Dynamic Stress-strain Response Research Articles

Dynamic response of OWT tripod pile foundation in clay considering scour

Tripod-supported offshore wind turbine (OWT) foundation must withstand wind, wave, and seismic loads. In addition, it may be threatened by scouring during its service life, which could affect its bearing capacity and the overall OWT dynamic response. This study develops a three-dimensional numerical model of OWT tripod pile foundation to investigate scour effects. The numerical model incorporates a simplified single bounding surface model to simulate the dynamic stress–strain response of clay soil. The results revealed that scouring can reduce the first-order natural frequency of tripod pile-OWT system; however, the reduction usually does not lead to resonance within the 1P frequency range. Nonetheless, as the scour depth increases under wind and wave loads, the horizontal displacement of the wind turbine structure increases monotonously; however, its peak acceleration increases initially then decreases slightly as the scour depth continues to increase. Under seismic loading only, the OWT response exhibits complex evolution pattern as the scour depth increases. On the other hand, the foundation horizontal displacement and rotation angle increase significantly under combined wind-wave-seismic loads when the scouring depth reaches three times the pile diameter. Finally, the scouring depth has a relatively small impact on the foundation vertical displacement.

Inverse design of functionally graded porous structures with target dynamic responses

Although functionally graded porous structures (FGPS) have been studied comprehensively due to their excellent mechanical and functional properties, the design process of FGPS with target stress response still dependent on continuous trial and error, which is not only time-consuming but also heavily relies on experience and intuition. This study proposes a novel inverse design framework of 2D FGPS with targeted dynamic stress-strain responses via a combination of conditional diffusion model and a residual neural network. Unlike traditional binary pixel representations, this approach utilizes nuclei position maps and color mapping technique to represent the structure configurations and cell wall thicknesses to improve the efficiency and performance of the model. Firstly, various functionally graded porous structures were constructed by employing Voronoi diagram techniques, and finite element simulations were conducted to calculate the nonlinear responses subjected to dynamic loadings. A dataset comprising 2100 FGPS and corresponding nonlinear stress-strain responses was established. Then, an inverse design framework is formulated by integrating a generator that uses a diffusion model to synthesize structures conditioned on specific target responses, with a predictor that employs a residual neural network to assess the responses of these structures. Finally, to demonstrate the effectiveness of the approach, the performance of the predictor and generator was thoroughly investigated. Structures with various target stress-strain responses were generated through the proposed method, and validated by finite element analysis. A detailed impact experiment was also carried out to verify the effectiveness of the proposed methods. The result shows that the framework can effectively generate new structures with objective nonlinear responses. This work offers a fast and efficient way to design FGPS that meet specific performance objectives.

A split Hopkinson pressure bar for experimental investigation of dynamic pulverization under very high strain rates.

Off-fault damage or pulverized rocks found in large-scale strike-slip faults are of great interest in earthquake research. In order to experimentally investigate rock pulverization, we developed a split Hopkinson pressure bar with compact dimensions and high-speed imaging. The developed experimental setup is capable of generating very high strain rates up to 1320s-1 with the satisfaction of stress equilibrium, which are essential to reproduce the dynamic pulverization observed in nature and obtain dynamic stress-strain responses accurately. High-speed imaging revealed that cracks initiate and propagate along the grain boundaries at very high speeds, while the dynamic stress-strain response suggested that energy dissipated into the fracture increases with stronger impacts. In addition, we show that the apparatus is capable of producing particle size distributions partly similar to those in naturally pulverized rocks of large-scale strike-slip faults. Thus, our developed system with compact dimensions opens new ways to understand the dynamics of the rock pulverization in off-fault regions of large-scale strike-slip faults.

