Logarithmic Strain Research Articles

A design strategy with the combination of neuro-regression and stochastic optimizations on the hyperelastic gasket

For numerous years, PVC and aluminum doors and windows have been integral components of buildings. The primary technical requisites for doors and windows encompass superior acoustic performance, thermal insulation, and effective sealing. Particularly, the sealing properties, crucially important, are ensured by the gaskets fitted onto the profiles. This paper aims to present a gasket design with a new methodology that includes a systematic modeling-optimization process based on multiple non-linear neuro-regression. Comprehensive research has been done by multiple non-linear neuro-regression analyses of gaskets due to deficient studies in the literature on hyperelastic materials. 17 candidate functional forms based on four basic mathematical structures (polynomial, trigonometric, logarithmic, and linear functions, and their hybrid or rational forms) have been proposed to model the FEM data of the gasket. Hybrid versions of three stochastic search algorithms, Differential Evolution, Random Search, and Simulated Annealing, are considered to solve highly non-linear, non-convex, multi-variables mixed continuous-discrete problems. The experimental results were compared with the numerical result using the finite-element analysis (FEA). Nonlinear static analyses were performed with Abaqus. Stress and logarithmic strain distributions are obtained. A good correlation was found between the experimental and the numerical results The optimum locations and numbers of the nodes have been found to obtain the minimum overflow distance and the maximum compression surface area for gaskets having the same topological structure.

Comparison of different elastic strain definitions for largely deformed SEI of chemo-mechanically coupled silicon battery particles

Amorphous silicon is a highly promising anode material for next-generation lithium-ion batteries. Large volume changes of the silicon particle have a critical effect on the surrounding solid-electrolyte interphase (SEI) due to repeated fracture and healing during cycling. Based on a thermodynamically consistent chemo-elasto-plastic continuum model we investigate the stress development inside the particle and the SEI. Using the example of a particle with SEI, we apply a higher order finite element method together with a variable-step, variable-order time integration scheme on a nonlinear system of partial differential equations. Starting from a single silicon particle setting, the surrounding SEI is added in a first step with the typically used elastic Green–St-Venant (GSV) strain definition for a purely elastic deformation. For this type of deformation, the definition of the elastic strain is crucial to get reasonable simulation results. In case of the elastic GSV strain, the simulation aborts. We overcome the simulation failure by using the definition of the logarithmic Hencky strain. However, the particle remains unaffected by the elastic strain definitions in the particle domain. Compared to GSV, plastic deformation with the Hencky strain is straightforward to take into account. For the plastic SEI deformation, a rate-independent and a rate-dependent plastic deformation are newly introduced and numerically compared for three half cycles for the example of a radial symmetric particle.

Towards a rational approach for multi-axial experimental campaigns for rubberlike material

This work takes up the developments around the logarithmic strain tensor and uses the invariants of this tensor to propose a new approach to multi-axiality of fatigue experiments for elastomers. This study leads to the introduction of a new notion, modality, which is intended as the microscopic counterpart of uni- and multi-axiality. This notion is quantified by the K3 invariant (mode of deformation) of the logarithmic strain tensor, and is used to rationalize tension–torsion experimental campaigns. It is illustrated using two examples: the perfect cylinder and the AE2 “diabolo” sample. We then propose a methodology for building a test campaign based on this new definition.

Evolutional behavior of viscoelastic materials: A formulation based on logarithmic approach

In this paper, a new formulation for large deformation of visco-elastometic materials is derived. The formulation is based on logarithmic strain, and the internal variable is defined as the viscous part of the logarithmic strain. A derivation of thermodynamically consistent formulation for visco-elastomeric materials is provided. The evolution equation which is related to the deviatoric part of the strain for viscoelastic formulation is solved by the implicit trapezoidal integration rule which leads to a recursive relation.

