The dynamic mechanical performance of SFRC specimens (compressive strength, peak toughness, ultimate toughness, and energy absorption capacity) demonstrated a clear strain enhancement effect. The dynamic stress-strain curves of SFRC reveal the material's good viscoelastic properties. Then, a viscoelastic constitutive model for SFRC considering damage under high strain was proposed, with parameter fitting based on SHPB test results. The constitutive model was applied to the numerical simulation by the user-defined material (UMAT) in ABAQUS. The dynamic stress-strain curves and damage patterns obtained by numerical simulation are basically consistent with the test results. This further demonstrates that the proposed constitutive model effectively describes the dynamic characteristics of SFRC.

Storage Life of Particle-Filled Polymer Composites Considering Aging Effects.

This study investigates the storage life of particle-filled polymer composites (PFPCs) under the influence of aging effects. High-temperature accelerated aging tests were conducted at 60 °C, 70 °C, and 80 °C for various days to analyze the impact of aging time and temperature on the mechanical behavior of the materials. A predictive model for crosslink density was established using the Arrhenius equation, and the relationship between crosslink density and relaxation modulus was determined based on polymer physics theory. On this basis, a viscoelastic constitutive model that incorporates aging effects was developed. Structural analyses of a PFPC column with a length of 2.3 m and outer diameter of 1.8 m were performed using the UMAT subroutine in ABAQUS. Subsequently, a safety margin assessment method based on dewetting strain was employed to predict the storage life of the PFPC column. The results indicate that the aging viscoelastic constitutive model effectively characterizes the hardening effects caused by aging in the composites during storage. The storage life for the PFPC column considering aging effects decreases from 22 years to 19 years compared to models that ignore such effects. This approach provides a reference for estimating the storage life of PFPC columns considering aging effects.

Research on Viscoelastic Impact Damage Constitutive Model and Its Behavioral Characteristics

To investigate the damage characteristics of viscoelastic materials under various impact scenarios, this study presents a viscoelastic impact damage constitutive model that incorporates a material coefficient, a variable fractional-order differential operator, and a damage factor. Split Hopkinson Pressure Bar experiments are conducted under single-impact and repeated-impact conditions. The results indicate that nonlinear features in stress-strain curves at different stages, exhibiting prominent strain rate dependency near the stress peak point in the single-impact scenario. In the repeated-impact scenario, the stress peak points decrease as the impact times increase, resulting in a corresponding decline in the material's load-bearing capacity. Furthermore, strain rate escalates the strain rate increases with an increase in impact times, making the material more susceptible to deformation. Parameter fitting and Sobol sensitivity analysis utilizing experimental data from both scenarios have been employed to explore the effects and patterns of single-parameter and multi-parameter coupling on the model, accurately delineating their influence. The findings reveal a strong coupling relationship among various parameters of the viscoelastic impact damage constitutive model in multiple impact scenarios, showing higher sensitivity to fluctuations in the viscoelastic coefficient and damage factor. These analyses have demonstrated the accuracy of the viscoelastic impact damage constitutive model in capturing dynamic impact damage characteristics of viscoelastic materials across various scenarios.

The role of unit cell topology in modulating the compaction response of additively manufactured cellular materials using simulations and validation experiments

Additive manufacturing has enabled a transformational ability to create cellular structures (or foams) with tailored topology. Compared to their monolithic polymer counterparts, cellular structures are potentially suitable for systems requiring materials with high specific energy-absorbing capability to provide enhanced damping. In this work, we demonstrate the utility of controlling unit-cell topology with the intent of obtaining a desired stress–strain response and energy density. Using mesoscale simulations that resolve the unit-cell sub-structures, we validate the role of unit-cell topology in selectively activating a buckling mode and thereby modulating the characteristic stress–strain response. Simulations incorporate a linear viscoelastic constitutive model and a hyperelastic model for simulating large deformation of the polymer under both tension and compression. Simulated results for nine different cellular structures are compared with experimental data to gain insights into three different modes of buckling and the corresponding stress–strain response.