Influence of Microstructure on the Dynamic Behaviour of Polyurethane Foam with Various Densities

Polyurethane foam is reinforced with varying proportions of metal loads and other components to increase shock absorption and mechanical impact. The main objective is to develop high-performance polymeric materials based on polyurethane foam developed with different compositions and specific densities. We monitor the growth distances and temperatures of the polyurethane foam in time to reach the optimum formulations. We conduct static compression tests and investigate the effect of drop weight on the deformation of polyurethane foam structures by dropping a weight from a specified height. Dynamic collisions cause deformations of the polyurethane foam structure. After investigating the low weight, we found that polyurethane foams have a good absorption coefficient at certain frequencies. Dynamic stress-strain response curves are used to characterize different stress rates. High-stress levels and similar strains indicate a high resistance to shock. We follow the evolution of microstructure structures by scanning electron microscopy (SEM) to observe deformation and fracture behavior with reversibility and recovery.

A numerical assessment of local strain measurements on the attenuation and modulus dispersion in rocks with fluid heterogeneities

SUMMARY The forced oscillation method is widely used to investigate intrinsic seismic wave dispersion and attenuation in rock samples by measuring their dynamic stress–strain response. However, using strain gauges to locally measure the strains on samples surfaces can result in errors in determining the attenuation and moduli of rocks with mesoscopic scale heterogeneities. In this study, we developed a 3-D numerical model based on Biot's poroelastic theory to investigate the effect of strain gauge location, number and size on attenuation and dispersion in response to wave-induced fluid flow. Our results show that increasing the strain gauge length, number, and size can reduce the error between local and bulk responses. In a homogeneous and isotropic rock with a quasi-fractal fluid heterogeneity at 12 per cent gas saturation, the relative error between local and bulk responses stays below 6 per cent when the strain gauge length surpasses 8.6 times the correlation length. As the gas saturation becomes larger, the ratio minimally changes non-monotonically, initially increasing and then decreasing. We also used the Monte Carlo method to demonstrate that local laboratory measurements can approximate the reservoir-scale response with a minimum relative error of 1.5 per cent as the sample number increases. Our findings provide guidance for (i) interpreting local low-frequency measurements in terms of bulk properties of rock and (ii) upscaling lab measurements to reservoir-scale properties.

The Influence of the Strain Rate and Prestatic Stress on the Dynamic Mechanical Properties of Sandstone-A Case Study from China.

A series of conventional dynamic uniaxial compressive (CDUC) tests and coupled static dynamic loading (CSDL) tests were performed using a split Hopkinson compression bar (SHPB) system to explore the variable dynamic mechanical behavior and fracture characteristics of medium siltstone at a microscopic scale in the laboratory. In the CDUC tests, the dynamic uniaxial strength of the medium sandstone is rate-dependent in the range of 17.5 to 96.8 s-1, while the dynamic elastic modulus is not dependent on the strain rate. Then, this paper proposes a generalized model to characterize the rate-dependent strength from 17.5 to 96.8 s-1. In the CSDL tests, with increasing initial prestatic stress, the dynamic elastic modulus and dynamic strength increase nonlinearly at first and then decrease. The results show that two classical morphological types (i.e., Type I and Type II) are observed in the dynamic stress-strain response from the CDUC and CSDL tests. By scanning electron microscopy (SEM), microscopic differences in the post-loading microcrack characteristics in the behavior of Type I and Type II are identified. In Class I behavior, intergranular fracture (IF) usually initiates at or near the grains, with most cracks deflected along the grain boundaries, resulting in a sharp angular edge, and then coalesces to the main fracture surface that splits the specimen along the direction of stress wave propagation. In contrast, Class II behavior results from the combined IF and transgranular fracture (TF).

Parameter range estimation and uncertainty analysis for high strain rate material response via model fusion

The dynamic stress–strain response of a material can be described by a number of different models of varying fidelity. However, an individual model’s ability to replicate the dynamic stress–strain response of a material can be hindered by experimental variability. Reification, an approach to fusing models and experimental data with inherent scatter, is presented. It is then used to determine the optimum parameters of the Johnson–Cook (JC) and Zerilli–Armstrong (ZA) models using a fusion of Split-Hopkinson Pressure Bar (SHPB) data and the JC and ZA models fit to the SHPB data using a traditional approach. The output of the fused model is a dataset that represents a “best-guess” sampling of the possible stress–strain response of a high strength steel. In the present work, the dynamic response of a newly developed steel, AF9628, is evaluated. Under the reification framework, the experimental variability and limitations of the mathematical model expressions are addressed by the optimized sampling of data and combined fitting process. The JC and ZA models are then re-fit to partitions of the fused dataset, which bound the responses of the traditionally fit JC and ZA models. The behavior of the re-fit models and the traditionally fit models are compared via a simulated Taylor anvil test.

