Rate-dependent Properties Research Articles

Evaluating concrete material models for blast analysis using 3D finite element analysis

Blast loads are extremely detrimental to structural elements of a building and can result in minor damage to complete failure of a building. Finite element analysis (FEA) is an effective tool to study the behavior of structural elements exposed to blast loading. The focus of this study was to evaluate the performance of three concrete material models available in LS-DYNA and compare the results to experimental results from blast loaded reinforced concrete (RC) panel supported on four sides (two-way bending). Concrete material models chosen for this study were Winfrith (MAT_84-85), Karagozian & Case (MAT_072R3), and Continuous Surface Cap Model (MAT_159). These are widely used in finite element modeling related to civil structures and can account for strain rate dependent properties. Each concrete material model was implemented with and without strain rate effects. The finite element model had concrete material as solid elements and steel reinforcement material as beam elements with simply supported boundary conditions. Results from two different blast loading methods are presented: (1) blast pulse load curve from experimental data (2) blast input by defining type, location, and amount of explosive in terms of TNT. The finite element models were evaluated by comparing fundamental period, peak displacement, and residual displacement to experimental results. In this study, the model using MAT_072R3 most closely matched experimental behavior in comparison to MAT_84-85 and MAT_159. Additional discussion is presented about: (1) single degree of freedom (SDOF) analysis, (2) comparison of numerical and experimental crack patterns, and (3) behavior of concrete material models accounting for compressive and tensile dynamic increase factors (DIFs).

Process dependent properties of glassy polymer films revealed by molecular dynamics simulations

A molecular dynamics (MD) framework has been proposed to systematically simulate process (but not cooling rate) dependent properties of glassy polymer films. With the coarse-grained (CG) polylactide (PLA) of low molecular weight (MW), the simulated thermal properties of glassy films are confirmed to be surely decided by the routes to prepare them. While the glassy films initially prepared from the melt bulk are stable, the glassy film initially constructed from the glassy bulk appears to be unstable, featuring highest potential energy among those films and different averaged heat capacity from the bulk counterparts. Inspired by physical vapour deposition (PVD), a surface formation process is further applied to the unstable film to generate stable glassy polymer films. Similar to the PVD, an optimal temperature at which the film is most stable can be identified with lower potential energy than the conventional films, for which free surface and enhanced order of the middle layer are responsible. This work paves a way for obtaining simulated models of stable glassy films and experimentally preparing advanced glassy films for high MW polymers, which otherwise are hard to be realized by the PVD process.

Thermal effects on the strain rate-dependent behavior of highly compacted GMZ01 bentonite

Investigation of thermal effects on the strain rate-dependent properties of compacted bentonite is crucial for the long-term safety assessment of deep geological repository for disposal of high-level radioactive waste. In the present work, cylindrical GMZ01 bentonite specimens were compacted with suction-controlled by the vapor equilibrium technique. Then, a series of temperature- and suction-controlled stepwise constant rate strain (CRS) tests was performed and the rate-dependent compressibility behavior of the highly compacted GMZ01 bentonite was investigated. The plastic compressibility parameter λ, the elastic compressibility parameter κ, the yield stress p0, as well as the viscous parameter α were determined. Results indicate that λ, κ and α decrease and p0 increases as suction increases. Upon heating, parameters λ, α and p0 decrease. It is also found that p0 increases linearly with increasing CRS in a double-logarithm coordinate. Based on the experimental results, a viscosity parameter α(s, T) was fitted to capture the effects of suction s and temperature T on the relationship between yield stress and strain rate. Then, an elastic-thermo-viscoplastic model for unsaturated soils was developed to describe the thermal effects on the rate-dependent behavior of highly compacted GMZ01 bentonite. Validation showed that the calculated results agreed well to the measured ones.