Constitutive modelling and systematic evaluation of asphalt concrete’s viscoelastic tension-compression asymmetry effect on pavement performance

ABSTRACT Asphalt concrete (AC) exhibits significant tension-compression (TC) asymmetry, which is currently not considered in pavement design. This study develops a novel temperature-dependent dual viscoelastic model to quantitatively capture the viscoelastic behaviour of AC. Unlike the conventional viscoelastic constitutive model, the proposed model decomposes strain into tensile and compressive components to characterise AC’s TC asymmetry. Additionally, a systematic modelling framework with intrinsic TC asymmetry is developed for the first time to predict the response of pavement under moving tire load. The results illustrate that implementing the proposed dual viscoelastic model enlarges both the vertical deformation of pavements and the tensile and shear strains in the AC layers, bringing it closer to the realistic scenario compared to the conventional model that only considers compression properties. Furthermore, high temperatures and low vehicular speeds exacerbate the substantial effects of AC’s TC asymmetry on asphalt pavement. This study provides a valuable method to capture AC’s TC asymmetry and predict pavement response more accurately, giving better insight into pavement response and enhancing pavement design and maintenance.

Rate-dependent energy dissipation of graded viscoelastic structures fabricated by grayscale vat photopolymerization

A major benefit of additive manufacturing technologies is precise control over structural topologies and material properties, which allows to tailor, for instance, energy absorption and dissipation. While vat photopolymerization is generally restricted to a single material, grayscale masked stereolithography (gMSLA) allows to customize material behavior by grading the light intensity within a structure. This study investigates the impact and opportunities of grayscale grading strategies on the rate-dependent mechanical behavior of structures fabricated by gMSLA. Considering the viscoelastic nature of polymers, rate-dependent energy dissipation is explored, introducing a parametric linear viscoelastic constitutive model for varying grayscales. The investigation includes the comprehensive characterization of mechanical properties, numerical finite element simulation, validation through experimental procedures, and exploration of dissipation energy under different strain rates. In this way, a rational function successfully determines the critical strain rate at which the maximum dissipation occurs. Overall, the research offers a comprehensive investigation of the mechanical dissipation behavior of graded 3D printed structures, laying the foundation for further studies and advancements aimed at optimizing these structures for enhanced energy absorption capabilities.

Quantitative analysis of asphalt concrete’s tension-compression asymmetry effects on pavement response through 3D numerical modeling with dual viscoelastic model

Asphalt concrete (AC) exhibits noticeable tension-compression (TC) asymmetry, but it is typically considered isotropic in pavement design. This study aims to quantitatively evaluate the effect of AC’s TC asymmetry on pavement response under loading through numerical modeling. To achieve this objective, a temperature-dependent dual viscoelastic constitutive model was applied to incorporate AC’s TC asymmetry into pavement modeling. Besides, three pavement structure models, including one with thick AC layers, one with thin AC layers, and one with a Portland cement concrete (PCC) base, were developed. The responses of the three pavement structures under traffic and environmental loading conditions were simulated. Modeling results showed that AC’s TC asymmetry can significantly increase the vertical strain in AC, leading to higher stress concentration and larger deformation in AC layers. Unlike the conventional understanding that tensile strain concentrates at the bottom of AC layers, high tensile strains were observed in the top AC layers, especially for the pavement with thick AC layers or a PCC base, which may lead to top-down cracking. High tensile strains were observed on the granular subbase for the pavement with thin AC layers, which may induce bottom-up cracking. Besides, AC’s TC asymmetry also significantly increases the shear strains, especially the horizontal shear strain in AC layers, which may result in debonding and shoving distresses in AC layers. It was also noticed that the pavement response highly depends on its temperature and vehicular speed. A higher temperature or lower vehicular speed leads to more significant AC’s TC asymmetry as well as its effects on asphalt pavement’s response. The outcomes of this study are expected to help enhance the design and maintenance of more durable asphalt pavement.

