Time-dependent Constitutive Model Research Articles

Modification of Uniaxial Stress-Strain Model of Concrete Confined by Pitting Corroded Stirrups.

To investigate the impact of stirrup pitting corrosion on the stress-strain model of core concrete under compression, this study, based on existing corroded steel specimens, establishes a probabilistic model of the residual cross-sectional area distribution of steel bars to reasonably evaluate the effect of pitting on the mechanical performance of stirrups. Considering the tension stiffening effect in reinforced concrete, a time-dependent damage model of corroded steel bars in concrete was determined, and the existing stress-strain model of concrete confined by stirrups was ultimately modified, establishing a time-dependent constitutive model that incorporates the effects of stirrup pitting corrosion. A comparison with previous experimental results indicates that the revised model presented in this paper can appropriately reflect the changes in the mechanical performance of concrete confined by corroded stirrups. The results of this study can provide theoretical support for the refined numerical analysis of reinforced concrete structures under the erosion of chloride ions.

Assessment of the strength deterioration of a coal pillar using a strain-softening time-dependent constitutive model

Assessment of the strength deterioration of a coal pillar using a strain-softening time-dependent constitutive model

Constitutive models based on titanium and its alloys for studying deformation and stresses in dental prosthesis: A comprehensive review

For optimized design and better functioning of dental implants, researchers to a great extent have used the finite element method (FEM) as a computational/numerical tool. It appears from the review that, despite a significant amount of success in understanding the deformation and stress fields generated in dental implants and its surrounding bone, there are still several inadequacies prevailing in the constitutive models used in dentistry. Therefore, the theoretical/computational basis of dental prosthesis’s deformation and stress analysis needs further improvement. To better understand the deformation and stresses produced in dental implants and their surrounding bone, the present work summarizes and discusses various constitutive models for titanium and its alloys as an implant material developed over the past few decades. The accomplishments and shortcomings of the current models are discussed. In addition, for completeness, the present study also summaries the effects of other factors in optimizing the dental implant. Critical findings indicate that longer dental implants effectively reduce stress gradients in the cortical peri-implant region. Threaded implants offer notable benefits, such as reduced bone stresses, enhanced osseointegration surface, and minimum slippage risk at the bone-implant junction. To further improve dental implant success rates, it is essential to consider the impact of dynamic loading and the viscoelastic behaviour of surrounding tissues. The use of porous implant structures shows promise in reducing maximum stress in cortical bone and enhancing load distribution, ultimately ameliorating the adverse effects of stress shielding in dental implant procedures. Further, some guidelines and research gaps have also been highlighted to develop more realistic time-dependent constitutive models of both implants and their surrounding bones.

Research on time dependent constitutive model and structural performance degradation prediction of silicon foam

The natural aging of silicone foam materials leads to a decline in their mechanical properties, which, in turn, affects the structural response of systems incorporating these materials. This study investigates the accelerated aging of silicone foam through stress relaxation tests, compression set tests, and uniaxial compression tests. By using the constitutive relationship as a bridge, a connection between stress relaxation and compression set is established, forming a predictive model for structural response. This model is validated against experimental results through finite element analysis. The high degree of accuracy between the predictive model and the experimental outcomes confirms its suitability for engineering applications.

Automated model discovery for muscle using constitutive recurrent neural networks