Temperature and strain rate-dependent compression properties of 3D-printed PLA: an experimental and modeling analysis

PurposeThis study aims to investigate the compression characteristics of the 3D-printed polylactic acid (PLA) samples at temperatures below the glass transition temperature (Tg) with varying strain rates and develop a thermo-mechanical viscoplastic constitutive model to predict the finite strain compression response using a single set of material parameters. Also, the micro-mechanical damage processes are linked to the global stress–strain response at varied strain rates and temperatures through scanning electron microscopy (SEM).Design/methodology/approachTg of PLA was determined using a dynamic mechanical analyzer. Compression experiments were conducted at strain rates of 2 × 10–3/s and 2 × 10–2/s at 25°C, 40°C and 50°C. The failure mechanisms were examined using SEM. A finite strain thermo-mechanical viscoplastic constitutive model was developed to analyze the deformations at the considered strain rates and temperatures.FindingsTg of PLA was determined as 55°C. While the yield and post-yield stresses drop with increasing temperature, their trend reverses with an increased strain rate. SEM imaging indicated plasticizing effects at higher temperatures, while filament fragmentation and twisting at higher strain rates were identified as the dominant failure mechanisms. Using a non-linear regression analysis to predict the experimental data, an overall R2 value of 0.98 was achieved between experimental and model prediction, implying the robustness of the model’s calibration.Originality/valueIn this study, a viscoplastic constitutive model was developed that considers the combined effect of temperature and strain rate for FDM-printed PLA experiencing extensive compression. Using appropriate temperature-dependent modulus and flow rate properties, a single set of model parameters predicted the rise in the gap between yield stress and degree of softening as strain rates and temperatures increased.

Rate-dependent tensile properties of paperboard and its plies

Abstract Tensile properties of paperboard have been characterized, and it has been shown that paper tensile properties are dependent on the strain rate. Tensile testing was done using strain rates in the range 10−4–3 s−1, which corresponds to crosshead movements ranging from 1 up to 24,000 mm/min, using an electro-mechanical testing machine. Two paperboards, and its free-laid top, middle and bottom plies were characterized in MD and CD. The testing was limited by the maximum crosshead speed of the testing machine. Initially 50 mm (grip to grip) long samples were tested, but to test even higher strain rates also short samples with length of 5 mm were tested. The results showed that ultimate strength increased by 9 % per decade increasing of testing rate, and Young’s modulus increased by 7 %. This shows that the previously reported rule of thumb of 10 % increase of in-plane strength per decade increase of strain rate holds. The testing here shows that this is valid also at strain rates as high as 3 s−1. Moreover, the strain at break in CD for long tensile specimens was observed to decrease when the strain rate exceeded 0.1 s−1, which resulted in straighter crack paths.

Continuous Softening as a State of Hyperelasticity: Examples of Application to the Softening Behavior of the Brain Tissue.

The continuous softening behavior of the brain tissue, i.e., the softening in the primary loading path with an increase in deformation, is modeled in this work as a state of hyperelasticity up to the onset of failure. That is, the softening behavior is captured via a core hyperelastic model without the addition of damage variables and/or functions. Examples of the application of the model will be provided to extant datasets of uniaxial tension and simple shear deformations, demonstrating the capability of the model to capture the whole-range deformation of the brain tissue specimens, including their softening behavior. Quantitative and qualitative comparisons with other models within the brain biomechanics literature will also be presented, showing the clear advantages of the current approach. The application of the model is then extended to capturing the rate-dependent softening behavior of the tissue by allowing the parameters of the core hyperelastic model to evolve, i.e., vary, with the deformation rate. It is shown that the model captures the rate-dependent and softening behaviors of the specimens favorably and also predicts the behavior at other rates. These results offer a clear set of advantages in favor of the considered modeling approach here for capturing the quasi-static and rate-dependent mechanical properties of the brain tissue, including its softening behavior, over the existing models in the literature, which at best may purport to capture only a reduced set of the foregoing behaviors, and with ill-posed effects.