A multifaceted approach using RVE homogenization methodology for identification of elastoplastic behavior of steel matrix composite: Application to deep-drawing process

The integration of cutting-edge materials and computational methods is now essential in contemporary engineering, especially in sectors where a deep comprehension of the mechanical behavior of reinforced composite materials is crucial. In this context, steel matrix composites, enhanced with reinforcing elements like TiB2, have garnered attention due to their potential for superior mechanical properties and wide-ranging applications. This article explores an innovative computational framework based on the Representative Volume Element (RVE) concept to examine the elastoplastic properties of a ferritic steel matrix reinforced with ceramic particles (TiB2). The finite element analysis (FEA) is performed with periodic boundary conditions (PBCs) to apply the specified loading to the RVE. As a first endeavor, the developed multi-faceted approach provides a broader perspective on shear behavior and the elastoplastic composite’s properties of Fe-TiB2 for various reinforcement volume fractions. Then, the focus of this study lies in its application to the deep-drawing process, a critical manufacturing operation with significant implications in industries such as automotive and aerospace. The established approach for homogenizing elasto-plastic Fe-TiB2 composites is applied to analyze the influence of reinforcement variation on several critical aspects during the deep-drawing process, including formability, forming force, Von Mises stress distribution, and logarithmic strain.

A New Constitutive Model Based on Taylor Series and Partial Derivatives for Predicting High-Temperature Flow Behavior of a Nickel-Based Superalloy.

Ni-based superalloys are widely used in aerospace applications. However, traditional constitutive equations often lack the necessary accuracy to predict their high-temperature behavior. A novel constitutive model, utilizing Taylor series expansions and partial derivatives, is proposed to predict the high-temperature flow behavior of a nickel-based superalloy. Hot compression tests were conducted at various strain rates (0.01 s-1, 0.1 s-1, 1 s-1, and 10 s-1) and temperatures (850 °C to 1200 °C) to gather comprehensive experimental data. The performance of the new model was evaluated against classical models, specifically the Arrhenius and Hensel-Spittel (HS) models, using metrics such as the correlation coefficient (R), root mean square error (RMSE), sum of squared errors (SSE), and sum of absolute errors (SAE). The key findings reveal that the new model achieves superior prediction accuracy with an R value of 0.9948 and significantly lower RMSE (22.5), SSE (16,356), and SAE (5561 MPa) compared to the Arrhenius and HS models. Additionally, the stability of the first-order partial derivative of logarithmic stress with respect to temperature (∂lnσ/∂T) indicates that the logarithmic stress-temperature relationship can be approximated by a linear function with minimal curvature, which is effectively described by a second-degree polynomial. Furthermore, the relationship between logarithmic stress and logarithmic strain rate (∂lnσ/∂lnε˙) is more precisely captured using a third-degree polynomial. The accuracy of the new model provides an analytical basis for finite element simulation software. This helps better control and optimize processes, thus improving manufacturing efficiency and product quality. This study enables the optimization of high-temperature forming processes for current superalloy products, especially in aerospace engineering and materials science. It also provides a reference for future research on constitutive models and high-temperature material behavior in various industrial applications.

Finite strain modelling of Shape Memory Alloys in the logarithmic strain space: A comparative study with other finite strain approaches

Finite strain models for Shape Memory Alloys (SMAs) offer significant advantages over small strain models in that they excel in their ability to characterize SMA behaviour under large strain and finite rotations while eliminating the inherent assumptions associated with the small strain framework. The paper at hand presents a numerical model for SMAs at finite strain, employing the logarithmic strain measure to obtain an additive split of the total strain into its elastic and inelastic (transformation) parts. Notably, the model maintains the thermodynamic consistency validated using the Clausius–Duhem inequality. Additionally, we compare this model with two other finite strain SMA models employing logarithmic strain measures: a hypoelastic model, which splits the rate of deformation tensor additively, and a hyperelastic model, which decomposes the deformation gradient multiplicatively. The numerical formulation for the three finite strain models is specifically tailored to address superelasticity in SMAs. It is derived from the established small strain model and seamlessly extended into the domain of finite strain framework. Several numerical examples are carried out to showcase the logarithmic strain space approach applied to SMAs and to compare its response with that of the other aforementioned finite strain models in SMAs. The meticulous examination reveals that the logarithmic strain space approach aligns well with the existing finite strain models, demonstrating its effectiveness and compatibility.