The stiffness of soft biological tissues not only depends on the applied deformation, but also on the deformation rate. To model this type of behavior, traditional approaches select a specific time-dependent constitutive model and fit its parameters to experimental data. Instead, a new trend now suggests a machine-learning based approach that simultaneously discovers both the best model and best parameters to explain given data. Recent studies have shown that feed-forward constitutive neural networks can robustly discover constitutive models and parameters for hyperelastic materials. However, feed-forward architectures fail to capture the history dependence of viscoelastic soft tissues. Here we combine a feed-forward constitutive neural network for the hyperelastic response and a recurrent neural network for the viscous response inspired by the theory of quasi-linear viscoelasticity. Our novel rheologically-informed network architecture discovers the time-independent initial stress using the feed-forward network and the time-dependent relaxation using the recurrent network. We train and test our combined network using unconfined compression relaxation experiments of passive skeletal muscle and compare our discovered model to a neo Hookean standard linear solid, to an advanced mechanics-based model, and to a vanilla recurrent neural network with no mechanics knowledge. We demonstrate that, for limited experimental data, our new constitutive recurrent neural network discovers models and parameters that satisfy basic physical principles and generalize well to unseen data. We discover a Mooney–Rivlin type two-term initial stored energy function that is linear in the first invariant I1 and quadratic in the second invariant I2 with stiffness parameters of 0.60 kPa and 0.55 kPa. We also discover a Prony-series type relaxation function with time constants of 0.362s, 2.54s, and 52.0s with coefficients of 0.89, 0.05, and 0.03. Our newly discovered model outperforms both the neo Hookean standard linear solid and the vanilla recurrent neural network in terms of prediction accuracy on unseen data. Our results suggest that constitutive recurrent neural networks can autonomously discover both model and parameters that best explain experimental data of soft viscoelastic tissues. Our source code, data, and examples are available at https://github.com/LivingMatterLab.

Understanding the mechanical “shakedown” of hydrogel ionotronics for realizing their highly functional stability

Hydrogel ionotronics (HI) has been extensively functionalized as artificial skins, soft robotics, and ultra-flexible displays over the recent years, and these applications require the involved materials to sustain prolonged cyclic stretching. However, HI devices suffer from a “shakedown” after prolonged cycling, as the stress-stretch curves change cycle by cycle. This mechanical failure often leads to functional instability of the HI devices, and the current literature discussing their structural origin and associated structure-property-function relationship is scarce. To this end, this work first discloses the molecular network response of HI devices for their shakedown behavior using the in situ small-angle X-ray scattering. Briefly, the stretching-induced orientation of the crosslinked network is unable to be fully relaxed during the cyclic stretching, which in turn leads to the partial disentanglement of the entangled network. Considering this mechanism, a time-dependent constitutive model is then proposed to quantitatively describe the shakedown behavior of HI devices. The model proposed herein precisely predicts the shakedown of HI devices and their corresponding cyclic stress-stretch curves, by using the parameters extracted from initial 70 cycles. Essentially, this work improves the in-depth understanding of fundamental issues related to structure–property-function relationships of HI devices, and thus, provides inspiration and guidance for designing highly stable and functional ionotronic devices.

Influence of degradation disease on tunnel stability based on a time-dependent constitutive model

The surrounding rock and lining of tunnels deteriorate with increasing operation time, which causes changes in the mechanical parameters of the lining material and then affects the stability of tunnels. According to the time degradation law of the lining proposed in this paper, the mechanical parameters of lining materials corresponding to different operation years of the tunnel can be obtained. Model tests of the lining without degradation and degradation for 10, 30, and 50 years were carried out. Based on the realistic failure process analysis (RFPA2D) system, the time-dependent failure constitutive model is introduced to simulate the degradation of the surrounding rock and lining. Based on the model test and numerical analysis, the influence of degradation on the mechanics and failure features of tunnel were studied. It was found that the degradation would impact the structural stress and the stability of the surrounding rock. The failure mode of the model and the loading stress were different with the degradation time. The longer the degradation time, the more serious the deformation of the vault, and the larger the damage area of the surrounding rock. The research results play an important theoretical guiding role in analysing the progressive failure process of the surrounding rock and lining and have great value in engineering applications for reinforcing and treating tunnel defects.