High strain rate response of ABS-M30i-based 3D printed, bio-inspired, bovine bone structure

To investigate osteoporosis caused by aging and the dynamic behavior of male bovine trabecular bone, three age groups of male bovine trabecular bone were chosen, and micro-computed tomography (CT) analysis was performed to develop an image-based bio-inspired computer-aided design (CAD) model of the bone structure. Further experimental and computational studies were carried out to examine the rate-dependent behavior and compressive energy-absorbing capacity of the structure as a function of age. To evaluate this study, a micro-CT-based CAD model of the structure was 3D printed using ABS-M30i material and subjected to quasi-static compression (low strain rate) and high strain rate (split Hopkinson pressure bar) compression. The findings show that 3D-printed bovine structures have distinct high-rate dependence at strain rates greater than 430 s−1, as well as sensitivity to strain rate in terms of peak stress, plateau stress, and energy absorption capacity. Using rate-dependent properties, the Johnson–Cook damage plasticity model was used in computational analysis to explain the dynamic behavior of bone due to osteoporosis. Overall, there is good agreement between the numerical simulations and the experimental data, which was obtained by verifying and validating the model against the experimental results.

Numerical modelling of reinforced fill over a void considering rate-dependent stiffness of the reinforcement

The problem of a reinforced fill over a void has been the subject of much research in the geosynthetics literature. Previous studies have mainly focused on finding closed-form solutions to predict the tensile loads and strains in the reinforcement layer once a void develops below the fill. In this paper, a 2D finite difference (FLAC) model that implements the hyperbolic isochronous load-strain model for the reinforcement by Bathurst and Naftchali (2021) is used to investigate the influence of the rate-dependent properties of polymeric geosynthetic reinforcement materials on reinforcement tensile strains and load, and overall system performance including vertical deformation at the reinforcement elevation and at the fill surface. The paper also investigates the influence of fill soil properties and constitutive model type, foundation condition, void geometry and fill height on system performance. The results of numerical modelling are compared to predictions made using the closed-form solution of Giroud et al. (1990) and in the BSI 8006-1 (2010) design code. The results of numerical modelling demonstrate that the choice of fill height to void width and the stiffness of the rate-dependent geosynthetic reinforcement layer are important to ensure that the maximum reinforcement strain, allowable strength and fill surface settlement criteria are not exceeded.

Mechanical properties of rock under uniaxial compression tests of different control modes and loading rates

To study the influence of control mode and loading rate on mechanical property of rock, uniaxial compression tests of four types of rocks (gray sandstone, red sandstone, mudstone and granite) are carried out under axial strain control mode and lateral strain control mode respectively. The characteristics of complete stress and strain curves, strength, brittleness and failure modes are analyzed. The results show that control mode has little influence on the pre-peak deformation, stress thresholds, while it has a greater impact on post-peak stress and strain curve, which makes the post-peak deformation stable and controllable, and shows the feature of Class II behavior. With lateral loading rates decrease, post-peak stress and strain curves appear more and more obvious fluctuations in the post-peak stage, and the time required for rock failure increases sharply, but the lateral control rate has little effect on the brittleness of rock. The failure mode of rock samples under axial strain control mode is mainly splitting failure, while that under lateral strain control is gradually changed to shear failure. The smaller the lateral loading control rate is, the more obvious the characteristics of shear failure is. Compared with uniaxial compression tests, under high confining pressure, the lateral dilation deformation is restricted, so peak strength is larger and stress redistribution can be better adjusted and stress fluctuation reduced accordingly in post-peak stage. The research results are an effective supplement to rate-dependent property of rocks and can provide some reference for deformation and strength characteristics research of brittle rock under lateral control mode.

Numerical and experimental analysis of inelastic and rate-dependent buckling of thin injection-moulded high-density polyethylene structure

Semi-crystalline polymers is an important group of materials that is used in a vast array of products. In this study, the rate-dependent properties of high-density polyethylene (HDPE) are investigated, both experimentally and theoretically. Experimental compression testing of a three-dimensional HDPE structure is performed and analysed numerically by use of the finite element method. In addition, an Eulerian constitutive material model for isotropic, semi-crystalline polymers is proposed. The model is able to account for such essential phenomena as strain-rate dependence, work hardening, pressure-dependence of inelastic deformations, and damage. The proposed material model was implemented in Abaqus as a VUMAT, which is an explicit implementation. The material model was calibrated by use of uniaxial tensile tests performed on HDPE dog-bone shaped samples, and the model was further explored by applying the VUMAT implementation to the compression tests of the HDPE structure. The simulation model was able to reproduce the experimental results well, both the uniaxial tests and the compression tests. In particular, the friction present in the compression tests seems to play an important role in determining the buckling mode of the structure.