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

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

Abstract 1007: A Novel Heterogeneous Murine Aortic Model Derived From Micro-computed Tomography

Introduction: Strength and structural stability of the aorta primarily comes from collagen that is mostly found in the media layer of the aorta along with elastin. The risk of life-threatening aortic rupture increases in cases of aortic aneurysm diseases due to local deformation and weakening of the aortic wall. How does local structure affect how the aorta responds to stress? We hypothesize that material and geometric heterogeneity affect the local biomechanics of the aortic wall and that the local responses to stress are not necessarily the same as the global response. Our goal is to develop a novel finite element model (FEM) of collagen and elastin behavior in murine aorta derived from high-resolution micro-computed tomography (microCT). This model will allow us to study how the aorta deforms to blood pressure at the local level. Approach: The collagen and elastin from 100 vertical slices of microCT scans of a murine aorta were segmented, smoothed and meshed to create 3D models for FEM and the aortic ring was divided into 8 sections of varying geometry and composition. Local stress-strain relationships were extracted from uniaxial loading conditions. Simulations were conducted where the stiffness of collagen was set equal to (1X) or made stiffer than elastin by a factor of 10 (10X) or 100 (100X). The average Young’s modulus, E, for each section was calculated and used as parameters for FEM of the aortic ring to investigate the global mechanical behavior of the aortic wall. Results/Conclusions: The strains generated in the radial direction are greater than the strains in the hoop direction in each of the 8 heterogeneous sections of the aortic ring. There was significant variability in the E values in the 10X and 100X systems. FEM of a materially uniform aortic ring yielded smaller maximum principal logarithmic strains compared to a ring that was materially heterogeneous. This study provides evidence that local structure and material distribution are important in aortic biomechanics. Pathogenesis of aneurysmal disease is dependent on collagen and elastin turnover. Aneurysm rupture results from mechanical failure: peak wall stress exceeds local tissue strength. This novel method will allow for development of a complex aortic fracture model to study aortic pathologies.

On twinning and shear banding in copper single crystals with rolling texture orientations plane strain compressed at high strain rate

Crystal lattice rotations developed in copper single crystals with (110)[1–1–2](Br), (110)[001](G), (112)[11–1](C), and S (346)[63–5](S) orientations have been examined to assess the role of an impact loading on twinning, deformation banding and shear banding. The single-crystalline specimens were channel-die compressed to logarithmic strains of 0.9 with a strain rate of 4.7 × 105 s−1. The microstructures were characterised using scanning (SEM) and transmission (TEM) electron microscope, whereas electron backscattered diffraction (EBSD) in SEM and X-ray diffraction have been applied to evaluate the texture evolution. The results showed that a very high strain rate promoted the formation of deformation twins in all orientations. However, a strong variation in the twin density and number of twin families was observed depending on the orientation of the single crystal. In the Br- and G-oriented crystals, only single needle-shaped twins were observed, whereas in the C- and S-oriented crystals, the formation of compact clusters of deformation twins of two generations on different twinning planes was identified. SEM/EBSD measurements revealed that deformation bands were formed in the crystallites with G and Br orientations, whereas shear bands (SBs) were observed in the C- and S-oriented crystals. This study demonstrates that the rotation of twin and matrix platelets in narrow areas of SBs developed in C- and S-oriented crystallites, combined with deformation twinning in the re-oriented primary matrix platelets can result in the formation of texture components near the {110}<001> orientation. Finally, a crystallographic model of the formation of SBs in twinned structures of face-centred cubic metals deformed at high strain rates is proposed.