Modelling underground excavations in rock masses with anisotropic time-dependent behaviour

When modelling rock masses that behave anisotropically and in addition present a time dependent behaviour, it is relevant to select a constitutive model able to represent their actual behaviour realistically. This article presents an alternative anisotropic time-dependent constitutive model able to predict the coupling between anisotropic behaviour and time-dependent (or viscous) behaviour. The viscous behaviour is simulated with the Burgers model and all elastic springs and viscous dashpots are considered to exhibit transversely isotropic properties. The proposed constitutive model has been implemented in the finite element method software CODE_BRIGHT. To verify the basic anisotropic elastic solution, it has been compared with that of PLAXIS results. And to verify the isotropic viscoelastic solution, it has been compared with analytical solutions. Furthermore, the proposed constitutive model has been used to predict the behaviour of samples from laboratory tests. Finally, parametric analyses have been carried out to investigate the influence of different factors on tunnelling responses, including the selection of different constitutive models, anisotropy of initial stresses and anisotropy of material properties. The proposed model provides an alternative method for the preliminary design of geotechnical engineering works involving geomaterials that exhibit anisotropic time-dependent behaviour.Article highlights• An anisotropic time-dependent model has been implemented in CODE_BRIGHT and validated.• The model can predict the coupled anisotropic time-dependent behaviour of geomaterials.• Parametric analyses have been performed to study the influence of different factors in ground response.

The thermal vibration of small-sized rotating fractional viscoelastic beams positioned on a flexible foundation in the light of the Moore–Gibson–Thompson model

The current analysis examined the thermoviscoelastic vibration of Pasternak-based viscoelastic microbeams using fractional calculus. The viscoelastic property of the foundation is described using the Kelvin-Voigt constitutive equation. Fractional calculus is widely recognized as one of the most powerful mathematical tools for modelling physical responses to many materials and is particularly suitable for creating time-dependent foundational models. A new Kelvin-Voigt type with fractional derivatives and fractional orders was introduced because it needs fewer parameters to represent the experimental data correctly. It is particularly well suited to the construction of time-dependent constitutive models. In addition, the Moore-Gibson-Thompson (MGT) equation of heat transfer and Euler-Bernoulli beam theories were used to derive the system equations. The microbeam is exposed to mechanical and thermal loads and ultrafast laser heating. The system equations governing the transient response of microbeams were combined into a single differential equation and processed by means of the Laplace transform technique. The influences of various parameters on microbeam behavior have been highlighted and explored in-depth, including viscosity modulus, axial pressure, fractional order, laser pulse length, and foundation parameters. Finally, previous models have been compared to validate the proposed theory and numerical solutions.

Long-term mechanical properties of bamboo scrimber

Bamboo scrimber (BS), a main bamboo composite, has wide application prospects in green buildings. As a viscoelastic biomass material, long-term mechanical properties are the key indicators for its safe lifetime service. In this study, both short-term and long-term tension tests parallel to grain of BS were conducted. The long-term mechanical properties of BS including the duration of load (DOL) and creep effects were investigated from the macro and micro levels. Results indicated that the DOL effect of BS was more severe than other structural wooden materials, but its relative creep strain was smaller. From microlevel characterization, the DOL effect was strongly correlated with its microfracture morphology and bamboo fiber damage, while the creep effect was related to the decomposition of hemicellulose. Finally, time-dependent constitutive models were developed and provided good prediction for the DOL factor and creep strain of BS under different load durations. This study was beneficial for the long-term safe application of BS as a new structural material.

Numerical modeling of delayed damage and failure of concrete structures under sustained loading

The combination of subcritical damage growth and creep deformation can cause delayed failure of concrete materials. Such a time-dependent failure behavior adds a new consideration in design of concrete structures. To investigate this behavior, a time-dependent constitutive model for concrete is proposed. The model is anchored by integration of the continuum damage mechanics and nonlinear creep theory. It captures several essential mechanisms responsible for delayed failure behavior of concrete, which include instantaneous softening damage, plasticity, subcritical damage growth, and nonlinear creep. The model is calibrated by the creep experiments on concrete specimens under uniaxial compression and three-point bending. It is shown that the model can well capture the time-dependent deformation and failure of concrete structures under a wide range of loading levels. The contributions of different individual mechanisms to the overall structural response are investigated. The calibrated model is then used to simulate the response of a reinforced concrete frame under sustained loading. The simulation yields the stress-life curve, which is an essential metric describing the delayed failure behavior of concrete structures.