Comparing flows of FENE-P, sPTT, and Giesekus model fluids in a helical static mixer

Helical static mixers are used widely for mixing of non-Newtonian fluid flows in the laminar regime. We study flows of three viscoelastic constitutive models (sPTT, FENE-P, and Giesekus) in the helical static mixer using computational fluid dynamics. These three models have similarities in steady viscometric flows in that they all exhibit shear thinning and their planar extensional viscosities can be matched, but their responses can differ in complex geometries. We observe flow distribution asymmetries at the element intersections for all three models, which hinders the mixing performance of the device. These have previously been observed with the constant shear viscosity FENE-CR model. The asymmetry behaves similarly between the sPTT and Giesekus models, however the FENE-P model behaves in a distinct manner; beyond a critical degree of elasticity, the asymmetry sharply changes direction. This was also observed previously with the FENE-CR model. These results suggest that shear thinning and second-normal stress differences (present in the Giesekus model) do not significantly influence mixing performance in the range of conditions studied. We show that increasing the aspect (length/diameter) ratio of the mixer elements mitigates the poor mixing caused by elasticity. Overall, this study provides insight into the behaviour of these well-used constitutive models in complex, industrially-relevant flows.

Electric-driven shape memory deformation control and verification of composite films based on PVA/WPU/SCFs

Based on the research of Polyvinyl alcohol (PVA)/Waterborne Polyurethane (WPU)/Short Carbon Fibers (SCFs) novel electrochemically shape memory composites, this study delved into an exploration of factors influencing the shape memory deformation of shape memory film samples when subjected to voltage stimulation. These main affecting factors encompassed sample thickness, activation voltage, and wire layout. Subsequently, based on the above conclusions, the viscoelastic constitutive model of PVA/WPU/SCFs composite was established based on Maxwell model and the deformation deflection of the composite film was predicted by shape memory recovery, and the electrothermal coupling simulation analysis and shape memory recovery and deformation simulation verification were carried out. Finally, based on the shape memory recovery performance of the composite film, a new reciprocating moving deformation structure was conceptualized, characterized by distinct cycles of motion, each analyzed individually.

Compressive mechanical properties of styrene-butadiene rubber under medium-low strain rates: Experiments and modeling

Styrene-butadiene rubber (SBR) is widely employed as a cushioning material in engineering applications to resist impact loadings due to its excellent mechanical properties and energy absorption capacity. This paper aims to investigate the compressive mechanical properties and constitutive model of SBR under medium–low strain rates both experimentally and theoretically. Firstly, quasi-static and dynamic compression tests of SBR were carried out under the strain rate up to 220 s−1 using an electronic universal testing machine and a drop-weight machine, respectively. Subsequently, the effect of loading rate on mechanical properties, strain rate sensitivity and energy absorption capacity was examined. The results indicate that SBR exhibits visco-hyperelastic characteristics with reversible compression deformation and strain rate dependency, ie., the yield stress, flow stress and dynamic increase factor (DIF) increase approximately exponentially with increasing logarithmic strain rate. In addition, the SBR exhibits excellent energy absorption capacity during compression, especially under higher strain rates and larger strain levels. Finally, a visco-hyperelastic constitutive model was proposed by replacing the nonlinear spring with a hyperelastic element in Zhu-Wang-Tang (ZWT) viscoelastic constitutive model to describe the nonlinear mechanical behaviors in SBR, and an acceptable agreement between experimental results and model predictions were observed. The findings of this research can provide a valuable guide for designing and optimizing the impact resistance of SBR structures.