Peculiarities of steel hardening under deformation conditions with external influence of a magnetic field

The strain resistance of a metal, its intensity of hardening, directly depends on the evolution of defects in the crystal lattice. The positive influence of a magnetic field (MF) on the movement of dislocations and their interaction with stoppers (magnetoplastic effect) is known. For the practical use of MF in forging technologies, generalized data on the strengthening of metals during plastic deformation are required. The results of using a constant MF with induction up to 1,2 T in the processes of testing samples for tension and compression were studied. Tensile tests were carried out on samples of steels St3, 20, U8, 40Cr, 09Cr16Ni4Nb, X10CrNiTi18-10, copper M3 and compression tests on steels St3, 09Cr16Ni4Nb, X10CrNiTi18-10, copper M3. Curves of metal hardening during deformation are plotted in the coordinates flow stress – logarithmic strain. The flow stress is determined by the ratio of the load to the cross-sectional area of the sample valid for a given moment of testing under uniform deformation. The change in flow stress of metals is described by the power function of the Ludwik-Hollomon equation. In tension and compression of ferromagnetic steels St3, 20, 40Cr, U8 and 09Cr16Ni4Nb, the impact of MF leads to an increase in the intensity of their hardening. This is most evident in hardened or high-strength steels. But for St3 steel softened by annealing, the effect is the opposite - in MF the intensity of hardening is somewhat less. Tension in MF of paramagnetic steel X10CrNiTi18-10 showed an increase in the intensity of hardening, but compression showed its decrease. Tension and compression of M3 copper in MF occur with a slight decrease in the intensity of hardening. The experiments carried out revealed the main effect of MF at the initial stage of deformation. The hardening curves were divided into straight and parabolic sections with the hardening coefficients determined for each of them. The main effect of MT on the primary stage of linear hardening has been revealed, where a decrease in the intensity of hardening (St3, 40Cr, X10CrNiTi18-10, M3), an increase (St3 and X10CrNiTi18-10) or a reduction (St3 annealed) in the duration of this stage is observed. Keywords: magnetoplasticity, tension, compression, hardening, stress, strain.

An isochronous stress ratio logarithmic strain curve based clay creep model considering the effects of hardening and damage

Creep is one of the typical mechanical properties of clay, and studying the creep mechanical properties of clay is of great significance to construction projects in clay sites. This study conducted creep tests on Chengdu clay and found that the soil mass underwent elastic deformation, decay creep deformation, steady-state creep deformation, and accelerated creep deformation. The isochronous stress ratio-logarithmic strain curves and their mathematical models were proposed to thoroughly analyze clay creep mechanical properties. Creep automatic feature points, such as linear elastic extreme point, initial yield point, long-term strength point, and plastic point, were identified on the curve. Considering the hardening and damage effects during creep loading, linear elastic and viscoelastic elements considering the time-dependent damage, a viscoplastic element considering the load hardening effect, and viscoplastic and plastic elements considering the load damage effect were established based on the element model and the Riemann–Liouville fractional derivative. Based on the mechanical properties of the whole clay creep process, the creep mechanical feature points, and the established element model, a clay creep model was proposed considering the hardening and damage effects. The rationality and regularity of the creep model were verified using the creep test data. This research accurately revealed the creep mechanical properties of clay and facilitated soil deformation prediction, thus providing technical guidance and references for construction projects in clay sites.

FEA-Based Stress-Strain Barometers as Forecasters for Corneal Refractive Power Change in Orthokeratology.