Seismic behaviour of granular slope under railway embankment in large-scale shaking table test

This study investigates shear zone development in a coarse-grained soil slope beneath a railway embankment under seismic action. Clarifying the dynamic stress and residual strain responses under different seismic excitations reveals the slope instability mechanism. A typical coarse-grained soil slope under construction of the Sichuan-Tibet Railway Railway was selected for large-scale shaking table model testing. The evolution of slope response parameters (dynamic displacement, acceleration, dynamic strain and residual strain, and dynamic earth pressure) was monitored. The seismic damage modes and resulting deformations of the embankment and slope were analysed. The evolution characteristics of a shear zone were described; the relationship among acceleration, dynamic stress, and dynamic strain was clarified; and the critical state of earthquake-induced slope instability was defined. The main conclusions are as follows: under seismic excitation, the slope slip surface forms mostly near the interface between the sand and breccia layers, and a weakness zone exists between the subgrade and slope surface. Under high-energy seismic excitation (i.e., PGA ≥ 0.4 g), positive peak acceleration is more suitable for assessing the elevation amplification effect. Considering the cumulative strain distribution contour maps, the growth characteristics in the dynamic stress peak area can describe the development of a shear slip zone. Acceleration amplification factors can reflect slope responsiveness, but the energy contained in the seismic waves determines deformation. When the ratio of dynamic to shear stress exceeds 2, the dynamic strain in the slope slip zone increases considerably with shear zone extension and slope instability. With increasing dynamic stress, the growth characteristics of residual strain exhibit stability, transition and failure states.

A continuous dynamic constitutive model for normal- and high-strength structural steels

The use of numerical models in the advanced analysis and design of steel structures, particularly under extreme loading conditions, is becoming increasingly widespread. A crucial component of such models is an accurate description of the material response. A systematic study into the dynamic constitutive modelling of structural steels is presented herein. The key features of the dynamic stress–strain characteristics of structural steels at various strain rates, i.e., test methods, material strength, strain-rate effect index and strain-rate effect models, are examined and discussed. Supplementary SHPB tests on both normal- and high-strength structural steels (Q235, Q355, Q460, and S960) under a wide range of strain rates up to 5000 s−1, filling gaps in existing datasets, are then carried out. A database of dynamic test results, containing 453 stress–strain curves, is systematically established and analyzed. Finally, a continuous dynamic constitutive model, capturing the dependency of both yield strength and strain rate, is proposed to predict the dynamic stress–strain response for structural steels, from normal- to high-strength material (235–960 MPa), and from static to high strain rate loading conditions (up to 5000 s−1).

Static and dynamic characterization of fiber reinforced sand: A numerical investigation

For the characterization of fiber-reinforced soil under static loading conditions, there is a wealth of literature. However, study on the dynamic behavior of fiber-reinforced soil is very limited. Now that earthquakes are occurring frequently around the world, the dynamic soil analysis has become important for all classes of geotechnical engineering problems. Through numerical simulation of triaxial specimens, the current study explores the behaviour of fiber-reinforced cohesionless soil. The numerical model was validated using existing laboratory triaxial compression testing literature. The stress–strain response of fiber-reinforced sand has been investigated using static and cyclic triaxial testing, as well as other combinations of fiber contents. Fiber-reinforced sand is tested for bulk modulus, shear modulus, and damping values. Effects of fiber contents on static and dynamic stress–strain response of fiber-reinforced soil are highlighted. It has been observed from results that, with an increase in fiber content modulus of elasticity, bulk modulus and shear modulus values increase while damping coefficients decrease for the same. It is believed that the highlighted numerical approach will be an alternative to laboratory experiments to determine the dynamic properties of fiber-reinforced soil.

