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In this work, the Mg-8Li-3Al-0.3Si (LAS830) alloy was prepared by the vacuum melting method. The as-cast alloy was subjected to backward extrusion at 250 °C and then spun at 250 °C. The microstructure and mechanical properties of the alloy during deformation were studied. The results showed that the LAS830 alloy primarily consisted of α-Mg and β-Li phases, and the AlLi, MgLi2Al, and Mg2Si phases were dispersed. After backward extrusion, the grains and AlLi phase were refined, the β-Li phase recrystallized, and the fine MgLi2Al phase precipitated. The spinning of the extruded alloy tubes resulted in the lamellar distribution of an α/β duplex microstructure, with even finer grains and more dispersed precipitates. The combined deformation significantly enhanced the alloy's strength and ductility, with the ultimate tensile strength reaching 235.4 MPa and an elongation of 15.74%. In addition, the average hardness of the α/β phase increases after backward extrusion, but the average hardness of the β-Li phase increases further after spinning. The as-cast LAS830 alloy exhibited a high work hardening rate but a low softening rate. With reverse extrusion, the work hardening rate decreased and the softening degree increased. Compared with backward extrusion, the work hardening rate and softening degree of the LAS830 alloy was reduced after spinning due to the combined effect of the lamellar distributed duplex microstructure and the dispersed second phases in the alloy, while its softening rate increased. [ABSTRACT FROM AUTHOR]

The Duffing equation containing a cubic nonlinearity is probably the most popular example of a nonlinear oscillator. For its harmonically excited, slightly damped, and softening version, stationary large amplitude solutions at subcritical excitation frequencies are obtained when standard semi-analytical methods like Harmonic Balance or Perturbation Analysis are applied. These solutions have the shape of a nose in the amplitude-frequency diagram. In prior work, it has been observed that these solutions may contain large errors and that high ansatz orders may be necessary when applying the Harmonic Balance or other semi-analytical methods to make them converge. Some of these solutions are observed to be asymptotically stable, while in most cases, they are unstable. The current paper aims to give a descriptive explanation for this behavior of the nose solutions, which is mainly related to the exact solution of the free undamped vibrations. Based on this, approximations of the nose solutions are calculated with a procedure combining properties of Perturbation Analysis and Harmonic Balance. Therein, the exact solution of the free undamped vibrations is taken as the zeroth approximation, while higher-order solution parts are calculated by balancing the harmonics, and the phase shift of the zeroth approximation is calculated by a residuum minimization. This method just requires the solution of a system of linear algebraic equations, while systems of nonlinear algebraic equations have to be solved in the case of directly applying Harmonic Balance. [ABSTRACT FROM AUTHOR]

The study investigated the creep-fatigue interaction behavior, fracture mechanism, and microstructure evolution of C630R ferritic/martensitic heat-resistant steel at 630 °C and 1% strain amplitude. The results indicate that C630R ferritic/martensitic heat-resistant steel exhibits noticeable cyclic softening behavior, with a decrease in the softening ratio from 0.46 to 0.40 as loading time increases. Microstructure evolution was examined using optical and scanning electron microscopes, revealing the appearance of secondary cracks on the longitudinal section of the sample. These cracks exhibited a curved expansion trend with multiple deformations and highly bifurcated micro-cracks at a low loading time of 30s. However, when the load holding time was increased to 300s, the fatigue cracks tended to expand in a straight line with fewer branches. Furthermore, the observed crack growth path under different loading times showed enrichment in Fe and Cr, with the crack tip containing Cr oxide, which helped prevent fatigue crack propagation. As the loading time increases, the rise in crack closure resulting from oxidation leads to a decrease in crack propagation. Electron backscatter diffraction observation revealed the formation of numerous substructures and recrystallized grains after varying holding times, enhancing the material's resistance to crack propagation. Moreover, the study found that with increasing load dwell time, the deformed grains decreased, and substructural grains became dominant (57.68% and 62.77% under 30s and 300s, respectively). This increased crack resistance resulted in shorter secondary cracks under prolonged load retention, with the secondary crack length decreasing from 146.36 μm at 30s loading time to 109.09 μm at 300s loading time. Additionally, the kernel misorientation angle value decreased significantly after different loading times, leading to a higher likelihood of cracks or holes forming in regions with high KAM values, where low-angle grain boundaries were formed.

A rigid block model with elasto‐plastic softening interfaces is developed for nonlinear static analysis of masonry structures subject to monotonic loading. Cracking, crushing, and shear failures are taken into account at interfaces, following a simple micro‐modeling approach. An optimization‐based formulation is used for the solution of the equation systems governing the behavior of the rigid block assemblage. A simple incremental solution procedure is implemented to take into account the material softening behavior and the effects of large displacements on equilibrium conditions. The interface models are validated against tension and shear tests on bi‐block prisms from the literature. Applications to numerical and experimental out‐of‐plane loaded masonry walls as well as to circular arches with mortar joints are presented to evaluate the effects of tensile strength and the accuracy of the developed model against responses involving P‐Δ effects. Comparisons with experimental tests on shear walls also involving cracking of the units in the failure mechanisms are finally reported to discuss the potentialities and limitations of the proposed modeling approach. [ABSTRACT FROM AUTHOR]

SiCp/2024Al composite was prepared by semi-solid stirring casting, and the distribution of SiCp was regulated by multi-step deformation of hot extrusion and multi-direction forging (MDF). The effects of SiCp distribution on the microstructure and properties of SiCp/2024Al composite ware studied. The results show that hot extrusion deformation cause SiCp to distribute along the extrusion direction (ED). After multi-directional forging, SiCp distribution is improved significantly, and it changes from directional distribution to uniform distribution. After 1MDF, the SiCp distribution along the ED changes to disordered distribution, and the mechanical properties of the material are sharply decreased. After 3MDF, the distribution uniformity of SiCp is improved, and the mechanical properties of the material are greatly improved. When the forging passes increase to 6, the distribution uniformity of SiCp is further improved, the mechanical properties of the material decrease with the partial SiCp breaking. When the forging number is 3, the mechanical properties of the composite are optimal, with yield strength, ultimate tensile strength and elongation are 264 MPa, 387 MPa and 7%, respectively. Compared with the directionally distributed composite, the uniform distribution of SiCp effectively relieves the local stress concentration, and the matrix alloy stores more dislocation. In addition, when the distribution uniformity of SiCp is improved, the Al2Cu phase is also refined. The diffuse distribution of Al2Cu phase hinders the slip of dislocation, resulting in a uniformly distributed composite with a higher work hardening rate and internal stress. In order to study the effect of SiCp distribution on softening behavior of composites, cyclic stress relaxation experiments are carried out. In the process of stress cycling, the uniformly distributed SiCp/2024Al composites with uniform distribution of SiCp and Al2Cu phases exhibit a better stress relaxation resistance.

