Strain Energy Research Articles

Multiple impact resistance and microstructure of hybrid fiber-reinforced fly ash/slag-based geopolymers after exposure to elevated temperatures

Engineered geopolymer composites (EGC) have garnered significant attention from researchers as a new environmentally friendly building material with superior tensile properties, impact resistance, and high-temperature resistance. This study focuses on the investigation of the dynamic mechanical properties of a hybrid fiber reinforced lightweight EGC containing ceramsite (LW-EGC) after exposure to elevated temperatures and multiple impacts. The effects of temperature, steel fiber content, and ceramsite types were taken into consideration. The analysis encompassed multiple impact stress-strain curves, dynamic peak stress and strain evolution, energy absorption, damage evolution, damage morphology, and microstructure changes following exposure to elevated temperatures. The experimental results revealed a significant decrease in the number of impacts endured by LW-EGC-M as the temperature increased. After 200 °C, the LW-EGC-M experienced 15 impacts, while after 800 °C, it only endured 2 impacts. Both cumulative energy absorption and cumulative damage of LW-EGC exhibited an exponential growth pattern with an increasing number of impacts. Microstructural analysis unveiled the emergence of a new nepheline phase after exposure to elevated temperatures, while the calcite in the matrix demonstrated gradual decomposition. Moreover, elevated temperatures led to a decreased Si/Al ratio in the matrix. The complete melting of PVA fibers after exposure to elevated temperatures resulted in the production of numerous interconnected pores in the matrix, leading to a decline in the mechanical strength of LW-EGC. This phenomenon also contributed to the reduction of internal pore pressures and the release of local vapor pressure generated by elevated temperatures.

N, S, Se-Codoped dual carbon encapsulation and Se substitution in pyrite-type FeS2 for high-rate and long-life sodium-ion batteries

The use of metal sulfides as anodes in sodium-ion batteries (SIBs) faces significant challenges due to slow reaction kinetics and extensive shuttling of sodium polysulfides (NaPSs). In response, a selenium-substituted iron disulfide encapsulated in a nitrogen-sulfur-selenium-codoped dual carbon framework (Se-FeS2@NSSC) has been engineered for high-performance SIBs. Selenium substitution within the FeS2 lattice improves electrical conductivity, facilitates favorable redox kinetics that reducing the possibility of NaPSs generation. Moreover, the dual NSSC encapsulation promotes Na+/electron transport and efficiently manages volume expansion during electrochemical processes. Strong interfacial interaction (Fe-S-C bonding) between Se-FeS2 and NSSC further suppress NaPSs shuttling, significantly alleviating the cell failure and thus prolonging its lifespan. Consequently, Se-FeS2@NSSC demonstrates a top-notch performance, achieving a notable capacity of 725 mAh g-1 at 0.5 A g-1, unparalleled rate capability (355.1 mAh g-1 at 30 A g-1), and sustained cyclic stability (89.6 % capacity is retained after 1250 cycles). Theoretical analyses underscore the critical role of selenium in diminishing bulk stress–strain energies, lowering energy barriers for Na+ diffusion, and decreasing Gibbs free energy for conversion reactions, thereby markedly bolstering electrochemical kinetics and overall performance of Se-FeS2@NSSC. The insights gleaned from this research foster advancements in developing next-generation anodes with high capacity and durability, representing a promising response to the existing hurdles in SIBs technology.

Microstructural evolution of GH4079 superalloy during hot deformation and heat treatment

Through hot compression and subsequent heat treatment experiments on GH4079 superalloy, the influence of different hot deformation and heat treatment conditions on the evolution of GH4079 superalloy microstructure was studied. The evolution of grains and γ′ phases under different thermomechanical conditions was investigated. The results indicate that at deformation temperatures above 1100 °C and strain rates ranging from 0.01 to 0.1 s−1, the primary mechanism of dynamic softening in the alloy is discontinuous dynamic recrystallization (DDRX). When the deformation temperature is below 1100 °C and strain rates range from 0.01 to 0.1 s−1, both continuous dynamic recrystallization (CDRX) and DDRX are the main dynamic softening mechanisms. Due to high strain energy accumulation, the samples deformed at lower temperatures (below 1100 °C) and then solution-treated at 1120 °C for 8 h exhibit significant increases in recrystallization volume fraction and recrystallization grain size. Conversely, the samples deformed at higher temperatures (above 1100 °C) and then solution-treated at 1120 °C for 8 h show minimal changes in recrystallization volume fraction and recrystallization grain size. After solution treatment at 1140 °C, the grain size of the alloy significantly increases. The samples deformed at higher strain rates exhibit the evolution of fine γ′ phases into elongated rod shapes during solution treatment, while larger γ′ phases undergo splitting processes.