Experimental Investigation on Multiscale Fracturing in Thermally Treated Sandstone under SHPB Impact Loading

To study the effect of temperature on the dynamic mechanical behaviors and fracture characteristics of thermally treated sandstone, compressive dynamic loading experiments were performed on a series of samples using a split Hopkinson pressure bar (SHPB). In the tests, the dynamic uniaxial compressive strength of the thermally treated sandstone was inversely proportional to the temperature treatment in the range of 200°C–1000°C, while the dynamic elastic modulus first increased and then gradually decreased after different temperature treatments. The results show that two classical mechanical types (i.e., Class I and Class II) are observed from the dynamic stress-strain responses of SHPB tests for thermally treated sandstone. By means of scanning electron microscopy (SEM), the microdifference of postloading microfracture characteristics in Class I and Class II behavior was identified. In Class I behavior, intercrystalline cracks (IE) are the chief form of cracks on the fracture surface of a specimen fractured by SHPB loading even though there some intracrystalline cracks may also be present. In contrast, Class II behavior results from the chief cracking type being intracrystalline cracks.

Modelling the dynamic compressive response of syntactic foam with hierarchical cell structure

Rate-dependent mechanical response of fly ash cenospheres polyurethane syntactic foams (CPSFs) with hierarchical cell structure was examined through dynamic compression tests. Quasi-static compression strength and specific energy absorption varied in the range of 9.5–29.5 MPa and 4.8–13.0 MJ/m3 within the density of 0.5–0.7 g/cm3. The thermal conductivity coefficient of CPSFs increased from 0.08 W/m/K to 0.13 W/m/K with density, while the specific heat capacity varied in a narrow range of 0.9–1.07 J/g/K. At high strain rates the strength and plateau stress of CPSFs with density of 0.6 g/cm3 increased 25%–39% and 13%–43%. The proposed foam is comparative potential in civil engineering according to its thermal insulation performance and excellent shock dissipation properties. Due to complicated microstructure, CPSFs exhibited different strain rate sensitive behaviors in the initial collapse stage and the stable collapse stage. A constitutive relation was developed to describe dynamic stress-strain response which includes the elastic stage, the initial collapse stage characterized by nonlinear stress increasing and decreasing process, the platform stage and the densification stage. The predictions shown good accordance with the experimental results in wide strain rate range.

Modeling of sand particle crushing in split Hopkinson pressure bar tests using the discrete element method

The discrete element method (DEM) has been extensively used to study the micro-mechanical behavior of sand subjected to quasi-static strain rates. In most of these studies, the sand specimens were prepared with an upscaled particle size distribution (PSD) to reduce the computational cost. However, the effectiveness of this upscaling approach in replicating the dynamic sand response is not well understood, especially at high stresses where significant particle breakage occurs. In this paper, several split Hopkinson pressure bar (SHPB) tests reported in literature are modeled in DEM using two methodologies: 1) applying the reported strain rates directly to the DEM specimen without accounting for wave propagation in the incident and transmission bars; and 2) modeling the complete SHPB test setup including the incident and transmission bars. The results show that with well-calibrated parameters for contact behavior and particle crushing, specimens with upscaled PSD provide similar dynamic stress-strain response and PSD evolution as those reported in literature. This study shows the importance of particle breakage in the stress-strain response under high stresses as the specimens without particle breakage provide a much stiffer response compared to the specimens with particle breakage. The developed DEM model may be a useful tool to model the complete SHPB test setup as the incident, reflected and transmitted stress waves can be accurately replicated.

Experimental and Numerical Study of Fracture Behavior of Rock-Like Material Specimens with Single Pre-Set Joint under Dynamic Loading.