The Duffing equation containing a cubic nonlinearity is probably the most popular example of a nonlinear oscillator. For its harmonically excited, slightly damped, and softening version, stationary large amplitude solutions at subcritical excitation frequencies are obtained when standard semi-analytical methods like Harmonic Balance or Perturbation Analysis are applied. These solutions have the shape of a nose in the amplitude-frequency diagram. In prior work, it has been observed that these solutions may contain large errors and that high ansatz orders may be necessary when applying the Harmonic Balance or other semi-analytical methods to make them converge. Some of these solutions are observed to be asymptotically stable, while in most cases, they are unstable. The current paper aims to give a descriptive explanation for this behavior of the nose solutions, which is mainly related to the exact solution of the free undamped vibrations. Based on this, approximations of the nose solutions are calculated with a procedure combining properties of Perturbation Analysis and Harmonic Balance. Therein, the exact solution of the free undamped vibrations is taken as the zeroth approximation, while higher-order solution parts are calculated by balancing the harmonics, and the phase shift of the zeroth approximation is calculated by a residuum minimization. This method just requires the solution of a system of linear algebraic equations, while systems of nonlinear algebraic equations have to be solved in the case of directly applying Harmonic Balance.

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Even though several stress–strain models have been proposed for fiber-reinforced polymer (FRP)-confined concrete columns subjected to axial compressive loading, very few models can predict an axial response featuring postpeak strain-softening behavior. Furthermore, the reliability of most of these models is limited to only a certain concrete strength class (either normal-, high-, or ultrahigh-strength concrete). This study aimed to develop an analytical model for determining the axial response of FRP-confined concrete applicable to cases with different levels of confinement stiffness and concrete strength. For this purpose, this research proposed a new confinement stiffness threshold dependent on the coupled concrete strength and column dimension size effects to classify quantitatively FRP-confined concrete's behavior in two distinguished subcategories: strain-hardening behavior and postpeak strain-softening behavior. For FRP-confined concrete with strain-hardening response, a parabolic–linear stress–strain relation was developed, where a new formulation was derived for the slope of the linear second portion, calibrated by 583 test data. To simulate FRP-confined concrete with postpeak strain-softening behavior, a new methodology was proposed whose key components were calibrated by using 121 test data. With these features, the proposed model can objectively account for the integrated influence of concrete strength and confinement stiffness on stress–strain response. The predictive performance of the developed stress–strain model was evaluated by comparing the predictions of a wide range of relevant experimental test data, which confirms the model's reliability and accuracy. Compared to the other existing stress–strain models, the proposed model performed better. [ABSTRACT FROM AUTHOR]

Using crumb rubber particles obtained from end-of-life tires as aggregate in concrete can reduce the environmental overburden caused by the huge accumulation of these scrap tires. However, reduction in the mechanical properties of concrete is observed with the incorporation of rubber aggregates. To counter this detrimental effect of crumb rubber in concrete, amorphous metallic fibers are added to balance the loss in strength and durability issues. Mechanical characteristics along with the fracture energy of rubberized fiber-reinforced mortar are presented here. Four mortar mix compositions were investigated; the first one is reference mortar (control mortar), the second mix containing 30 kg/m3 of metallic fibers, the third mix containing 30% of rubber aggregates as replacement of sand by equivalent volume and fourth containing both rubber aggregates and metallic fibers with the dosage 30% and 30 kg/m3, respectively. Compression tests, modulus of elasticity and direct tension tests were conducted for mechanical characterization. Deformation capacity, residual post-cracking strength and fracture energy of these composite mortar mixes were evaluated through uniaxial direct tension tests. The fracture energy was determined from the obtained complete softening curves. Test results show a reduction in mechanical properties with the incorporation of crumb rubber as aggregates in mortar. However, a significant increase in fracture energy was observed in rubberized fiber-reinforced mortar mixes. Moreover, the mortar mixes containing both rubber aggregates and metallic fibers show positive synergetic effect resulting in enhanced post-cracking residual tensile strength, strain capacity and energy dissipation capacity. [ABSTRACT FROM AUTHOR]

60NiTi alloy is an important biomedical, structural and functional material. In this paper, the effects of heat treatment (temperature, time and cooling rate) on the microstructure and properties of 60NiTi alloy were studied, and the softening and hardening mechanisms were revealed. The results showed that the number of Ni4Ti3 phase enhanced with an increase of the cooling rate and the precipitation of Ni3Ti phase was inhibited after annealing at 950∼1075 °C followed by water-cooling. The orientation relationship between NiTi matrix and Ni4Ti3 phase obey the rule: [111]NiTi//[0001]Ni4Ti3 and (123¯)NiTi//(112¯0)Ni4Ti3. The faster the cooling rate was, the higher the hardness of the alloy was. The hardness of alloy under different cooling rate ranked from high to low was water-cooling, oil-cooling, liquid nitrogen-cooling, air-cooling and furnace-cooling. The hardness of the 60NiTi alloy was 316 HV after annealing at 1075 °C for 4 h followed by furnace-cooling, and the hardness sharply increased to 669 HV after annealing at 1075 °C for 4 h followed by water-cooling. The phase transformation of Ni4Ti3→Ni3Ti during cooling mainly contributed to the hardness decrease of the 60NiTi alloy.