To improve the effectivity of patient-specific finite element analysis (FEA) to predict refractive power change (RPC) in rigid Ortho-K contact lens fitting. Novel eyelid boundary detection is introduced to the FEA model to better model the effects of the lid on lens performance, and stress and strain outcomes are investigated to identify the most effective FEA components to use in modelling. The current study utilises fully anonymised records of 249 eyes, 132 right eyes, and 117 left eyes from subjects aged 14.1 ± 4.0 years on average (range 9 to 38 years), which were selected for secondary analysis processing. A set of custom-built MATLAB codes was built to automate the process from reading Medmont E300 height and distance files to processing and displaying FEA stress and strain outcomes. Measurements from before and after contact lens wear were handled to obtain the corneal surface change in shape and power. Tangential refractive power maps were constructed from which changes in refractive power pre- and post-Ortho-K wear were determined as the refractive power change (RPC). A total of 249 patient-specific FEA with innovative eyelid boundary detection and 3D construction analyses were automatically built and run for every anterior eye and lens combination while the lens was located in its clinically detected position. Maps of four stress components: contact pressure, Mises stress, pressure, and maximum principal stress were created in addition to maximum principal logarithmic strain maps. Stress and strain components were compared to the clinical RPC maps using the two-dimensional (2D) normalised cross-correlation and structural similarity (SSIM) index measure. On the one hand, the maximum principal logarithmic strain recorded the highest moderate 2D cross-correlation area of 8.6 ± 10.3%, and contact pressure recorded the lowest area of 6.6 ± 9%. Mises stress recorded the second highest moderate 2D cross-correlation area with 8.3 ± 10.4%. On the other hand, when the SSIM index was used to compare the areas that were most similar to the clinical RPC, maximum principal stress was the most similar, with an average strong similarity percentage area of 26.5 ± 3.3%, and contact pressure was the least strong similarity area of 10.3 ± 7.3%. Regarding the moderate similarity areas, all components were recorded at around 34.4% similarity area except the contact pressure, which was down to 32.7 ± 5.8%. FEA is an increasingly effective tool in being able to predict the refractive outcome of Ortho-K treatment. Its accuracy depends on identifying which clinical and modelling metrics contribute to the most accurate prediction of RPC with minimal ocular complications. In terms of clinical metrics, age, Intra-ocular pressure (IOP), central corneal thickness (CCT), surface topography, lens decentration and the 3D eyelid effect are all important for effective modelling. In terms of FEA components, maximum principal stress was found to be the best FEA barometer that can be used to predict the performance of Ortho-K lenses. In contrast, contact pressure provided the worst stress performance. In terms of strain, the maximum principal logarithmic strain was an effective strain barometer.

Study on the dynamic mechanical properties of winding‐block axial structure considering short circuit strain rate effect

AbstractTransformers may suffer multiple short‐circuit impacts during long‐term operation, and axial instability is one of the typical types of serious accidents caused by short‐circuit faults. The axial instability form of the winding‐block structure is analysed, and the dynamic solution of the winding short‐circuit electromagnetic force is obtained by establishing the three‐dimensional magnetic‐circuit‐force multi‐physical field coupling simulation model. The influence of strain rate on the cushion block constitutive equation is corrected, and the modified model is verified by short‐circuit impact test and quasi‐static test. The research results show that for 110 kV 31.5 MVA transformers, the maximum electromagnetic axial resultant force of winding is 363.16 kN, and the ultimate tilt force is 1214.2 kN. The pre‐tightening force configuration is accordingly recommended to range from 363.16 to 608.28 kN, which is narrowed by 18.49% compared with the static calculation method; Meanwhile, adding a logarithmic strain rate correction term to the classical constitutive equation of the cushion block can achieve a good correction of the stress‐strain relationship with the coefficient of determination above 0.99, and the cushion block has a larger elastic modulus under high strain rate load. The research results provide an important theoretical reference for the axial stability structure of transformers.

Damage in a comprehensive model for shape memory alloys in logarithmic strain space

Shape memory alloys (SMAs) possess considerable complexity in response to thermomechanical load due to their strong dependence on strain, stress, temperature and history. This high complexity is a limiting factor in the fatigue analysis of SMA structures. With this in mind, a comprehensive phenomenological model is developed to address nearly all of the features in SMAs with a particular focus on the development of damage. Due to the fact that many SMA structures experience large deformations, the model is developed in finite strains using the logarithmic strain space approach. Besides the balance of linear momentum, the model includes the heat conduction equation and two micromorphic nonlocal balance laws. The latter are introduced to regularize the softening associated with the damage and transformation. The material model incorporates a damage evolution law that depends on the integration of a simplified dissipation term. The model is applied to a few examples to observe the interaction of the features and to illustrate the applicability of the model for rupture and fatigue analysis. The interaction of the features is shown to produce a reasonable representation of the cyclic loading of wires at different loading rates. Rupture is shown to occur due to a large amount of plastic strain and can be performed due to the nonlocal approach for the damage. The fatigue analysis shows some promising accuracy but only if the dissipated area is captured properly.