The Split Hopkinson Pressure Bar (SHPB) is an apparatus for testing the dynamic stress-strain response of the cement mortar specimen with pre-set joints at different angles to explore the influence of joint attitudes of underground rock engineering on the failure characteristics of rock mass structure. The nuclear magnetic resonance (NMR) has also been used to measure the pore distribution and internal cracks of the specimen before and after the testing. In combination with numerical analysis, the paper systematically discusses the influence of joint angles on the failure mode of rock-like materials from three aspects of energy dissipation, microscopic damage, and stress field characteristics. The result indicates that the impact energy structure of the SHPB is greatly affected by the pre-set joint angle of the specimen. With the joint angle increasing, the proportion of reflected energy moves in fluctuation, while the ratio of transmitted energy to dissipated energy varies from one to the other. NMR analysis reveals the structural variation of the pores in those cement specimens before and after the impact. Crack propagation direction is correlated with pre-set joint angles of the specimens. With the increase of the pre-set joint angles, the crack initiation angle decreases gradually. When the joint angles are around 30°–75°, the specimens develop obvious cracks. The crushing process of the specimens is simulated by LS-DYNA software. It is concluded that the stresses at the crack initiation time are concentrated between 20 and 40 MPa. The instantaneous stress curve first increases and then decreases with crack propagation, peaking at different times under various joint angles; but most of them occur when the crack penetration ratio reaches 80–90%. With the increment of joint angles in specimens through the simulation software, the changing trend of peak stress is consistent with the test results.

Experimental investigations on the in-plane dynamic compressive behavior and upper limit of constant strain rate for 2D twill weave carbon fiber reinforced composite

The in-plane dynamic compressive behavior of a 2D twill weave carbon fiber reinforced composite was investigated using the split Hopkinson pressure bar (SHPB) apparatus. Constant strain rate loading was achieved with the adoption of pulse shapers within the experiments. A non-dimensional parameter was adopted to verify the stress equilibrium state of the specimens, which ensured the effectiveness of the experimental results. The upper limit of constant strain rate for the composite, which determines the achievable range of constant strain rate, was analytically estimated and verified by the experimental results. On this basis, the dynamic compressive behavior of the composite was investigated within the strain rate range of 193/s-846/s. The stress-strain curves were obtained under the studied strain rates, an empirical equation for the strengths under different strain rates was summarized. Based on the experimental results, a viscoelastic constitutive model was adopted to characterize the dynamic stress-strain response. Finally, the deformation process of the specimens recorded through high speed photography was discussed. Together with the microscopic observations, typical damage modes of the specimens were summarized

Dynamic stress–strain response of graphene nanocomposites

The dynamic stress–strain response of a polyvinyl alcohol (PVA) – graphene oxide (GO) nanocomposite is examined through tensile testing over a strain rate range of 0.003–1200/s, as well as via theoretical microscale modeling. PVA-GO samples with various GO content were prepared and subjected to uniaxial tension using a universal testing machine and a split Hopkinson tension bar arrangement. In previous studies by the authors [1,2], interfacial slip between the GO flakes and PVA matrix was identified as a key mechanism in the mechanical behavior of the nanocomposite, and a modified Mori-Tanaka (M-T) approach was developed to accommodate the effect of slip. The modified M-T method was employed to model the stress–strain response of the PVA-GO nanocomposite at various strain rates, and close agreement between the theoretical and experimental results was observed. The rate sensitivity of PVA and its nanocomposites was analyzed by determining the initial elastic stiffness of specimens and their stress corresponding to a strain of 0.1, as functions of logarithmic strain rate (log(ε˙)); it was found that both these parameters increase linearly with log(ε˙). Moreover, the rate of increase in initial elastic stiffness with log(ε˙) increases with GO content. In terms of the relationship between the stress at a strain of 0.1 and the logarithmic strain rate (logε˙), both PVA and its nanocomposites display curves with similar profiles.

Radial and axial inertia stresses in high strain rate deformation of polymer foams

Polymer foams are widely used in applications that require impact energy absorption. Experimental characterization of the impact response of polymer foams is challenging. The primary challenges associated with the characterization of polymer foams in high strain rate conditions are the significant effects of inertia and material compressibility. In this work, we develop analytical solutions for radial and axial inertia stresses that develop during high strain rate deformation of polymer foams. The effects of strain rate increase rate, test piece geometry, density, and Poisson's ratio are discussed in detail. We also provide and discuss results from a case study on the impact response of a closed-cell foam subjected to controlled impact loading, focusing on the importance of inertial effects on the characterization of the dynamic stress-strain response. The analytical approach presented in this work facilitates the determination of the concurrent effects of material compressibility and inertia stresses in the dynamic deformation response of compressible materials.