In this investigation, fine micro-zone specimens in the heat-affected zone (HAZ) of TIG welded spray formed 7055 aluminum alloy were obtained by heat treatment method. The softening behavior and mechanism of HAZ of this alloy under single pass TIG welding were investigated. Severe non-uniformities of microstructures and mechanical properties were found, according to which the HAZ was divided into the solid solution zone and the over-aging zone. The most heavily softened area of HAZ occurred in the over-aging zone at the position corresponding to the peak thermal cycling temperature of 230–350 °C. The lowest microstructures value was 105 HV, the lowest tensile strength was about 410 MPa. The elongation was slightly higher than that of the base material. The main causes of softening in the over-aging zone were the dissolution of the coherent precipitate η′ and the growth and coarsening of the non-coherent precipitate η.Thermal cycle temperature in the solid solution zone was about 350–536 °C. Mechanical properties in this zone were higher than those of the over-aging zone. After natural aging, mechanical properties recovered to more than 90% of the base material. Microhardness reached 180 HV and tensile strength reached 570 MPa when the thermal cycle temperature was 450 °C. At the same time, the elongation in the solid solution zone was higher than that of the base material. The high mechanical properties were the results of the combined action of the increased ratio of large angle grain boundaries, the increased solid solubility and the formation of coherent GPI zone.

Force-based elements with plastic hinge integration are often used to simulate the nonlinear behavior of reinforced concrete (RC) columns experiencing softening behavior. The response from these models can be highly sensitive to the assumed plastic hinge length, L p . The objective of this paper is to evaluate the accuracy and sensitivity of the global and local behaviors of RC columns to the assumed L p . The evaluation is conducted using unregularized and regularized material stress-strain relationships. Additionally, a regularized confined concrete crushing energy equation is proposed to increase the accuracy of the numerical results and reduce their sensitivity to the assumed L p . [ABSTRACT FROM AUTHOR]

In this paper, the strain‐controlled low‐cycle‐fatigue (LCF) test and low‐cycle‐fatigue‐creep (LCFC) test of a cast Al‐Si‐Cu alloy at 350°C were investigated. A significant softening behavior can be observed in the tests, the strain amplitude has an effect on softening speed, and the dwell time has an effect on both softening ratio and softening speed. Microscopic observation indicated that the compressive load of creep could result in a significant amount of plastic deformation and lead to the eutectic silicon particles rupture and the propagation of dimples, causing the softening behavior and the decrease of failure life of Al‐Si‐Cu alloy. Based on the experiment data, a modified visco‐plasticity model combining Chaboche model and θ‐projection model was proposed to capture the cyclic stress response. The modified model could simulate the softening behavior and hysteresis loop for LCF test and LCFC test of Al‐Si‐Cu alloy accurately. Highlights: The softening behavior of LCF and LCFC was experimented and studied.The microstructure evolution of LCF and LCFC were studied.The effect of creep on LCFC and the fracture mechanism of LCFC were investigated.An improved modified model was established by combining Chaboche model and θ‐projection model [ABSTRACT FROM AUTHOR]

This article presents numerical analysis of typical folded-plate structures by the finite strip method (FSM) taking into account geometrical and material nonlinearity. Harmonic coupled FSM is used for geometrical nonlinear analysis, whereas rheological-dynamical analogy for the analysis of softening behavior. The efficiency of this novel method is demonstrated on the structures that are experimentally investigated and described in cited literature. [ABSTRACT FROM AUTHOR]

Energy piles are a profitable solution for extracting shallow geothermal energy and have recently attracted increasing attention. However, the thermomechanical response of energy piles considering shaft resistance softening has not been sufficiently studied, which hinders the perfection of design methods for energy piles. To this end, an improved generalized nonlinear softening model was first developed to describe the thermomechanical loading–unloading–reloading response of energy piles. The parameters of the improved model can be easily calibrated using an interface direct shear test. We then proposed a nonlinear load-transfer approach for the thermomechanical analysis of energy piles considering the softening behavior of skin resistance by continuously describing the nonlinear load-transfer regime. The proposed approach was validated by comparing it with experimental measurements and other numerical methods. Finally, a parametric study was performed to assess the effects of various related parameters on the thermomechanical response of the energy pile. The results indicate that the proposed approach enriches the current methods for energy pile design and provides a helpful tool for obtaining the thermomechanical behavior of energy piles in the case of softening. [ABSTRACT FROM AUTHOR]

The Al-27Si alloy was prepared using spray deposition and subsequently incorporated into Mg-Li alloy by vacuum melting furnace to produce a novel Mg-8Li-3Al-0.3Si (LA83–0.3Si) duplex alloy. The effect of final rolling deformation (30%, 40%, 50% and 60%) on the microstructure, mechanical properties, work hardening, and softening behavior was researched. Results indicated that the LA83–0.3Si alloy mainly comprised of α-Mg, β-Li, AlLi, and Mg 2 Si phases. The rolling deformation process induced elongation of the α-Mg and β-Li phase along rolling direction, facilitating the formation of α/β laminar structure, notably enhancing the strength and ductility. Increased final rolling deformation further prompted the formation of the α/β laminar structure and refined the precipitates. Consequently, the LA83–0.3Si alloy's strength progressively increased while elongation slightly diminished. At 60% deformation, the ultimate tensile strength of the LA83–0.3Si alloy reached 331 MPa, with the elongation sustained to 10.9%. The rolling process led to a reduction in the work hardening rate and an increase in the softening rate. With the increase of the final rolling deformation, the work hardening rate decreases and the softening rate further increases. However, the work hardening rate increases, and the softening rate decreases due to the decreasing of the hardness ratio of α-Mg and β-Li phases at 60% deformation. [Display omitted] • The low-sized granular Mg 2 Si phase was formed by adding Al-27Si master alloy prepared by spray deposition to Mg-Li alloy. • The highest strength of the alloy sheet with large final rolling deformation is 331 MPa, and the EL is maintained at 10.9%. • The layer structure weakens the hardening behavior of Mg-Li alloy and improves the softening behavior. [ABSTRACT FROM AUTHOR]

The critical temperature condition for softening behavior of AISI P21 steel during laser-assisted heat treatment is suggested by three-dimensional transient simulation with a finite different method. Temperature history of the cross-sectional region during laser-assisted heat treatment at 1273 K was simulated. The critical temperature condition for formation of the softening zone was assumed to range from 900 to 1008 K, based on this peak temperature history. Formation of the softening zone was simulated based on the assumed critical temperature condition. Morphology and area of simulated softening zone was compared with the experimentally obtained results, and these were well matched. In this regard, critical temperature condition for formation of the softening zone during laser-assisted heat treatment was identified to range from 900 to 1008 K. [ABSTRACT FROM AUTHOR]