Constitutive model of viscoelastic dynamic damage for the material of gas obturator in modular-charge howitzer

In order to investigate the mechanical response behavior of the gas obturator of the breech mechanism, made of polychloroprene rubber (PCR), uniaxial compression experiments were carried out by using a universal testing machine and a split Hopkinson pressure bar (SHPB), obtaining stress-strain responses at different temperatures and strain rates. The results revealed that, in comparison to other polymers, the gas obturator material exhibited inconspicuous strain softening and hardening effects; meanwhile, the mechanical response was more affected by the strain rate than by temperature. Subsequently, a succinct viscoelastic damage constitutive model was developed based on the ZWT model, including ten undetermined parameters, formulated with incorporating three parallel components to capture the viscoelastic response at high strain rate and further enhanced by integrating a three-parameter Weibull function to describe the damage. Compared to the ZWT model, the modified model could effectively describe the mechanical response behavior of the gas obturator material at high strain rates. This research laid a theoretical foundation for further investigation into the influence of chamber sealing issues on artillery firing.

Analysis of the mechanical response of solid rocket engine propellant under acceleration shock

The increased-range solid rocket engine of new ammunition often needs to withstand extremely high acceleration overload, leading to damage to the propellant’s structural integrity. To address this issue, this paper constructs a nonlinear viscoelastic constitutive model for the CMDB propellant by using low- and high-strain rate mechanical property tests. Combined with the secondary development of explicit dynamics and numerical simulation technology, the mechanical response of a certain type of solid rocket propellant under different acceleration impacts is analyzed. The results show that under acceleration impact loads, the propellant will compress, rebound, and recover over time, continuously cycling. Its axial displacement, maximum equivalent stress, and maximum equivalent strain exhibit irregular sinusoidal wave-like periodic cycles. Looking at the time when the peaks appear, the time when the maximum equivalent stress appears always lags behind the time when the maximum axial displacement peak appears. Due to the viscous effect of the viscoelastic material of the propellant, the time when the equivalent strain peak appears will lag behind the equivalent stress. Because of the material’s damping effect, both the peak values of the maximum equivalent stress and equivalent strain decrease over time. Under continuous high acceleration impact loads, this viscous damping phenomenon continuously diminishes, and the peak value of the propellant’s axial displacement gradually increases.

Temperature and Strain Rate Related Deformation Behavior of UHMWPE Fiber-Reinforced Composites.

As they possess the qualities of high specific strength, high specific modulus, high specific energy absorption, and excellent designability, ultra-high molecular weight polyethylene (UHMWPE) fiber-reinforced composites have gradually replaced traditional materials such as ceramics and steel plates as the main ballistic protection materials. Using an improved test method, the uniaxial tensile tests of UHMWPE fiber-reinforced composites at two strain rates of 10-4 s-1 and 10-2 s-1 and a temperature range from -20 °C to 80 °C are carried out to study the effects of strain rate and temperature on the tensile behavior of UHMWPE fiber-reinforced composites. The experimental results indicate that the tensile responses exhibit nonlinear characteristics and the sensitivity of strain rate and temperature. The yield strength and modulus decrease with increasing temperature and increase with the increase in strain rate. A phenomenological viscoelastic constitutive model composed of a nonlinear spring and a nonlinear Maxwell element is proposed to characterize the temperature and strain rate dependent deformation behavior of UHMWPE fiber-reinforced composites before yielding. The results show that the model can accurately predict the tensile nonlinear viscoelastic responses of UHMWPE fiber-reinforced composites before yielding over a wide temperature range under quasi-static loading.

Investigation on A Viscoelastic Creep Damage Constitutive Model for HTPB Propellant and Its Application in Finite Element Analysis

Solid rocket motor (SRM) is typically kept in storage for a significant portion of its lifespan. During storage, the propellant grain creeps under the action of gravity. To investigate the creep properties of hydroyl-terminated polybutadiene (HTPB) propellant under long-term loading, a creep damage constitutive model is developed based on the generalized Kelvin model and continuum damage mechanics theory. Parameters for this model are determined through creep tests conducted on HTPB propellant under various stress levels. Furthermore, to enable the application of the developed propellant constitutive model in the finite element analysis of SRM, the derived constitutive equation is transformed into an incremental form and integrated into the user subroutine UMAT of the finite element analysis platform ABAQUS. Subsequent to this, a three-dimensional SRM model containing the case, the insulator, and the propellant grain is established. The mechanical response of the grain under thermal and gravitational loads is calculated and analyzed. The results indicate that the stress concentration region in the grain is located at the stress release boot in the forward dome of the motor, where damage occurs. The methods employed in this paper and the conclusions drawn can serve as a reference for evaluating the structural integrity and storage lifespan of the SRM.