The time-dependent behaviour and failure mechanism of dacite under unloading condition

To obtain time-dependent responses of rock in excavation engineering projects, a series of creep tests of dacite are conducted through stepwise unloading of confining pressure. Based on the test results, time-dependent behaviour and unloading failure mechanism of dacite are studied in terms of creep rate, failure mode, long-term strength, and time-dependent damage. According to the creep rate, creep deformation can be divided into decelerating creep stage, steady creep stage, and accelerating creep stage during the last unloading failure process. Time-dependent deformation exhibits an anisotropic characteristic. Local shear bands are found in failed samples, which is markedly different from tensile failure in a short-term unloading test. Time-dependent damage of dacite under unloading condition is the result of combined effects of cracks. Creep failure of dacite under unloading condition caused by concentrating in a local zone and coalescing to form one or more macroscopic shear bands. This study gives an insight to understand the mechanism of unloading creep failure of rock and provides an experimental foundation for developing a time-dependent constitutive model under unloading condition.

Study on the Tri-axial Time-Dependent Deformation and Constitutive Model of Glauberite Salt Rock under the Coupled Effects of Compression and Dissolution

Solution mining for glauberite salt rock is a long-term process that takes several years to several decades. Therefore, deposit deformations and subsidence of ground surfaces are time-dependent deformation problems that should consider the effect of water dissolution. In order to investigate the time-dependent deformation characteristics of glauberite salt rock, tri-axial time-dependent deformation tests were conducted under the condition of 4 MPa confining pressure and 5 MPa axial pressure with infiltration pressures of 3, 2, 1, and 0 MPa, respectively, and the micro-CT scan system was used to scan the glauberite specimens before and after the experiment in order to study the fracture evolution inside the specimen, and a damage constitutive model was established to fit the time-dependent deformation curves based on the damage mechanics and effective stress principle. To simulate the solution mining process, the time-dependent deformation process of glauberite salt rock was divided into three stages: hydraulic connection stage, water-saturated stage, and drainage stage. The results demonstrate that the hydraulic connection time for glauberite salt rock decreases with increasing infiltration pressure. The time-dependent deformations of the specimens at the hydraulic connection and saturated-water stages are significantly affected by the effective stress and continual mineral dissolution. At the drainage stage, the softening degree of the solid skeleton mechanical properties, which is caused by the dissolution effect and infiltration pressure loading history, decides the deformation of glauberite salt rock. In addition, the degree of softening inside glauberite salt rock caused by dissolution becomes more severe with increasing infiltration pressure using the micro-CT scan technology. Lastly, the time-dependent damage constitutive model is able to describe the tri-axial time-dependent deformation behavior of glauberite salt rock, and the variations of time-dependent deformation parameters further indicate the damage evolution of the solid skeleton mechanical properties of glauberite caused by infiltration pressure and dissolution effect.

Study on seismic behavior reduction of typical joints for monolithic precast concrete frame structures with ages

PurposeMonolithic precast concrete frame structures have been promoted and developed in recent years. Owing to material deterioration and a weaker structural integrity, monolithic precast concrete frame structures may suffer from insufficient seismic capacity as service time increases. A typical joint of monolithic precast concrete frame structure is studied in this paper. The purpose of this paper is to perform numerical modeling of the typical joint subjected to low cyclic load at different ages and analyze the hysteretic behavior reduction with ages under common atmosphere environment.Design/methodology/approachExisting un-carbonated concrete, carbonated concrete and corroded rebar are all considered as deterioration factors for the typical joint, whose constitutive models are introduced into the finite element model to study. Moreover, time-dependent constitutive model of existing un-carbonated concrete and mechanical model of bond between precast and cast-in-place concrete are established on the basis of existing experimental data. Then, finite element method is used to investigate the seismic property reduction of the typical joint, where nonlinear springs are set to simulate bonding between precast and cast-in-place concrete.FindingsAnalyzing the results, the reduction of reaction force from skeleton curves of the joint is significant in the first 30 years of service time, and slows down after 30 years. Besides, the ductility, secant stiffness and equivalent viscous damping coefficient of the typical joint remain almost unchanged in the first decade, but decrease obviously after 10 years.Originality/valueThe originality of the paper consists in the following. The time-dependent constitutive model of existing un-carbonated concrete is established and used in finite element method. Besides, bonding between precast and cast-in-place concrete is considered using nonlinear springs. There is a reference value for the seismic performance assessment of existing monolithic precast concrete frame structures.