A phase field framework for corrosion fatigue of carbon steel

Corrosion fatigue damage occurs when metallic materials are subjected to cyclic loading in a corrosive medium. In this study, a phase field framework is proposed to predict the corrosion fatigue of carbon steels. The coupling effect of fatigue and corrosion is explicitly implemented in the proposed phase field framework by coupling the displacement field, electrochemical field and phase field. A degradation function of the interface free energy density with the consideration of elastic and plastic strain energies is introduced to account for the fatigue damage accumulated during the corrosion fatigue process. The applicability of this framework is validated by accurately capturing the pure fatigue and corrosion fatigue behaviors of compact tension specimens, particularly the acceleration effect of corrosion on the fatigue crack growth. The propagation morphology and rate of the corrosion fatigue crack in single pit and multiple pit models are studied. The distribution of stress state and strain energy density induces the directionality of crack propagation. The influence of loading frequency on the corrosion fatigue process is discussed in detail. Due to the corrosion-fatigue coupling effect, the corrosion rate increases with increasing of the loading frequency, resulting in an accelerated corrosion fatigue process. Moreover, the significance of the plasticity in the prediction of corrosion fatigue is emphasized.

Thermodynamics and kinetics of cation partitioning between plagioclase and trachybasaltic melt in static and dynamic systems: A reassessment of the lattice strain and electrostatic energies of substitution

Most of the solidification history of magmas beneath active volcanoes takes place in chemically and physically perturbed plumbing systems where the growth of crystals is collectively governed by a range of kinetic processes related to the dynamics of crustal reservoirs and eruptive conduits. In this context, we have experimentally investigated the partitioning of major, minor, and trace cations between plagioclase and trachybasaltic melt under conventional static (no physical perturbation) and dynamic (melt stirring) crystallization regimes. Slow interface reaction kinetics are established between the advancing crystal surface and the adjacent melt, as the result of the combined control of a small degree of effective undercooling, prolonged diffusive relaxation, and convective homogenization. The kinetic aspects of plagioclase growth influence the partitioning of trace cations during transport of structural units across the crystal-melt interface, with consequent departure from macroscopic equilibrium in the system. The type and number of charge–balanced and −imbalanced configurations produced by the accommodation of trace cations into the coordination polyhedron can be thermodynamically rationalized in terms of lattice strain and electrostatic partitioning energetics. However, the overall solution energy accompanying trace cation kinetic substitutions cannot be entirely deconvoluted from major component activities in both melt and plagioclase phases. The emerging view that slow interface kinetic processes may lead to strong compositional dependence for the partition coefficient in dynamic subvolcanic environments contrasts markedly with the conventional idea that the energetics of cation partitioning are dominantly controlled by the effect of isothermal changes in the bulk system.

Omnidirectional soft pneumatic actuators: a design and optimization framework.

Soft pneumatic actuators (SPAs) play a pivotal role in soft robotics due to their unique characteristics of compliance, flexibility, and adaptability. There are plenty of approaches that examine the modeling parameters of SPAs, aiming to optimize their design and, thus, achieve the most advantageous responses. Current optimization methods applied to SPAs are usually performed individually for each design parameter without considering the simultaneous effect all parameters can have on the output performance. This modeling shortcoming is essential to be addressed since customized SPAs are used in a variety of applications, each with different output requirements. This study provides a generalized design optimization framework for modeling the SPA performance for their motion profiles, the produced strain energy while being deformed, and their stiffness characteristics. Utilizing experimentally validated finite element methods, all geometrical and material parameters of the models are investigated in response surface methodology optimization using the central composite design approach. The results showcase the entire design space of omnidirectional SPAs, along with their output performance, providing guidelines to the end user for design optimization. The offering of this modeling process for SPAs can be adapted to the demands of any potential application and ensure the best performance with respect to the required output responses.