Effect of Viscoelastic Characteristics on the Real Contact Area of Polishing Pad Surface

Real contact area (RCA) between polishing pad and workpiece surface is one of the most important parameters indicating the mechanical action strength of chemical mechanical polishing (CMP), which has a dominated effect on the material removal. However, the effect of pad viscoelastic characteristics on RCA is not clear. In this study, a contact status measurement device that can apply cyclic load and record contact images is developed to study the viscoelastic behavior of the pad and its influence on RCA. The results show that when the pad undergoes cyclic compression load during CMP, the pad asperity layer gradually accumulates viscoelastic deformation and the RCA increases obviously, which can be mostly recovered after a long time. In particular, the accumulation and recovery of viscoelastic deformation lead to a significant change of the relationship between RCA and pressure, from linear to nonlinear and then to linear. Furthermore, an RCA model is established based on the viscoelastic constitutive model of pad and the mathematical relationship between RCA and pad deformation to explain the influence of pad viscoelastic behavior on RCA. This study is expected to provide new insights into RCA, and to give support for predictive control of the material removal during CMP.

Characterization of Potting Epoxy Resins Performance Parameters Based on a Viscoelastic Constitutive Model.

To describe the evolution of residual stresses in epoxy resin during the curing process, a more detailed characterization of its viscoelastic properties is necessary. In this study, we have devised a simplified apparatus for assessing the viscoelastic properties of epoxy resin. This apparatus employs a confining cylinder to restrict the circumferential and radial deformations of the material. Following the application of load by the testing machine, the epoxy resin sample gradually reduces the gap between its surface and the inner wall of the confining cylinder, ultimately achieving full contact and establishing a continuous interface. By recording the circumferential stress-strain on the outer surface of the confining cylinder, we can deduce the variations in material bulk and shear moduli with time. This characterization spans eight temperature points surrounding the glass transition temperature, revealing the bulk and shear relaxation moduli of the epoxy resin. Throughout the experiments, the epoxy resin's viscoelastic response demonstrated a pronounced time-temperature dependency. Below the glass transition temperature, the stress relaxation response progressively accelerated with increasing temperature, while beyond the glass transition temperature, the stress relaxation time underwent a substantial reduction. By applying the time-temperature superposition principle, it is possible to construct the relaxation master curves for the bulk and shear moduli of the epoxy resin. By fitting the data, we can obtain expressions for the constitutive model describing the viscoelastic behavior of the epoxy resin. In order to validate the reliability of the test results, a uniaxial tensile relaxation test was conducted on the epoxy resin casting body. The results show good agreement between the obtained uniaxial relaxation modulus curves and those derived from the bulk and shear relaxation modulus equations, confirming the validity of both the device design and the testing methodology.

Mechanical insights into jawbone characteristics under chronic kidney disease: A comprehensive nanoindentation approach

The mechanical properties of the jawbone play a critical role in determining the successful integration of dental prostheses. Chronic kidney disease (CKD) has been identified to abnormally accelerate bone turnover rates. However, the impact of CKD on the mechanical characteristics of the jawbone has not been extensively studied. This study sought to evaluate the time-dependent viscoelastic behaviors of rat jawbones, particularly in the scenarios both with and without CKD. We hypothesized that CKD might compromise the bone's innate toughening mechanisms, potentially owing to the time-dependent viscoelasticity of the bone matrix proteins. The maxillary and mandibular bones of Wistar rats were subjected to nanoindentation and Raman micro-spectroscopy. Load-hold-displacement curves from the cortical regions were obtained via nanoindentation and were mathematically characterized using a suitable viscoelastic constitutive model. Raman micro-spectroscopy was employed to identify nuanced vibrational changes in local molecular structures induced by CKD. The time course of indenter penetration onto cortical bones during the holding stage (creep behavior) can be mathematically represented by a series arrangement of the Kelvin–Voigt bodies. This configuration dictates the overall viscoelastic response observed during nanoindentation tests. The CKD model exhibited a reduced extent of viscoelastic contributions, especially during the initial ramp loading phase in both the maxillary and mandibular cortical bones. The generalized Kelvin–Voigt model comprises 2 K–Voigt elements that signify an immediate short retardation time (τ1) and a subsequent prolonged retardation time (τ2), respectively. Notably, the mandibular CKD model led to an increase in the delayed τ2 alongside an increase in non-enzymatic collagen cross-linking. These suggest that, over time, CKD diminishes the bone's capability for supplementary energy absorption and dimensional recovery, thus heightening their susceptibility to fractures.