3D multiphysics modeling aided APU development for vehicle applications: A thermo-structural investigation

Solid oxide fuel cells (SOFC) are suitable for on-board electricity generation as Auxiliary Power Unit (APU) to support the electric power supply in heavy-duty vehicles. In order to satisfy the requirements of a lightweight fuel cell stack for mobile applications, thin-walled components must be used for the stack structure. This necessity is associated with material, process and design difficulties that must be solved in order to achieve a successful utilization. In this work a novel lightweight SOFC stack design with metal-supported cell was studied both numerically and experimentally. The metallic components are made from the Intermediate Temperature Metal (ITM), a high performance, high chromium ferritic stainless steels alloy. The multiphysics modeling approach (fluid dynamics, heat transfer, structural mechanics) was utilized in this work to predict the temperature distribution and the thermo-structural behavior of the new developed design. Geometric details of the fuel cell stack components as well as appropriate nonlinear, temperature and time-dependent constitutive models were developed to describe the material behavior. Experimental data were used to determine the material model parameters and validated the simulation results. The three-dimensional stress and deformation distributions in the individual stack components were evaluated and their maximum values for elements at risk were identified. Thus, the developed model enables the investigation of sustainability and serviceability of the structural elements to ensure a reliable operation of the stack. The developed computational model can be used as a design tool for parametric studies and optimization analysis to investigate the effects of process boundary conditions, material properties as well as geometrical design parameters and their variation on the induced thermal stresses.

Negative creep of soils

After unloading, the deformation of soils cannot be stable immediately, but continues to expand over time even under constant pressure. In this paper, the expansive deformation over time when effective stress is kept constant is defined as the negative creep, while the compressive creep is described as the positive creep. The division between positive creep and negative creep is named the stable normal compression line (SNCL), on which the stress–strain behaviour of the soil is time-independent. Based on the concept of the SNCL and test results, a new formula for creep is proposed. This formula is simple in form and has less parameters, and both negative creep and positive creep can be well predicted. By incorporating this formula into the current yield function of the unified hardening model, a new time-dependent current yield function is built. Combining the yield function, a flow rule, and transformed stress method, a new three-dimensional time-dependent constitutive model considering both positive and negative creep for clays is derived and presented. The new model is then validated by test results, including multistage loading oedometer tests, triaxial undrained creep tests, and triaxial undrained compression tests at the constant strain rates.

Program implementation of quantifying the nonlinear time-dependent deformation of high concrete dams based on MSC.Marc

Deformation is a comprehensive performance of concrete dam structures, especially the time-dependent deformation, a key index for evaluation of the structure behaviors, health status, and their evolution of a dam in long-term service. Aiming at the inherent time-dependent deformation behaviours of dam concrete and foundation rock, nonlinear time-dependent constitutive model is suitably established for the deformation of high concrete dams in this paper. Then, the time-dependent deformation equations for dam concrete and foundation rock in three-dimensional stress state are studied, and the corresponding segmentation criteria based on the Drucker-Prager yield function is proposed. On this basis, on the platform of the general commercial finite element software MSC.Marc, implementation method of the second development program of the established nonlinear time-dependent constitutive model is proposed. The correctness of the established model and its second development method based on MSC.Marc are verified by an example. The analysis and back analysis results of the inherent time-dependent deformation of a high concrete gravity dam show the engineering practicability of the established model.