Elastic Localization With Particular Reference to Tape-Springs

Abstract Many elastic systems localize under applied displacement, precipitating into regions of lower and higher strain; further displacement is accommodated by growth of the high strain region at a constant load. Such systems can be studied as propagating instabilities, focusing on the work required to propagate the high strain region, or as two-phase energy minimization problems. It is shown that the Maxwell “equal-areas” construction, and the related common tangent construction, provide the solution to either approach. A new, graphical, proof of the Maxwell equal-areas construction using total strain energy diagrams is presented. Tape-springs are investigated as a case study, with localization presenting as the formation of elastic folds—developable regions with high curvature. One notable property of tape-spring folds is that the fold radius is approximately equal to the initial transverse radius. This result was first proven by Rimrott, and later improved by Calladine and Seffen. A further improvement is obtained here by application of the common tangent construction, and all solutions are shown to be approximations to the Maxwell equal-areas construction in the limit of zero thickness.

A covariant formulation for finite strain modelling of orthotropic elasticity and orthotropic plasticity with plasticity-induced evolution of orthotropy: Application to natural fibres

We introduce a rate-independent model for orthotropic elastic and orthotropic plastic material behaviour in a hyper-elasto-plastic framework at finite strains. The model is based on the postulate of covariance and does not rely on a multiplicative decomposition of the deformation gradient. Furthermore, a plastic-deformation-induced evolution of orthotropy is considered, similar to the notion of plastic spin. We propose that the orthotropic strain energy function and the orthotropic yield criterion are guided by identical structural tensors that evolve with plasticity. The modelled material behaviour is significant for natural fibres such as flax, hemp, or pulp fibres. Our formulation has three findings. Firstly, the covariant formulation of plasticity provides rate equations for the plastic variables and the structural tensors suitable for reproducing stress–strain diagrams of natural fibres. Secondly, the introduction of plastic-deformation-induced evolution of orthotropy in the proposed covariant setting results in a non-associative plasticity algorithm. Thirdly, the covariant setting allows the incorporation of suitable constitutive equations for the structural tensors to evolve orthotropy. The latter successfully models the stiffness increase in stress–strain diagrams of cyclic tensile tests of natural fibres.

Thickness-extensible higher order plate theory with enforced C1 continuity for the analysis of PEEK medical implants

Plate-like structures had been thoroughly studied in literature over years to reduce the computational space from 3D to 2D. Many of these theories suffer either from satisfying the free traction condition or thickness extensibility in addition to the consistency of transverse shear strain energy. This work presents a higher order shear deformation thickness-extensible plate theory (eHSDT) for the analysis of plates. The proposed eHSDT satisfies the condition of free traction as other theories do but it also satisfies the condition of consistency of transverse shear strain energy which is neglected by many theories in the area of plates and shells. The implementation of the proposed theory in displacement-based finite element procedure requires continuity of derivatives across elements. This necessary condition was achieved using the penalty enforcement method for derivative-based nodal degrees of freedom across the standard 9-nodes Lagrange element. The theory was tested for elastic bending deformation of Polyether-ether-ketone (PEEK) which is one of the basic materials for medical implants. The theory showed good accuracy compared to experimental data of the three-points bending test. The present eHSDT was also tested for different conditions with a wide range of aspects ratios (thin to thick plates) and different boundary conditions. The accuracy of the proposed eHSDT was verified against exact solutions for these conditions which showed the advantage over other approaches and commercial finite element packages.

Nonlinear viscoelastic effect on the fatigue performance of wood tar-based rejuvenated asphalt