A fractional-order modelling and parameter identification method via improved driving training-based optimization for piezoelectric nonlinear system

The accurate identification of the parameters of fractional-order systems is still a challenging problem. The purpose of this paper is to establish a fractional hysteresis model based on a Bouc-Wen differential equation and an improved driving training-based optimization (DTBO) parameter identification method to accurately characterize the nonlinear characteristics of the piezoelectric hysteresis system. In this paper, there are two contributions. On the one hand, an accurate fractional-order hysteresis model is proposed and its rate-dependent property is proved based on the definition of fractional calculus; on the other hand, an improved DTBO optimization method with enhanced performance is proposed to achieve excellent precision and robustness for the purpose of parameter identification. The unique features of the improved DTBO algorithm include an instructor-learner separation strategy, a new update mechanism of instructor position, and an improved phase of the learner group. The results show that the output of the model is consistent with that of the actual piezoelectric platform. Compared with the standard DTBO algorithm and Antlion Optimization algorithm, the improved DTBO algorithm has better performance. The novelty of this paper is that a new high-performance heuristic optimization method is proposed for the particular problem of the parameter identification of fractional-order hysteresis models. The proposed method holds promise as a good candidate in the field of hysteresis modelling and identification.

Hysteresis inversion-free predictive compensation control for soft pneumatic actuators based on a global Koopman modeling strategy

Soft pneumatic actuators (SPAs) have increasing applications in soft robotic design owing to their good compliance, excellent adaptability, and high force density characteristics. However, the inherent hysteresis nonlinearity severely degrades the control performance of SPAs. To compensate for the hysteresis effect, one solution is to build an inverse mathematical model. Nevertheless, in this method, the control performance still highly depends on the accuracy of the built inverse model. At the same time, the computational burden of deriving the inverse model is overwhelming. In addition, the physical constraints of the input pressure of SPAs are hardly handled by the inversion-based method. This paper proposes an inversion-free model predictive controller (IFMPC), which is designed based on a global Koopman linear model (GKLM). In the above GKLM-IFMPC strategy, the inverse hysteresis model is not required. Instead, a global hysteresis model can be established without considering the effect of rate-dependent property. Additionally, the control law is derived in an explicit form. With the constrained quadratic programming technique, the proposed method still works well when dealing with the physical constraints of SPAs. To verify the effectiveness of the proposed method, several comparative experiments are performed on a two-dimensional (2D) SPA. The results show that the proposed hysteresis global modeling and control framework has satisfactory tracking performance over some existing strategies even with strong hysteresis nonlinearity.

Implementation of Fracture and Flow Stress Models for AA5052-H32 Sheet Deformed Through Shock Tube–Based Forming Technique

Abstract Selection of flow stress models and fracture models to model sheet deformation at high strain rates is of great concern. The same is attempted in the present work during shock tube impact forming of 1-mm-thick AA 5052-H32 sheet using a rigid nylon striker. Lab scale experiments and finite element simulations using DEFORM 3D are conducted for the purpose. Johnson–Cook flow stress model and Modified Johnson–Cook flow stress model along with fracture models like normalized Cockcroft and Latham model, Rice and Tracey model, Oyane model, and McClintock model are tested for their accuracy and consistency. The fracture strain and fracture pattern evaluation suggest that the modified Johnson–Cook flow stress model and Rice and Tracey fracture model are suitable for fracture prediction, and it is better to use these together for fracture evaluation. An alternate method of evaluating rate-dependent tensile properties of sheet at higher strain rates is proposed and delivered acceptable fracture prediction results. Finite element simulations using Hollomon power law predict a strain rate of 1925/s at a striker velocity of 49.79 m/s, which is in the range of values in literature for explosive forming. Systematic shock tube forming experiments for calibrating the fracture models are acceptable.