Shaking table tests of coastal bridge piers with different levels of corrosion damage caused by chloride penetration

Coastal bridges in a marine environment are vulnerable to corrosion damage, which reduces the seismic capacity of the structures during a long-term service period. This paper presents the results of shaking table tests conducted for coastal bridge piers by considering the effect of a non-uniform corrosion. Four structural specimens with different degrees of corrosion at the designed splash and tidal zone are first fabricated by the electrochemical accelerated corrosion method. After subjecting the specimens to a series of gradually increasing ground motions, the natural period, damping ratio, displacement and acceleration responses, and average curvature distribution of the structures are analyzed. Based on the time-dependent constitutive models of the reinforcements, the finite element models of the aging columns are constructed. Four possible seismic failure modes are identified for the bridge piers through the evolution of the curvature distribution form during the entire service period. The results indicate that the structural seismic performance degrades continuously with the increase in the corrosion level. The significant performance difference between the atmospheric, splash and tidal, and submerged zones will probably result in the plastic hinge transfer phenomenon.

Three-dimensional FE2 method for the simulation of non-linear, rate-dependent response of composite structures

In this paper, a two scale Finite Element method (FE2), is presented to predict the non-linear macroscopic response of 3D composite structures with periodic microstructure that exhibit a time-dependent response. The sensitivity to the strain rate requires an homogenization scheme to bridge the scales between the macroscopic boundary conditions applied and the local evaluation of the strain rate. In the present work, the effective response of composite materials where the matrix has a local elasto-viscoplastic behavior with ductile damage are analyzed using periodic homogenization, solving simultaneously finite element problems at the microscopic scale (unit cell) and at the macroscopic scale. This approach can integrate any kind of periodic microstructure with any type of non-linear behavior for the constituents (without the consideration of non-linear geometric effects), allowing to treat complex mechanisms that can occur in every phase and at their interface. The numerical implementation of this simulation strategy has been performed with a parallel computational technique in ABAQUS/Standard,with the implementation of a set of dedicated scripts. The homogenization process is performed using a user-defined constitutive law that solve a set full-field non-linear simulations of a Unit Cell and perform the necessary homogenization of the mechanical quantities. The effectiveness of the method is demonstrated with three examples of 3D composite structures with plastic or viscoplastic and ductile damage matrix. In the first example, the numerical results obtained by this full field approach are compared with a semi-analytical solution on elastoplastic multilayer composite structure. The second example investigates the macroscopic response of a complex viscoplastic composite structure with ductile damage and is compared with the mean field Mori-Tanaka method. Finally, 3D corner structure consisting of periodically aligned short fibres composite is analysed under complex loading path. These numerical simulations illustrate the capabilities of the FE2 strategy under non-linear regime. when time dependent constitutive models describe the response of the constituents.

Pressure, hydrolytic degradation and plasticization drive high temperature blistering failure in moisture saturated polyimides

Polyimides and polyimide matrix composites are used in electronics, automotive, aerospace and other applications, particularly in situations where high temperature resistance and low weight are required. Under conditions in which polyimides have absorbed water, either by exposure to high humidity or by direct immersion, if the material is rapidly heated it may fail by high pressure water vapor induced blistering and/or delamination. Such hygrothermal failures can be a limiting factor to the use of polyimides and their composites in extreme environments. Despite prior experimental studies, the mechanisms of such failures remain a question due to the lack of complete material model for polyimide. In this work, a novel time, temperature and moisture dependent constitutive model is developed and presented for the first time. This model is built on previous experimental and modeling studies of high temperature viscoelastic and viscoplastic deformation in the polyimide HFPE-II-52 and on studies of the effects of moisture degradation on the mechanical properties. The model is implemented in a finite element simulation providing a means for the study of blistering under different heating rates and moisture levels. The results show for the first time that high temperature blistering failures are driven not only by steam pressure and thermal softening but by the synergy of pressure loading and material softening due to hydrolytic degradation and plasticization.