The nonlinear viscoelasticity (NLVE) effects of rejuvenated asphalt are often neglected during fatigue degradation, potentially leading to misjudgment of its true fatigue performance. To more accurately quantify the fatigue life of rejuvenated asphalt under NLVE effects, frequency sweep (FS), incremental stress sweep (ISS), and linear amplitude sweep (LAS) tests were used to study two types of rejuvenated asphalt. FS and ISS tests respectively obtained the dynamic modulus |G*|LVE and |G*|NLVE representing the linear viscoelasticity (LVE) and NLVE of rejuvenated asphalt, and incorporated them into the simplified viscoelastic continuum damage (S-VECD) model to establish the fatigue failure criterion and predict the fatigue life of rejuvenated asphalt under high strain levels in LAS tests. The findings indicate that the NLVE-based-S-VECD model quantifies fatigue damage in rejuvenated asphalt lower than the LVE model, and the fatigue life of rejuvenated asphalt increases significantly after considering the NLVE effect. Besides, the failure difference (∆GR) and failure area difference (∆A) defined during the modeling process explain the impact of NLVE on the fatigue failure criterion average pseudo strain energy release rate (GR) of rejuvenated asphalt, validating the necessity of incorporating NLVE into the fatigue performance analysis of rejuvenated asphalt. Therefore, it's necessary to account for the impact of NLVE effect on the fatigue performance of rejuvenated asphalt in engineering practice, which will contribute to the development and application of rejuvenator.

Experimental study on energy and damage evolution of dry and water-saturated dolomite from a deep mine

The deformation and failure of a rock is closely related to the strain energy consumption during the load process of rock. To investigate the effect of water on energy evolution and damage characteristics of dolomite samples from a deep mine, the uniaxial compression tests were carried out on dry and water-saturated dolomite samples at different burial depths (900 m–1200 m). The effects of water on the evolution characteristics of elastic and dissipative energy ratios ( Ue/ U and Ud/ U) during rock deformation and failure was analyzed. Based on the variation rate of damage factor ( Df), a new brittleness index is proposed, which can effectively characterize the brittleness characteristics of water-bearing dolomite. The results show that the uniaxial compressive strength and elastic modulus of the water-saturated dolomite are significantly reduced compared to dry sample. The energy and damage evolution process of dolomite can be divided into four stages: initial damage stage, stable damage stage, pre-peak accelerated damage stage and post-damage stage. The variation rate of damage factor of the rock samples in the stable damage stage and the pre-peak accelerated damage stage appeared to increase significantly after water saturation treatment. Compared with water-saturated samples, more pronounced energy hardening characteristics and brittleness characteristics were observed in dry samples. In addition, the possible impact on the stability of deep rock engineering after the deterioration of rock mechanical properties and energy storage properties caused by water was analyzed. Groundwater can somewhat reduce rock burst proneness. However, it also has the potential to lead to greater rock engineering destabilization and failure hazards.

A simplified approach for predicting last ply failure load of VO-notched laminated composite components

In this study, the last ply failure (LPF) load of composite laminates with VO-notches under pure mode I and mixed mode I/II was investigated experimentally, analytically, and numerically. The efficiency of the virtual isotropic material concept (VIMC) in combination with a new combined failure criterion was also evaluated. The J-integral and average strain energy density failure criteria were combined with VIMC. Using analytical expressions for the J-integral and the average strain energy density (ASED), the prediction of the fracture load of notched components was simplified and expedited. The experimental fracture loads of notched specimens were determined for quasi-isotropic and cross-ply laminates under mode I and mixed mode I/II. The fracture loads were predicted using analytical expressions for the J-integral and ASED, combined with VIMC. The VIMC-ASED and VIMC-J-integral failure criteria demonstrated good accuracy in predicting the LPF, with the highest accuracy for mode I, slightly reduced accuracy for mixed mode I/II. VIMC, in combination with energy-based failure criteria, effectively predicts the fracture load. The use of analytical expressions further simplified and expedited the prediction process without losing accuracy, making it a practical approach for engineering applications. Additionally, this approach significantly reduces the time and cost associated with extensive experimental testing.

On the importance of the cracking process description for dynamic crack initiation simulation

A dynamic implementation of the coupled criterion under quasi-static loading, based only on the mean velocity during crack initiation, is proposed. It relies on a simultaneous node release method. It consists of computing the dynamic incremental energy release rate by simultaneously opening a crack of a finite length during a given time increment rather than progressively opening smaller crack increments following a velocity profile as in the progressive node release method. Both methods result in significantly different kinetic energy variations as a function of the crack length, and thus different incremental energy release rates for large enough crack velocities, for which the kinetic energy magnitude is similar to the elastic strain energy magnitude. Both simultaneous node release method and progressive node release method can however be equivalently used for small enough crack velocities since similar incremental energy release rates are obtained with both methods. Inverse identification of fracture properties based on dynamic crack initiation at a hole in Brazilian disk specimens yields critical energy release rates in the same order of magnitude as the one obtained based on dynamic crack propagation modeling.