A simple spectral representation of a second-order symmetric tensor and its variation

The spectral decomposition of a second-order, symmetric tensor is widely adopted in many fields of Computational Mechanics. As an example, in elasto-plasticity under large strain and rotations, given the Cauchy deformation tensor, it is a fundamental step to compute the logarithmic strain tensor.Recently, this approach has also been adopted in small-strain isotropic plasticity to reconstruct the stress tensor as a function of its eigenvalues, allowing the formulation of predictor–corrector return algorithms in the invariants space. These algorithms not only reduce the number of unknowns at the constitutive level, but also allow the correct handling of stress states in which the plastic normals are undefined, thus ensuring a better convergence with respect to the standard approach.While the eigenvalues of a symmetric, second-order tensor can be simply computed as a function of the tensor invariants, the computation of its eigenbasis can be more difficult, especially when two or more eigenvalues are coincident. Moreover, when a Newton–Raphson algorithm is adopted to solve nonlinear problems in Computational Mechanics, also the tensorial derivatives of the eigenbasis, whose computation is still more complicated, are required to assemble the tangent matrix.A simple and comprehensive method is presented, which can be adopted to compute a closed form representation of a second-order tensor, as well as their derivatives with respect to the tensor itself, allowing a simpler and numerically accurate implementation of spectral decomposition of a tensor in Computational Mechanics applications.

Exploring mechanical properties and failure mechanisms of aramid and PBO crystals through molecular dynamics simulations

Molecular dynamics simulations were used to analyze the mechanical properties and failure processes of poly(p-phenylene-terephthalamide) (PPTA), poly(p-phenylene-benzimidazole-terephthalamide) (PBIA), PBIA–PPTA (formed by 1:1 copolymerization of PPTA and PBIA), and poly(p-phenylene-benzobisoxazole) (PBO) crystals at different strain rates and temperatures. The failure stress and strain were found to be linear with the temperature and logarithmic strain rate. Moreover, based on the kinetic theory of fracture and the comprehensive simulation results, we formulated a model that describes the failure stress of the aforementioned crystals under varying strain rates and temperatures. Through the analysis of the failure process, we found that in PPTA, PBIA, and PBIA–PPTA crystals, the bond failure probability is correlated with the strain rate and temperature. The examination of bond lengths and angles unveiled that bonds with larger initial aligning angles are more susceptible to failure during the strain process. Intriguingly, the stretching process induced a conformational change in the PBO molecular chain, leading to a deviation from the linear relation in its stress–strain curve.

A large strain thermoplasticity model including recovery, recrystallisation and grain size effects

AbstractIn manufacturing, thermomechanical processes such as static annealing and hot working are commonly used to tailor the microstructure of metals to achieve favourable macroscopic material properties that meet specific application requirements. To improve sequential manufacturing processes and to accurately predict the microstructural changes of the material along the process chain, physically motivated constitutive models are required that simultaneously account for the effects of recovery and recrystallisation, as well as grain size dependencies. To this end, Cho et al. [Int. J. Plasticity 112, 123–157 (2019)] proposed a macroscopic hypo‐elasticity based large strain thermoplasticity model that aims at the unification of the effects of static and dynamic recovery and recrystallisation, as well as grain growth and refinement. In the present contribution, the hypo‐elasticity based large strain recrystallisation formulation proposed by Cho et al. is transferred to a hyper‐elasticity based large strain thermoplasticity framework to overcome the limitations typically accompanied with hypo‐elasticity based formulations. For this purpose, an isotropic temperature dependent hyper‐elastic Hencky type formulation defined in logarithmic strains is combined with a temperature dependent von Mises yield criterion. The recrystallisation modelling approach by Cho et al. is adopted, assuming a non‐associated temperature dependent proportional hardening rate in the form of an Armstrong‐Frederick type hardening minus recovery format, wherein the proportional hardening related internal variable is interpreted as a measure of dislocation density. It is shown that the hyper‐elasticity based format results in a thermodynamical consistency condition that effectively constrains the physically motivated evolutions of recrystallised volume fraction and average grain size. To investigate the capability of the model to predict the material response of unified recrystallisation thermodynamically consistently, representative thermomechanical sequential loading conditions including static annealing and hot working are studied.