The prediction of equilibrium paths in the presence of brittle fractures remains a challenge, despite the advances in the fracture modelling techniques. Difficulties arise in the solution of the equilibrium equations in the presence of material and structural instabilities. This work proposes a continuation method with multiple restrictions to solve the nonlinear system of equilibrium equations and overcome global convergence problems owing to the sudden energy release in fracture propagation analyses. The method combines simultaneously the cylindrical arc-length and the dissipation-energy control methods. In addition, this method allows the use of algorithms for the solution of linear systems of equations, which do not require the assembly of the global stiffness matrix. Numerical examples of tensile-mode and mixed-mode fracture propagation are presented and compared with experimental results. A zero-thickness interface element with linear softening damage model simulates mixed-mode fracture. The results show the accuracy, robustness, and effectiveness of the proposed continuation method even for challenging fracture problems. [ABSTRACT FROM AUTHOR]

The controllability of the position and thickness of the compressed layer in the sandwich compression wood is primarily based on the yield stress distribution during a hydrothermal treatment. In this study, the variation law of the yield stress of poplar wood was analyzed in the moisture content (MC) range of absolute dryness to saturation and the temperature range of 30–210℃. A prediction model of wood yield stress response to MC and temperature was developed and the formation of sandwich compression was analyzed. The yield stress of the wood was influenced by the thermal effect and plasticizing effect. In the process of increasing temperature and MC, the yield stress decreased gradually. And the yield stress change rate was 0.29–0.46 MPa in the MC range of 5–10%. The prediction model of wood yield stress was developed by a multiple linear regression analysis. This example demonstrated that coupling distributions of MC and temperature were formed upon heating at 180℃, which led to a gradient distribution of the glass transition temperature and yield stress inside the wood. This phenomenon resulted in the sandwich softening behavior under the coupling of moisture and heat, which was the key formation mechanism of sandwich compressed wood. [Display omitted] • The wood exhibited sandwich softening behavior via the coupling of moisture and heat. • The wood softening was characterized by yield stress and glass transition temperature. • Sandwich softened wood was made into sandwich compressed wood under mechanical force. [ABSTRACT FROM AUTHOR]

This paper introduces the experimental and modeling investigations of the shear ultra-low-cycle fatigue of the structural steel considering the plastic deformation histories. The pure-shear cyclic tests, including nine constant-deformation-range (CR), nine varying-deformation-range (VR), and one random cyclic tests (RD), are performed for the Q345 structural steel. The CR cyclic tests suggest that the shear ULCF damage evolution consists of linear accumulation, nonlinear accumulation, crack initiation and propagation stages. The shear ULCF life depends upon the deformation ranges defined as the difference between the deformations at the forward and backward turning points but is not governed by the maximum deformation amplitude. The larger deformation range results in less ULCF life. Therefore, in the proposed shear damage model, the kinematic equivalent plastic is newly introduced to characterize the relative intensity of the plastic deformation compared to the mid-configuration during the entire cyclic loading, based on the notion of memory surface. The damage accumulation rate factor, nonlinearly related to this new plastic variable, is used to control the damage evolution with respect to different strain ranges. Compared to the conventional Lode parameter enhanced cyclic void growth model (LCVGM) and stress weighted ductile fracture model (SWDFM), the proposed model exhibits significantly higher accuracy in predicting the shear ULCF life under all concerned cyclic loading patterns, as indicated by the considerably low average errors of 2.42% for CR tests, 1.04% for VR tests, and 0.96% for RD test. In particular, it confirms the validity of the proposed model under the arbitrary random cyclic loading similar to the seismic action. [Display omitted]. • The shear ULCF failure of Q345 structural steel has been investigated. • The plastic-deformation-history dependencies are considered. • The shear ULCF life decreases along with the increase in the deformation range. • The kinematic equivalent plastic strain is proposed to control the damage rate. • The shear ULCF damage model is validated under irregular random cyclic loading. [ABSTRACT FROM AUTHOR]

In some temperature regimes NiTi can be deformed to strain of 5–7% that recovers fully on unloading. Under tensile loading it traces a closed hysteresis with two stress plateaus associated with the reversible solid-state phase transformation between the austenitic (A) and the martensitic (M) phases, during which the deformation localizes and propagates through the specimen. Hallai and Kyriakides (2013) extracted the underlying softening response associated with A-M transformation from a tensile test on a NiTi strip laminated between two hardening steel face-strips that ensured that it deformed uniformly. The test finishes with the laminate permanently deformed to a strain of 6%. Extraction of the softening response of the M-A transformation requires compressing the thin laminate back to zero strain. The present paper presents a new experimental set-up that enables completion of the load/reverse load test on such a laminate by laterally supporting the specimen during compression to prevent buckling. The extracted response of NiTi exhibits softening branches with up-down-up trajectories for both the A-M and M-A transformations, and Maxwell stresses that match those of the stress plateaus of the tensile hysteresis of a NiTi strip. The extracted response is used to calibrate a custom SMA constitutive model, which when incorporated in a finite element analysis reproduces the measured hysteresis of NiTi nearly perfectly for the first time. Extraction of the complete underlying partially unstable response of SMAs enables modeling of the unstable behavior of SMA structures with the confidence provided by measured data. • SMA phase transformation causes propagation of localized deformation. • Phase transformation is modeled as partial softening in the constitutive model. • Experimental method for extracting the underlying up-down-up transformation response. • Calibration of constitutive model to the extracted up-down-up responses. [ABSTRACT FROM AUTHOR]

Softening behavior occurs in heat-affected zone of many types of high strength steels causing the deterioration of mechanical properties. In this study, the softening behavior of 22SiMn2TiB joint was revealed by experimental and numerical analysis. The microstructure and hardness of the joint were tested and analyzed. The numerical simulations of the temperature field were carried out to obtain the thermal cycle. Based on the continuous cooling transformation diagram, the phase transformation was investigated. The results indicated that the microhardness in the HAZ was significantly decreased, and its minimum value was 273 HV which was 63.5% of base metal. The softening behavior occurs in intermediate critical heat-affected zone and the subcritical heat-affected zone, and its peak temperature is between 853.7 °C (Ac3) and 450 °C. When 22SiMn2TiB steel was heated above 732.3 °C (Ac1), martensite begins to transform into austenite. With different cooling rates, austenite may transform into martensite, bainite and ferrite, and the volume fraction of soft phases could increase resulting in the softening. When the peak temperature is between 732.3 and 450 °C, the recovery phenomenon and the decomposition of martensite caused softening with the decrease in the dislocation density and martensite. [ABSTRACT FROM AUTHOR]