Simulation of Localized Stress Impact on Solidification Pattern during Plasma Cladding of WC Particles in Nickel-Based Alloys by Phase-Field Method

As materials science continues to advance, the correlation between microstructure and macroscopic properties has garnered growing interest for optimizing and predicting material performance under various operating conditions. The phase-field method has emerged as a crucial tool for investigating the interplay between microstructural characteristics and internal material properties. In this study, we propose a phase-field approach to couple two-phase growth with stress–strain elastic energy at the mesoscale, enabling the simulation of local stress effects on the solidified structure during the plasma cladding of WC particles and nickel-based alloys. This model offers a more precise prediction of microstructural evolution influenced by stress. Initially, the phase field of WC-Ni binary alloys was modeled, followed by simulations of actual local stress conditions and their impacts on WC particles and nickel-based alloys with ProCAST and finite element analysis software. The results indicate that increased stress reduces grain boundary migration, decelerates WC particle dissolution and diffusion, and diminishes the formation of reaction layers and Ostwald ripening. Furthermore, experimental validation corroborated that the model’s predictions were consistent with the observed microstructural evolution of WC particles and nickel-based alloy composites.

On the evolution of β1/β′ coupled-structures in Mg–Y–Nd alloys: A simulation study

In magnesium alloys based on the Mg–Y–Nd system, the key strengthening precipitate phases, β1 and β′, often form coupled-structures, with β′ precipitates invariably attached to both ends of the β1. A question here is how the attached β′ precipitates evolve as the β1 lengthens within the solid magnesium matrix. To investigate this, this study uses a multi-scale model based on a three-dimensional phase field approach to simulate the evolution of β1 and β′ precipitates in a β1/β′ coupled-structure. The simulation results reveal that, during the evolution process, the β1 precipitate lengthens, while the attached β′ precipitates grow only at the side located along the direction of β1 extension and dissolves at the opposite side. This results in a visual effect where the β′ precipitates appear to “move” within the solid matrix. This phenomenon is governed by the interplay between chemical free energy and elastic strain energy. Chemical free energy promotes uniform growth of the β′ precipitates. However, the elastic strain energy, generated by the β′ precipitates and the stress field concentrated at the end of the β1 plate to which they are attached, favours growth of only one side of the β′ precipitates while causing dissolution at the other side. When the evolution of a coupled-structure is influenced by neighbouring coupled-structures, the evolution of β′ precipitates is strongly driven by the minimization of elastic strain energy. In general, the β′ precipitates tend to grow under tensile stress fields and dissolve under compressive stress fields.

Thermodynamic and propulsive characterization of nitro-substituted quadricyclane

This investigation delves into the potential of Octa-nitro Quadricyclane (ONQC), a nitro-substituted quadricyclane, as a next-generation energetic material. Employing a robust B3LYP-gCP-D3/6-31G(d) computational approach, the study evaluates key material properties of ONQC, including strain energy (700.2 kJ/mol), enthalpy of formation (668.6 kJ/mol), and density (2.08 g/cm³). These enhanced properties result in predicted increases of 124 % in detonation pressure and 49.5 % in detonation velocity compared to TNT, significantly surpassing the performance of conventional high-energy density materials. Additionally, ONQC's suitability as an energetic additive in bipropellant formulations was evaluated with NASA's Chemical Equilibrium with Applications (CEA) software. The primary focus was on bipropellant formulations employing kerosene-based fuels (RP-1, JP-10, JP-5, etc.) and liquid oxygen (LOX) as the oxidizer. Incorporating ONQC into propellant formulations provides substantial improvements in specific impulse and reduces oxidizer requirements. This makes ONQC a promising candidate for advancing propulsion technology.