Cavity reverse expansion considering elastoplastic unloading and application in cast-in-situ bored piles

The construction process of a cast-in-situ bored pile is too complicated to be described by the cavity expansion theory with a single process. An exact unified semi-analytical solution for both cylindrical and spherical cavities reverse expansion after unloading in drained soil is developed. The non-associated Mohr-Coulomb model and definition of logarithmic strain are adopted in the reverse plastic zone. This model can be used to solve the stress and displacement fields of the soil around a bored pile along both the horizontal and depth directions. Parametric analysis shows that the effect of the unloading phase does not change the ultimate pressure of cavity reverse expansion compared with in situ expansion. The cavity cannot re-expand to its initial radius even though the cavity pressure reloads to the initial value. The increase of internal friction angle, cohesion, and Young's modulus has a positive effect on radius recovery, while the dilatancy angle has a negative effect. A simulation of the construction process of cast-in-situ bored piles is presented, where the role of boring, mud wall protection, and concrete placement is defined. An example that describes the stress and displacement fields around a pile shows that the total radial displacement of soil around the pile is dominated by contraction displacement. And it is closely related to depth and horizontal distance. The results of both parameter analysis and example analysis demonstrate that a low reverse cavity pressure corresponds to a stress-reduction area surrounding the cavity.

A new constitutive model and hot processing map of 5A06 aluminum alloy based on high-temperature rheological behavior and higher-order gradients

To develop a high-precision constitutive model and hot processing map for 5A06 aluminum alloy, the hot deformation behavior of the alloy was investigated through isothermal compression experiments and microstructure analysis experiments, which were conducted at temperatures ranging from 573 K to 773 K and at strain rates ranging from 0.01 to 10 s−1. Firstly, a new constitutive model, which is based on the partial derivatives of the experimental flow data and does not significantly increase the material parameters, was proposed. Secondly, a comparison and analysis of the predictive accuracies of both the new model and the classic model were conducted. Finally, the new constitutive model was used to construct the hot processing maps of the 5A06 aluminum alloy, and the optimal hot processing parameters were validated through metallographic experiments. The results show that a high-precision constitutive model can be constructed with a small number of material parameters by considering the second-order approximation between logarithmic stress and temperature, as well as the third-order approximation between logarithmic stress and logarithmic strain rate. The mean square errors of the new model were significantly lower than those of the Arrhenius model and Hense-Spittle model for all strain rates and temperatures. There were significant differences in the prediction accuracy of the AH and HS models at different temperatures and strain rates, indicating their accuracy was dependent on temperature and strain rate. The coefficients of the new model were significantly higher than those of the AH and HS models. Moreover, the proximity of predicted values to experimental values was ranked in descending order as follows: new model, AH model, and HS model. The energy dissipation rate is relatively high when the strain rate is lower than 10 s-1 and the temperature is higher than 623 K. The instability factor is larger than zero for all conditions except when the strain rate is equal to 10 s−1. The optimal hot working temperature range for 5A06 aluminum alloy is 623–700 K, and the strain rate should be in the range of 0.01 s−1 to 1 s−1. The microstructure analysis matches the predicted results from hot processing maps, which can guide the hot working process of 5A06 aluminum alloy.