• Fiber type, length, and volume fraction influence UHPC's tension softening behavior. • DTTs are used to formulate an empirical relationship for the tension softening region. • The proposed tension-softening curves are effectively validated using 4PBT specimens. • Response of surface of softening parameters can be utilized in finite element (FE) modeling without resorting to performing DTTs. Fracture simulation of concrete structures, which entails generating rational and accurate crack growth through the material, requires the tension softening curve as a constitutive property. Unlike regular concrete, the tension softening behavior of ultra-high performance concrete (UHPC) is highly pronounced and extends to large deformation levels. However, data about this property and, especially, how it is affected by key variables (i.e. , fiber dosage and type of fiber used) is lacking. In this paper, a set of direct tension tests (DTT) are conducted to formulate an empirical relationship for UHPC in the tension softening range. The experimental variables are fiber type (two kinds of straight fiber and hooked), fiber length (l f = 13 , 19 or 30 mm), and fiber volume fraction (V f = 1.0 % , 1.5 %, and 2.0 %). The energy absorption capacity of UHPC is found to be different for different type of fibers, due to a difference in strain hardening as well as the pronounced softening phase. A dimensionless tension-softening curve for UHPC that is a function of fiber type, length and volume fraction is proposed as a generalized softening expression (expressed using two parameter a and b) and then implemented into a hybrid rotating/fixed crack smeared crack model. Four-point bending test (4PBT) specimens that correspond to the DTT specimens are made and tested to provide validation data. These validations confirm the model's adeptness at accurately emulating all facets of the 4PBT specimen's response. Following the validation, a response surface for parameters ' a ' and ' b ' is developed, enabling the generation of the softening curve across the entire spectrum of l f , V f , and fiber type, without having to monitor the entire range of the softening response. [ABSTRACT FROM AUTHOR]

Candidate materials for next generation neural recording electrodes include shape memory polymers (SMPs). These materials have the capability to undergo softening after insertion in the body, and therefore reduce the mismatch in modulus that usually exists between the device and the tissue. Current SMP formulations, which have shown promise for neural implants, contain ester groups within the main chain of the polymer and are therefore prone to hydrolytic decomposition under physiological conditions over periods of 11–13 months in vivo, thus limiting the utility for chronic applications. Ester free polymers are stable in harsh condition (PBS at 75°C or NaOH at 37°C) and accelerated aging results suggest that ester free SMPs are projected to be stable under physiological condition for at least 7 years. In addition, the ester free SMP is compatible with microfabrication processes needed for device fabrication. Furthermore, they demonstrate in vitro biocompatibility as demonstrated by high levels of cell viability from ISO 10993 testing.

The non-linear in-plane primary resonance of functionally graded porous (FGP) sinusoidal arches made of graphene platelet reinforced composites (GPLRC) subjected a transverse harmonic excitation is investigated in this paper. To eliminate the coupling of inner forces and facilitate the derivation, the neutral plane-based equations of motion are established considering the force and bending moment equilibrium conditions. By utilizing an incremental harmonic balance (IHB) technique, the frequency response features, dynamic time history, and limit cycle under primary resonance and 1/2 super-harmonic resonance are determined. FE analysis is conducted to verify the accuracy of the presented results. To further examine the computational efficiency of IHB procedure, a fourth order Runge–Kutta method is used to determine the structural responses as a counterpart. Comprehensive parametric studies are then carried out, particular focus is paid to the cases of material compositions, geometric properties, and dynamic parameters on the frequency response characteristics. It is found that the increasing porosity coefficient significantly exacerbates the left-inclined softening behaviors of the frequency response curves. On the contrary, the left-inclined effect continues to weaken as the GPL weight fraction gradually grows. • Primary resonance of an FG-GPLRC arch under a transverse harmonic excitation is studied. • An incremental harmonic balance procedure is utilized to determine the dynamic response. • Affected parameters on frequency response features are comprehensively analyzed. • Fourth-order Runge–Kutta method is used as a counterpart to verify the accuracy of the presented results. [ABSTRACT FROM AUTHOR]

A one-dimensional nonlinear elastic chain, known as Fermi–Pasta–Ulam system, is analyzed in the static field. The chain is made of elements admitting a quartic potential, with softening nonlinear behavior. When the chain is subject to pure tension, it exhibits a multi-degenerate hill-top bifurcation, from which several softening branches bifurcate. On each path, the springs either behave softening or hardening, in all the possible combinations, making the response non-unique. Both exact and asymptotic solutions are pursued, and the multitude of the bifurcated paths is illustrated by bifurcation diagrams. A proof of their instability is given. The role of the imperfections is commented, either in modifying the equilibrium paths and in unfolding the degenerate bifurcation. • A one-dimensional nonlinear elastic chain, known as Fermi–Pasta–Ulam system, is analyzed in the static field. • The chain is made of elements admitting a quartic potential, with softening nonlinear behavior. • The chain exhibits a multi-degenerate hill-top bifurcation, from which several softening instable branches bifurcate. • Both exact and asymptotic solutions are pursued, and the multitude of the bifurcated paths is illustrated by bifurcation diagrams. • The role of the imperfections is commented, either in modifying the equilibrium paths and in unfolding the degenerate bifurcation. [ABSTRACT FROM AUTHOR]