An anisotropic bounding surface elastoplastic constitutive model for frozen sulfate saline silty clay under cyclic loading

To study the mechanical properties of frozen saline soil under cyclic loading, the cyclic tri-axial compressive experiments of 36 samples are performed for frozen saline silty clay with 0.0, 0.5, 1.5 and 2.5% of Na2SO4 contents at the temperature of −6 °C, respectively. The experimental results illustrate that the effect of the salt contents and confining pressures on the strength and deformation properties of frozen sulfate saline soils under cyclic loading is significant. To understand the deformation characteristics of frozen sulfate saline silty clay (this kind of saline soil), a bounding surface elastoplastic constitutive model is presented based on the test results and bounding surface plasticity theory. The proposed model includes the effects of salt contents and confining pressures on dynamic characteristics, therefore, it can suitably describe the dynamic stress-strain response of frozen saline soil under cyclic dynamic loading. This proposed model includes: (1) Critical stress ratio calculation formula, considering the effect of salt contents and confining pressures, is proposed. Critical stress ratio and bounding surface shape parameter varying with confining pressures are introduced into plastic potential surface function and bounding surface function to describe pressure melting and crushing characteristics of frozen soils under high confining pressures. (2) The influence of the initial anisotropy and the induced anisotropy by dynamic loads on bounding surface of rotation hardening is considered. A non-associated flow rule together with a mixed hardening rule is used to describe the plastic flow rule and hardening rule of soils during cyclic loading, respectively. (3) A radial mapping rule with mobile mapping origin is employed to simulate elastoplastic properties of soils during cyclic loading. By comparing its simulated results with the test results of cyclic triaxial compression tests, it is found that the proposed model in this paper can well predict deformation characteristics of this kind of saline soil under cyclic loading.

Dynamic stress-strain response of high-energy ball milled aluminium powder compacts

Ball milling is a bulk powder manufacturing process used in the creation of dispersion strengthened and nanostructured materials. Fundamentally, these powders have not been dynamically characterized in a green state prior to hot consolidation. The understanding of high strain-rate compaction on void collapse and particle interaction for such systems can help the development of predictive models for impact events of porous metallic structures that may be employed as energy absorbers, reactive structures, and intermetallic materials. This study investigates high strain-rate impact of porous green compacts of as-received and high-energy ball milled (HEBM) aluminium powders characterized under dynamic compression using a split-Hopkinson pressure bar (SHPB) in a passive confinement configuration. The plastic deformation of the powder compacts and crush up were shown to be strain-rate insensitive within the strain rate range of 1000–2100 s−1 and as a result, were modelled adequately with a second order P-α model. The as-received aluminium and HEBM aluminium powders appear to have the same strain-hardening coefficient and strength index as solid aluminium after yielding. The respective stress-strain responses of green compacts follow the same trend but differ only in strength as result of porosity and pre-strain experienced prior to dynamic compression. The HEBM powder was found to be twice as strong as the untreated as-received aluminium powder.

Elastomeric Microlattice Impact Attenuators

Summary Impact-attenuating materials are designed to absorb impact energy through the collapse of pores within the material below a threshold force (or acceleration), thereby mitigating damage or injury. Recent advances in additive manufacturing techniques have enabled the fabrication of cellular materials with architected lattice topology. Here it is demonstrated that, via design of cellular architecture, the dynamic stress-strain response of elastomeric lattices can be tailored to achieve impact-attenuation performance exceeding state-of-the-art foams for both single- and multi-hit scenarios. The additional degrees of freedom in the design of the cellular architecture of lattice-based impact attenuators are then leveraged to optimize their performance for a typical helmet impact scenario wherein the contact area increases during deformation. An improvement over state-of-the-art vinyl-nitrile foam helmet pads is achieved during a standard helmet test, leading to lower head acceleration. This breakthrough could pave the way to helmets with improved injury protection.