A high fidelity multiscale approach for compression-after-impact behavior of 2D triaxially braided composites

In the current study, limited research has been conducted on modeling high-velocity impacts and their effect on residual strength. Though the simulation of compression after low-velocity impact are mature, these methods still have some numerical issues when utilized in the case of high-velocity impacts. Thus, a brand-new method suitable for continuous simulation of compression after high-velocity impact was implemented. As for the modeling techniques for 2DTBC, both the research on the model structure and constitutive behavior is still crude and imprecise. To address this situation, a high fidelity multiscale approach which contains a more accurate RUC model, a strain rate sensitive viscoelastic constitutive model and a novel subcell model was established. The HVI and CAI examples were conducted based on this framework and most results showed an error of less than 5% in both the simulation of impact resistance and residual performance. Also, the damage morphologies of simulated results demonstrated its capability and effectiveness.

Study on the permanent deformation of asphalt mixtures based on the modified Burgers model

Based on the confined test results and the viscoelastic constitutive model of asphalt mixtures, a three-dimensional finite element model of an asphalt pavement was established to study the effect of different working conditions on asphalt pavement. With the actual pavement structure response, a comparative analysis was conducted to assess the stress and strain experienced by the asphalt pavement under various working conditions. The results show that the asphalt pavement structure model can reflect the effect of different working conditions on asphalt pavement; the transverse stress and strain of asphalt pavement are most significantly affected by the working conditions during cornering, and the position of the maximum value is concentrated on the outer edge line of the wheel and a distance away from it; however, the longitudinal tensile stress and strain of the asphalt pavement are most significantly impacted by the working conditions of driving and braking, and the position of the maximum value is mainly distributed in the center line of the single wheel. The research results can provide a reference for the design of asphalt pavement structures.

Prediction of shape distortions in thermosetting composite parts using neural network interfaced visco-elastic constitutive model

The work aims to enhance the capabilities of a Finite Element tool, specifically related to a rheological thermo-chemo-viscoelastic constitutive model. This enhancement is intended to improve the tool’s ability to predict the distortions in composite parts caused by the polymerization of the thermoset composite matrix. These distortions occur due to internal residual stress generated by the inherent anisotropic properties of the thermoset composite material, including coefficients of thermal expansion and chemical shrinkage. The research work’s improvement is tied to the precise modelling of curing behaviour, which literature acknowledges as having a significant impact on manufacturing defects. In order to accommodate the influence of curing behaviour on various process variables—specifically, different thermal loading rates—a neural network model is implemented as an alternative to a standard diffusion cure-kinetics model. The neural network model is trained using Differential Scanning Calorimetry data and is integrated with the classical visco-elastic constitutive model to more accurately predict the progression of distinct thermoset resin states. This transition between cure states is assessed using two cure state variables: the degree of cure and the glass transition temperature. The enhanced predictions of state transitions lead to accurate assessments of internal residual stresses, especially when dealing with thick components subjected to thermal fluctuations. The anisotropic properties of thermoset composites, crucial for numerical analysis, are captured at various stages of cure. Ultimately, this methodology is employed to compare process-induced defects in the case study of the Z-shaped carbon/epoxy woven part, and the defects closely align with experimental measurements.