Viscoelastic (VE) dampers can effectively mitigate the vibration of structures under dynamic loading depending on better energy dissipating capability and are widely applied in practical engineering. On the basis of the studies on the mechanical properties of the VE material, the nonlinear behaviors of the VE damper are frequency dependent which can be elucidated by the changes in storage modulus and loss factor parameters. In this paper, experimental results of the VE damper reveal that the mechanical performance of the VE damper is correlative with the displacement amplitude. Therefore, a modified fractional derivative model is proposed to reflect the softening behavior of displacement amplitude on the VE damper. This result demonstrates that the modified model is reasonably practicable and can accurately evaluate the characteristic parameters of the VE damper. In order to apply the proposed constitutive model to finite element software, an equivalent method is presented to transform this model into the generalized Maxwell model. A three-dimensional finite element model of the VE damper is established with ABAQUS for numerical analysis. And compared with the experimental results, it is indicated that the equivalent generalized Maxwell model is available. This work verifies the conversion of the fractional derivative model to the linear VE model is feasible and provides a useful approach for the utilization of the fractional derivative model of the VE damper in finite element software. • Investigated the softening effect of displacement amplitude on the VE damper. • Improved the fractional derivative model of the VE damper. • Proposed an equivalent conversion of the linear VE model and fractional derivative model. [ABSTRACT FROM AUTHOR]

The full-range simulated hysteresis loops based on the proposed CVOID model under random loading. [Display omitted] • Plastic-deformation-history effects on cyclic ductile fracture have been investigated. • Cyclic tests of three center-holed specimens are conducted using various protocols. • Prestrain-induced enhanced ductility effect is experimentally identified. • A new cyclic void-induced damage model is proposed. • The proposed model is validated under different loading protocols and triaxialities. This paper presents the experimental and modeling studies of the plastic deformation history effects on the cyclic ductile fracture of thin steel sheet under high triaxiality. The center-holed plate specimens with three cutting radiuses are tested respectively under three cyclic loading protocols, i.e., the ascending-descending (AD), the descending-ascending (DA), and the random deformation amplitude. The prestrain-induced enhanced ductility effect is identified through comparisons between AD and DA testing, as the earlier applied large deformation might reduce the damage accumulation rate when the subsequent lower deformation amplitude is applied. A new cyclic void-induced damage model (CVOID model) is proposed to characterize the damage accumulation and succeeding softening evolution. The damage accumulation is attributed to the void growth and shrinkage subjected to cyclic deformation, which will trigger the softening initiation and development due to the internal micro-crack propagation. Furthermore, a new plasticity state variable is introduced to quantify the current plastic deformation state to consider the reduced damage rate dependent on the prestrain effect. Using the proposed CVOID model, the full-range cyclic hardening–softening behaviors can be accurately predicted under all concerned triaxialities and loading protocols, especially under random cyclic loading. It achieves better prediction of the cyclic softening behaviors than three conventional models (i.e., the CVGM, SWDFM, and the JIA cyclic fracture model), as indicated by the profound percentage errors of the accumulated critical deformation (AcD) lower than 2.1% compared with the errors from 20% to 60% via the existing models. [ABSTRACT FROM AUTHOR]

The softening behavior of skin friction is commonly observed from load-displacement responses of axially loaded piles in stiff clay, sensitive clay, and dense sands at a large loading level. This paper presents a generalized and novel elastoplastic load-transfer model to predict the load-displacement response of axially loaded piles in clay considering the degradation of skin friction. In this model, the soil around piles is divided into the shear band immediately adjacent to piles and the soil outside shear bands. An elastoplastic model in terms of the critical state theory-based modified Cam-clay model is developed to describe the mechanical behavior of shear bands. The elastoplastic model can explicitly consider both hardening and softening behaviors of skin friction. The elastic behavior of the soil outside shear bands is represented by a modulus degradation model, which captures the shear modulus degradation with the shear strain. Subsequently, an elastoplastic load-transfer model possessing generalized ability to describe both hardening and softening behaviors is developed by combining these two theoretical models. Predictions of the load-settlement curves are compared with the measured values from three well-documented cases to verify the proposed model. Good agreements demonstrate that the proposed load-transfer model provides reasonable and effective prediction for bearing performance of piles. [ABSTRACT FROM AUTHOR]

An energy harvester composed of a microcantilever beam with a tip mass and a fixed electrode covered with an electret layer is investigated when subject to an external harmonic base excitation. The tip mass and fixed electrode form a variable capacitor connected to a load resistance. A single-degree-of-freedom model, derived based on Newton’s and Kirshoff’s laws, shows that the tip mass displacement and charge in the variable capacitor are nonlinearly coupled. Analysis of the eigenvalue problem indicates the influence of the electret surface voltage and electrical load resistance on the harvester linear characteristics, namely the harvester coupled frequency and electromechanical damping. Then, the frequency−response curves are obtained numerically for a range of load resistance, electret voltage and base excitation amplitudes. A softening nonlinear effect is observed as a result of decreasing the load resistance and increasing the electret voltage. It is found that there is an optimal electret voltage with the highest harvested electrical power. Below this optimal value, the bandwidth is very small, whereas the bandwidth is large when the electret voltage is above this optimal value. In addition, it is noted that for a certain excitation frequency, the harvested power decreases or increases as a function of electrical load resistance when the coupled frequency is closer to short- or open-circuit frequency, respectively. However, when the coupled frequency is between the short-circuit and open-circuit frequencies, the harvested power has an optimal resistance with the highest power. Increasing the excitation amplitude to raise the harvested power could be accompanied with dynamic pull-in instability and/or softening behavior depending on the electrical load resistance and electret voltage. However, large softening behavior would prevent the pull-in instability, increase the level of the harvested power, and broaden the bandwidth. These observations give a deeper insight into the behavior of such energy harvesters and are of great importance to the designers of electrostatic energy harvesters.

Al–Zn–Mg–Cu alloys are used extensively in high-speed train applications; however, the occurrence of softening in the heat-affected zone after welding limits their development. In this work, the effect of the welding thermal cycle on the softening and aging behaviors of a 7xxx aluminum alloy was investigated by examining the state of the strengthening precipitates. The microstructure and solvus temperature range of the precipitates of 7N01P-T4 were characterized using TEM and DSC analysis, respectively. It was found that the softening behavior of the aluminum alloys was closely related to the volume fraction and size of the hardening precipitates, which were greatly affected by the peak temperature of the welding thermal cycle. In addition, η′ and η precipitates were observed to be primarily responsible for the increase in the mechanical and electrical properties during the room-temperature natural aging. A phenomenological connection was thus uncovered between the characteristic parameters of the thermal cycle and the precipitation behavior, providing insight for the design of the welding process for 7N01 alloys. [ABSTRACT FROM AUTHOR]