Impact of cryogenic treatment on mechanical and electro active actuation properties of soft polymers

AbstractThe goal of this study is to investigate the change in stretchability property of soft polymers before and after cryogenic treatment. To achieve this, the influences of cryogenic treatment on the rate dependent tensile properties, hysteresis behavior, and stress‐relaxation of soft polymers are extensively analyzed. Results indicated that the effects of cryogenic treatment for both VHB and Ecoflex samples on mechanical responses were more prominent at low strain rate. It was also observed that VHB polymer could exhibit more strain rate sensitivity than Ecoflex sample after cryogenic treatment. For stress relaxation test, both cryo‐treated polymer samples were found to yield less overall stress and takes longer time to reach equilibrium stress in comparison to untreated polymer. Extensive experimental findings showed that the amount of energy dissipated while cooling below glass transition temperature (Tg), causes stress softening with lowering of viscoelastic property. On the other hand, there is a good enhancement of the electro‐active actuation strain for the cryo‐treated VHB 4910 and Ecoflex specimens. The results of this work could be used as a helpful guide for applying cryogenic treatment to improve electro‐mechanical properties of soft polymers, as the theory underlying this treatment has not been well explored

Evaluation of time dependent mechanical properties through nanoindentation of different compositions of 2D Ruddlesden Popper and 3D lead halide perovskites

Hybrid organic-inorganic perovskite (HOIPs) films' simplicity in manufacturing, both in solution and at low temperatures, foresees its application in deformable technologies including flexible photovoltaics, sensors and displays. The next generation of flexible optoelectronic devices may be possible owing to the special characteristics of hybrid organic-inorganic perovskites (HOIPs). However, it is necessary to have a thorough knowledge of the mechanical response of hybrid organic-inorganic perovskites(HOIPs) to dynamic strain to successfully use them in deformable devices. In the current study, a range of perovskites: 3D, butylammonium(BA) based 2D and quasi-2D, phenylethylammonium(PEA) based 2D and quasi-2D perovskite have been fabricated with particle sizes ranging in 5–10 nm as found using TEM. The nanoindentation creep and stress relaxation experiments prove the time and rate-dependent mechanical properties of this 2D, quasi-2D, and 3D HOIPs crystal though varying in their magnitudes. We observe that the 3D as well as BA based perovskite show strain rate sensitivity whereas PEA based perovskite samples were relatively insensitive towards the rate of loading. Propagation and interaction of dislocation are much more difficult in PEA-based perovskite, which has a triclinic crystal structure and are less symmetrical as compared to the BA based and 3D perovskite orthorhombic and tetragonal structure respectively. The knowledge offered by this work is crucial for creating perovskite devices that can endure mechanical deformations.

Precision Motion Control of a Piezoelectric Actuator via a Modified Preisach Hysteresis Model and Two-Degree-of-Freedom H-Infinity Robust Control.

The nonlinear hysteresis phenomenon can occur in piezoelectric-driven nanopositioning systems and can lead to reduced positioning accuracy or result in a serious deterioration of motion control. The Preisach method is widely used for hysteresis modeling; however, for the modeling of rate-dependent hysteresis, where the output displacement of the piezoelectric actuator depends on the amplitude and frequency of the input reference signal, the desired accuracy cannot be achieved with the classical Preisach method. In this paper, the Preisach model is improved using least-squares support vector machines (LSSVMs) to deal with the rate-dependent properties. The control part is then designed and consists of an inverse Preisach model to compensate for the hysteresis nonlinearity and a two-degree-of-freedom (2-DOF) H-infinity feedback controller to enhance the overall tracking performance with robustness. The main idea of the proposed 2-DOF H-infinity feedback controller is to find two optimal controllers that properly shape the closed-loop sensitivity functions by imposing some templates in terms of weighting functions in order to achieve the desired tracking performance with robustness. The achieved results with the suggested control strategy show that both hysteresis modeling accuracy and tracking performance are significantly improved with average root-mean-square error (RMSE) values of 0.0107 μm and 0.0212 μm, respectively. In addition, the suggested methodology can achieve better performance than comparative methods in terms of generalization and precision.