Numerical study on structured sandwich panels exposed to spherical air explosions

There is a need to develop innovative protective shield structures to withstand extreme loads, such as impact and blast loading. Sandwich structures that absorb significant kinetic energy as strain energy through plastic deformation offer superior protection. This study conducts a numerical analysis of structured sandwich protective structures subjected to airblast loads using finite element modeling. First, an experimental result from the literature was used to validate and verify finite element models of an architected sandwich structure modeled in Abaqus/Explicit software. Second, parametric studies were conducted on sandwich structures with additional layers of insert plates and newly proposed core topologies for viable shield protection against airblast loading. The finite element analysis results indicated that, under the same impulsive load, the control sandwich panel exhibited higher kinetic energy, demanding a proportionally larger internal energy. Conversely, sandwich structures with additional inner core insert plates dissipated the imposed kinetic energy more efficiently, due to the inelastic plastic deformation of the proposed core configurations. Moreover, the energy absorption capacity and back sheet displacement time-history were significantly improved by dense-hierarchical inner core configurations. Additionally, the parametric study analysis showed that increasing the number of insert plates and designing the core topology of cellular walls to be redundant, dense-hierarchical, and braced against buckling significantly reduced core collapse mechanisms such as folding, buckling, and crushing. However, despite these benefits, a reversed effect on the areal specific energy absorption index was observed.

Vibration based dual-criteria damage detection method using deep neural networks in highway bridges with steel girders

This article introduces a new method for assessing the damage in steel girders of highway bridges using deep neural networks. The method uses modified forms of modal strain energy damage index and modal flexibility damage index to train the neural network and prevent unsafe decisions. The neural network is trained using damage indexes achieved from numerical simulations of the bridge with different damage scenarios. Three types of neural networks, including convolutional neural network (CNN), Long short-term memory (LSTM) neural network, and conventional artificial neural network (ANN) are compared to achieve the best performance. The proposed method overcomes previous detection problems such as false-positive indications, limited damage locations, and scenarios, and insufficient accuracy in cases with multiple damage scenarios. The results show that the proposed method and CNN can accurately identify unspecified damage locations and severity in multi-span highway bridges. The new training method of the CNN deep neural network systems overcomes some shortcomings in ANN, such as being time-consuming, having a low convergence rate, and experiencing data overfitting. Additionally, the CNN training scheme can limit the need for massive amounts of input data and increase the speed and accuracy of network training, especially in multiple damage scenarios.

A “poor-man’s” deformation plasticity based approach to topology optimization of elastoplastic structures

This paper presents a topology optimization framework utilizing a deformation plasticity model to approximate the isotropic hardening von-Mises incremental elastoplasticity model under monotone proportional loading. One advantage of the model is that it is based on a yield surface allowing for precise matching to uniaxial elastoplastic isotropic hardening response. The deformation plasticity model and the incremental plasticity model coincides for proportional loading and since the deformation plasticity model is path-independent, the computational cost and implementation complexity reduce significantly compared to the conventional incremental elastoplasticity. To investigate the deformation plasticity model combined with topology optimization, we compare three common elastoplastic optimization objectives: stiffness, strain energy and plastic work. The possibility to limit the peak local plastic work while maximizing the strain energy is also investigated. The consistent analytical sensitivity analysis which only requires the terminal state is derived using adjoint method. Numerical examples demonstrate that the proportionality assumption is reasonable and the deformation plasticity model combined with topology optimization is a competitive alternative to cumbersome incremental elastoplasticity.

Effect of CO2 Nanobubble Water on the Fracture Properties of Cemented Backfill Materials under Different Aggregate Fractal Dimensions

In order to cope with climate change and achieve the goal of carbon neutrality, the use of carbonization technology to enhance the performance of cement-based materials and achieve the purpose of carbon sequestration has become a very promising research direction. This paper considers the use of CO2NBW as mixing water for cement-based materials, aiming to improve the carbonization efficiency of materials to achieve the goal of carbon neutrality. This time, the effect of CO2NBW on cementitious filling materials under different aggregate fractal dimensions was studied through uniaxial compression tests and acoustic emission technology. The effect of CO2NBW on the mechanical properties and crack evolution of the material was discussed. The results showed that CO2 nanobubbles significantly improved the strength of cemented filling materials under different fractal dimensions, and the uniaxial compressive strength was most significantly improved by 23.04% when the fractal dimension was 2.7824. In addition, the characteristics of acoustic emission ring counts and energy parameters indicate that CO2 nanobubbles help improve the overall pore structure of the sample, affecting the macroscopic strength. However, the addition of CO2 nanobubbles reduces the limit energy storage ratio of elastic strain energy, which indicates that excessive CO2 concentration may affect the hydration reaction of the cementing material.