In this paper, an operable strategy to enhance the output power of piezoelectric energy harvesting from vortex-induced vibration (VIV) using nonlinear magnetic forces is proposed for the first time. Two introduced small magnets with a repulsive force are, respectively, attached on a lower support and the bottom of a circular cylinder which is subjected to a uniform wind speed. Experiments show that the natural frequency of the VIV-based energy harvester is significantly changed by varying the relative position of the two magnets and hence the synchronization region is shifted. It is observed that the proposed energy harvester displays a softening behavior due to the impact of nonlinear magnetic forces, which greatly increases the performance of the VIV-based energy harvesting system, showing a wider synchronization region and a higher level of the harvested power by 138% and 29%, respectively, compared to the classical configuration. This proposed design can provide the groundwork to promote the output power of conventional VIV-based piezoelectric generators, further enabling to realize self-powered systems. [ABSTRACT FROM AUTHOR]

Various electrically-assisted (EA) plastic forming technologies have been developed for difficult-to-form materials such as magnesium alloys in recent years. However, very few studies have been conducted on EA micro-forming, especially determining the size effect on electrically-induced softening behavior. In this study, uniaxial micro-tension tests at various current densities were conducted to investigate the effects of grain size and specimen size on the electrically-induced softening behavior of magnesium alloy AZ31 specimens. It was found that the electrically-induced softening parameter (i.e., the ratio of the tensile strength in EA to that in non-EA test with the higher softening at the smaller value) followed an inverse-S-shaped function of current density. A relatively lower current density would be sufficient for larger sample sizes and smaller grain sizes to achieve a higher softening effect, indicating that grain number may be an important factor influencing electrically-induced softening. These size effects on electrically-induced softening were used to modify a semi-empirical softening function of current density, which could effectively predict the electrically-induced softening behaviors of five metals. The current density threshold in EA tension was defined and formulated based on the semi-empirical softening function, which nonlinearly increased with grain size, but decreased with specimen size and electrical resistivity. [ABSTRACT FROM AUTHOR]

The present work mainly focuses on the regulation of the bimodal microstructure (fine recrystallized grains and elongated un-recrystallized grains) on the work hardening and softening behaviors of Mg-6Zn-1Gd-0.3Ca alloy. Meanwhile, the grain refinement mechanism was discussed through EBSD. The results show the work hardening capacity of the alloy increases with improving the volume fraction of fine recrystallized grains, which is mainly due to the increase of dislocation storage rate caused by grain coarsening. The stress reduction (∆ P 1) value in the early stage of tensile deformation is the biggest for the alloy with fine recrystallized grains of ∼66.8 %, which is attributed to the greater stored energy can provide greater driving force for softeing effect. However, the stress reduction (∆ P i(i=2,3,4)) values of the alloys in the later stage of tensile deformation decrease monotonically with the increase of fine recrystallized grains amount. Moreover, the analysis shows that the fine recrystallized grains of Mg-6Zn-1Gd-0.3Ca alloy are mainly formed by dynamic recrystalliztion (DRX). • The most of the fine equiaxed grains in the as-extruded Mg-6Zn-1Gd-0.3Ca alloys come from DRX, and a small amount are formed by SRX. • The work hardening effect of the as-extruded Mg-6Zn-1Gd-0.3Ca alloys increases with the increase of extrusion temperature. • The highest stored energy of the alloy extruded at 300 °C in the early stage of plastic deformation causes the highest ∆ P 1 value. However, the ∆ P 2 , ∆ P 3 and ∆ P 4 values of the as-extruded alloys decrease monotonically with the extrusion temperature increases from 260 °C to 340 °C, which are mainly attributed to that the grain size and secondary phase amount of the as-extruded Mg-6Zn-1Gd-0.3Ca alloy increase with the increase of extrusion temperature. [ABSTRACT FROM AUTHOR]

Waste tires are extensively being used in civil engineering applications to improve flexibility and elastic properties of the base foundation material. Moreover, by using pure tires or soil-tire mixtures, rubber stockpiles, which cause lots of environmental contaminations, are being consumed. The objective of this research is to study the strength and elastic modulus variations of sands when combined with rubber materials in different sizes and percentages. Triaxial experiments were performed on various sand-rubber mixtures using static triaxial apparatus. Samples were constructed at the maximum dry density and optimum moisture content to consider engineering applications in dry regions. The results show that rubber content and rubber-sand particle size ratio, D50,r=D50,s, significantly affect the mixture behavior in the manner which increase in the former and decrease in the latter, leading to a more softening behavior. Furthermore, specific combination of sand and rubber, which may improve the elastic properties of the mixture, is proposed as a flexible base layer. [ABSTRACT FROM AUTHOR]

The influence of the stress regime change and associated softening can be significant on unsaturated expansive soil slope stability due to soil swelling upon wetting, which cannot be considered in conventional hydrological models. In this paper, the shallow expansive soil slope failure mechanism is addressed in the framework of an infinite slope formulation. The unsaturated soil elasto-plastic constitutive relationship is utilized for interpretation of stress regime evolution induced by expansive soil swelling during infiltration. The extended Mohr–Coulomb failure criterion for unsaturated soils is used as the yield surface, under which the nonlinear elastic behavior is considered by quantifying the effect of two stress state variables (net stress and suction) on elasticity parameters. The strain softening behavior in unsaturated soils is accounted for via reducing the material parameters of the yield surface with respect to plastic deviatoric strain. A numerical exercise is performed on a relatively gentle slope in Regina, Canada with highly expansive soil properties, using the developed computer program that implements the constitutive model into infinite slope formulation. The results suggest that neglecting the swelling-induced stress change and associated softening behavior can significantly overestimate the stability of expansive soil shallow layer under infiltration, in terms of both failure occurrence and failure time. Additional parametric study shows that all the considered parameters (including initial stress condition, softening rate and slope angle) have a considerable effect on the failure time and failure depth of the shallow deposit, which have important implications for the engineering design of expansive soil slopes. [ABSTRACT FROM AUTHOR]