Response of Topological Soliton lattice structures subjected to dynamic compression and blast loading

A novel topological soliton lattice (TSL) unit cell with fascinating behavioral characteristics is developed. Lattice structure as well as the sandwich composite panels are both constructed. Numerical simulation is utilized to simulate the dynamic compression and blast behavior of the proposed structures considering the rate-dependent properties, elastoplastic response and nonlinear contact. Mooney–Rivlin (MR) hyperelastic constitutive model and Generalized Maxwell model are used to model the TSL structure, and Johnson–Cook material model is implemented to model the plate material. The numerical model is validated by comparing with the experimental results. A series of parametric studies are conducted to gain insight into the effects of loading velocity, number of core layers, equivalent TNT loads and panel thickness on the dynamic mechanical behavior of the TSL lattice and sandwich structures. Testing results indicated that the proposed TSL lattice possessed an attractive mechanical behavior, which was relevant to the specific geometric parameters and loading conditions. The proposed novel lattice would expand the design space for the development of future materials with customized response characteristics.

Green laser powder bed fusion based fabrication and rate-dependent mechanical properties of copper lattices

Additive manufacturing of pure copper (Cu) via laser-powder bed fusion (L-PBF) is challenging due to the low energy absorptivity under infra-red laser. As a result, 3-dimensional architectures, known for excellent load-bearing and energy absorption capabilities, have not been fabricated in pure Cu, so far. This study, for the first time, Cu lattice structures are fabricated through laser-powder bed fusion (L-PBF) with green laser (λ = 515 nm). Structural and microstructural analysis confirm that the lattice structures consist of well-defined unit-cells and show dense microstructure. The deformation behavior is investigated under a wide range of strain rates from ∼0.001 /s to ∼1000 /s. The stress–strain curves exhibit a smooth and continuous deformation without any post-yield softening, which can be attributed to the intrinsic mechanical properties of Cu. Correlated with post-mortem microscopy examination, the rate-dependent deformation behavior of pure Cu lattice structures is investigated and rationalized. The current work suggests that the complex Cu architectures can be fabricated by L-PBF with green laser and are suitable for dynamic loading applications.

Rate-dependent properties of resistance-welded carbon fiber-reinforced polyetheretherketone joints: Simulations and experiments

The rate-dependent characteristics of the resistance-welded joints of thermoplastic composites are investigated via simulations and experiments. A rate-dependent cohesive zone model based on the Kohlrausch–William–Watts formulation is proposed to capture the mechanical response of the joints at different loading rates, which is validated by the experimental results in terms of stiffness, strength, and failure. The proposed model is equivalent to the generalized Maxwell model with only eight input parameters to describe the welding interface's time- and history-dependent mechanical response. The stress distribution, crack emergence, and damage evolution of welded joints at different loading rates are revealed through numerical calculations. Additionally, the experimental results indicate that the strength of the joint is enhanced with the increase in the loading speed, as the strengthening effect caused by the high strain rate and the shorter loading time results in a tightly bonded stainless-steel/matrix interface and a rougher fracture surface.

XFEM Analysis of Strain Rate Dependent Mechanical Properties of Additively Manufactured 17-4 Precipitation Hardening Stainless Steel

AbstractAdditively manufactured (AM) specimens of 17-4 precipitation hardening (PH) stainless steel (SS) corresponding to the three-point bend test, compact tension test, and single edge cracks were analyzed using the extended finite element method (XFEM) approach. A two-dimensional and three-dimensional elastic-plastic simulation were conducted using “abaqus 6.14” software based on the experimental results and validated with the simulation results. In XFEM, the partition of unity was used to model a crack in the standard finite element mesh. Based on simulation results, the present study compares the mechanical properties of AM 17-4 PH stainless steel samples with those of wrought 17-4 PH samples. Stress intensity factor and J integral were used to measure fracture toughness of the specimens. The change in fracture toughness with strain rate was evaluated by simulating two-dimensional compact tension specimens. The presence of defects such as pores resulting from entrapped gas, un-melted regions, and powder particles resulting from lack of fusion were the main reasons for lower elongation to failure of laser powder bed fusion (L-PBF) produced 17-4 PH SS reported in the literature.