This contribution proposes a general constitutive model to simulate the orthotropic stiffness, pre-peak nonlinearity, failure envelopes, and the post-peak softening and fracture of textile composites. Following the microplane model framework, the constitutive laws are formulated in terms of stress and strain vectors acting on planes of several orientations within the material meso-structure. The model exploits the spectral decomposition of the orthotropic stiffness tensor to define orthogonal strain modes at the microplane level. These are associated to the various constituents at the mesoscale and to the material response to different types of deformation. Strain-dependent constitutive equations are used to relate the microplane eigenstresses and eigenstrains while a variational principle is applied to relate the microplane stresses at the mesoscale to the continuum tensor at the macroscale. The application of the model to a twill 2 × 2 shows that it can realistically predict its uniaxial as well as multi-axial behavior. Furthermore, the model shows excellent agreement with experiments on the axial crushing of composite tubes, this capability making it a valuable design tool for crashworthiness applications. The formulation is computationally efficient, easy to calibrate and adaptable to other kinds of composite architectures such as 2D and 3D braids or 3D woven textiles. [ABSTRACT FROM AUTHOR]

Nonlinear dynamic responses of a Micro-Electro-Mechanical Systems (MEMS) mirror with sidewall electrodes are presented that are in close agreement with previously-reported experimental data. An analysis of frequency responses reveals softening behavior, and secondary resonances originated from the dominant quadratic nonlinearity. The quadratic nonlinearity is an electromechanical coupling effect caused by the electrostatic force. This effect is reflected in our mathematical model used to simulate the dynamic response of the micro-mirror. The effects of increased forcing and decreased damping on the frequency response are investigated as the mirrors are mostly used in vacuum packages. The results can predict MEMS mirror behaviors in optical devices better than previously-reported models. [ABSTRACT FROM AUTHOR]

Considering that rock failure is a gradual process when subjected to triaxial stress conditions, a new statistical damage constitutive model is proposed to describe the progressive failure of rocks. The model is based on continuous damage mechanics and maximum entropy theory while the commonly used statistical damage model is based on continuous damage mechanics and the conventional Weibull distribution, which is used to describe the strength of mesoscopic rock elements. Weibull distribution is a distribution function with a specific assumption that the nth central moment and the geometric mean of the statistical variable are constant. The maximum entropy distribution is the only unbiased distribution and the Weibull distribution is a special case of the maximum entropy distribution. According to the maximum entropy theory, the damage variable is defined without any prior assumptions of the theoretical distributions. The rock is hypothesized to be divided into two parts: the damaged portion and undamaged portion. The bearing capacity of the damaged part is also considered in the new model so that it is more in accordance with the actual situation. The mesoscopic rock elemental strength is calculated based on energy release rate principles to avoid the deficiencies in using the conventional stress or strain criteria approaches, and the effect of rock initial fissures is emphasized. A new method is presented to determine the unknown parameters in the constitutive equations. The applicability of the new statistical damage constitutive model is verified by experimental data. It is shown that the theoretical model is in good agreement with the test data trend and can simulate the softening behavior of rock well. Admittedly, the proposed model proposed in this paper is a basic model without considering some important aspects of rock deformation mechanics, such as the absences of the complex stress conditions. The purpose of this paper was to illustrate that the constitutive model can be established in the framework of continuous damage mechanics and maximum entropy theory. [ABSTRACT FROM AUTHOR]

The effects of the V R / V D ratio (the volume fraction ratio of recrystallized grains and coarse deformed grains) on the work hardening and softening behaviors of Mg–6Zn-1Gd-0.12Y alloy were studied in detail by detecting the variation of dislocation density. The alloys with different V R / V D ratios were successfully fabricated by rolling and subsequently different annealing processes. It was shown that the higher V R / V D ratio closely related to the nucleation and growth of recrystallized grains could be obtained by an increase in annealing temperature. An increase in the V R / V D ratio from 0.16 to 24 reduced the work hardening rate in stage Ⅲ, while increased the work hardening rate in stage Ⅳ, which was closely related to the initial dislocation density and dislocation evolution. Low V R / V D ratio in the alloy, with high initial dislocation density, was identified to be beneficial for improving the work hardening rate in stage Ⅲ. And an increased V R / V D ratio could promote dislocation multiplication by stimulating the yield phenomenon due to the lack of initial dislocation density, and improve the work hardening rate in stage Ⅳ. With the V R / V D ratio increased, the softening behavior of the alloys increased in stage Ⅲ, and first decreased and then increased in stage Ⅳ. This was because the alloy with the lower dislocation density was easy to deform due to few obstacles, which accelerated the softening in stage Ⅲ, and improved dislocation density after yielding provided the strong driving force for the softening in stage Ⅳ. Meanwhile, the cycle stress relaxation tests further manifested that the stress drop values (Δ σ p) of the alloys were in close contact with the initial dislocation density and dislocation evolution influenced by the V R / V D ratio. As a result, when the V R / V D ratio was 1.6, the Mg–6Zn-1Gd-0.12Y alloy had excellent strength and toughness match owing to a dynamic balance between the work hardening rate and softening rate. • A transition stage appears between stage Ⅲ and stage Ⅳ of work hardening rate curve as V R / V D ratio is larger than 1.6. • The work hardening behavior of Mg–6Zn-1Gd-0.12Y alloy with different V R / V D ratios plays a significant role on the softening of Mg–6Zn-1Gd-0.12Y alloy. • High YS (～243.31 MPa), UTS (～304.4 MPa) and excellent EL (～30%)are achieved in Mg–6Zn-1Gd-0.12Y alloy when V R / V D is 1.6. [ABSTRACT FROM AUTHOR]

The fracture criterion was characterized for an AZ31 Mg alloy plate with the 3.0 mm thickness at the elevated temperature of 250 °C in this work. In order to properly characterize the fracture criterion, its mechanical properties were also characterized. As for mechanical properties, simple tension tests were performed to calibrate the Hill1948 yield function. Also, in order to account for the hardening deterioration (softening) behavior beyond the uniform deformation limit, the flow curves of the Mg alloy plate were numerically obtained based on the inverse calibration method, in which strain rate sensitivity was also considered. As for the fracture criterion, effective fracture strains, which are dependent on stress triaxiality and deformation paths, were numerically characterized utilizing experimental data based on specimens with four different shapes newly developed. For comparison purposes, empirical fracture criteria such as the Cockcroft-Latham, Brozzo, Ayada and Clift models were also calibrated. For validation purposes, the five fracture criteria were applied for a real part (an EL-cover) drawing case and the result confirmed that the fracture criterion developed in this work performed best among the five models tried out. [ABSTRACT FROM AUTHOR]