Nonlinear Creep Research Articles

Experimental investigation of the short-term creep recovery of hardened cement paste at micrometre length scale

This paper presents an experimental investigation on the short-term creep recovery of cement paste at micrometre length scale. Micro-cantilever beams were fabricated and tested with 8 different loading series using the nanoindenter. It is found that cement pastes show high recovery ratios (>80%) even subjected to very high stress levels. Relatively lower recovery ratios and non-linear creep were also observed for w/c 0.4 samples under high stress levels. A good agreement is found between the results predicted using the linear superposition principle and the experimental results except for the measured non-linear creep in w/c 0.4 samples. It is suggested that the short-term creep recovery may be associated with the microscale stress redistribution or the reversible internal water movement. The observed non-linear creep under the highest stress level may be due to the higher density of microcracks generated during the loading stage, which may further promote the water transfer.

Deformation and instability properties of cemented gangue backfill column under step-by-step load in constructional backfill mining.

Constructional backfill mining with cemented gangue backfill column can solve the environmental issues caused by mining activities and the accumulation of waste gangue at a low cost. To study the deformation and instability properties of cemented gangue backfill columns during the advancement of coal mining face, five step-by-step loading paths were adapted to mimic the different loading processes of the roof. The lateral deformation at different heights and axial deformation of the sample were monitored. The results show that the deformation and instability of the backfill column have the properties of loading paths and are affected by the step-by-step loading path. When stress-strength ratio (SSR) is less than 0.6, the lateral of backfill column shrinks during the creeping process. In high-stress levels, lateral creep strain develops faster than axial creep strain. The backfill column has characteristics of axial creep hardening and lateral creep softening during the step-by-step loading process. The instantaneous deformation modulus and instantaneous Poisson's ratio show an upward trend. The strength of backfill column under the step-by-step load is related to loading paths and is no less than uniaxial compressive strength. The non-uniformity of the lateral deformation of backfill column leads to excessive localized deformation that mainly occurs in the middle, causing the overall instability. The development of cracks of backfill column under step-by-step load could be divided into 4 stages according to SSR. Under different step-by-step loading paths, the axial creep strain rate is nearly a constant before entering the accelerated creep stage. A nonlinear creep constitutive model with a creep strain rate trigger was proposed to depict the development of axial strain under step-by-step load. This research could provide a scientific reference for the design of the advancing distance and cycle for the hydraulic support, and reinforcement of the backfill column.

Precision tracking of a 2-DOF stick-slip positioner using modeling-free inversion-based iterative control and modified inverse hysteresis compensator

This paper presents the precision control of a 2-DOF stick-slip positioning stage that exhibits friction nonlinearity, hysteresis nonlinearity, creep nonlinearity and cross-coupling phenomenon. Considering the complexity of friction nonlinearity model, the controller was established based on modeling-free inversion-based iterative control (MIIC), which could improve the tracking performance of repetitive trajectory. In order to reduce the influence of hysteresis and cross-coupling for data-based controller, the hysteresis compensator was added based on a modified inverse Prandtl-Ishlinkskii model, and the decoupling control strategy was utilized to eliminate the coupling error. In addition, the proportion-integration-differentiation (PID) controller was adopted to form the feedforward/feedback controller and guarantee the robustness. The developed controller was applied to a 2-DOF stick-slip positioner with comparative experiments. Experimental results indicate that the performance of proposed controller is superior to pure PID controller and even PID controller combined with hysteresis compensator. And comparing with conventional MIIC controller, the influence of nonlinear disturbance could be effectively reduced.

An Experimental Study on the Creep Characteristics of Sandstone in the Interval of Different Critical Stresses

Creep tests on brittle sandstone specimens were performed to investigate the time-dependent characteristics in the interval of different critical stresses. The results showed that failure will not occur when the loaded stress σ1 is less than the critical stress of dilation σcd, while all specimens were destroyed when σ1 is larger than σcd. In addition, the value of σcd was very close to the long-term strength obtained by the method of the isochronous stress-strain curve. Therefore, σcd can be regarded as the long-term strength of the sandstone specimens. When σ1 is larger than σcd, the time required for the failure of specimen tf decreases with the increase of σ1; the creep rate dε/dt increases with time t, and the specimen will be destroyed when it reaches a maximum value (dε/dt)max. Both relationships tf and σ1 and (dε/dt)max and σ1 can be described by the exponential function. Then, a nonlinear damage creep model considering the deformation damage and strength damage in the interval of different critical stresses was established, which can describe the whole creep process and predict the failure time of sandstone specimens.

Stability analysis of wooden arches with account for nonlinear creep

Introduction. The paper deals with the calculation of wooden arches taking into account the nonlinear relationship between stresses and instantaneous deformations, as well as creep and geometric nonlinearity, are considered. The analysis is based on the integral equation of the viscoelastoplastic hereditary aging model, originally proposed by A.G. Tamrazyan [1] to describe the nonlinear creep of concrete. Materials and Methods. The creep measure is taken in accordance with the work of I.E. Prokopovich and V.A. Zedgenidze [2] as a sum of exponential functions. The transition from the integral form of the creep law to the differential form is shown. The relationship between stresses and instantaneous deformations for wood under compression is determined from the Gerstner formula, and elastic work is assumed under tension. The solution is carried out using the finite element method in combination with the Newton-Raphson method and the Euler method according to the scheme that involves a stepwise increase in the load with correction of the stiffness matrix taking into account the change in the coordinates of the nodes with the sequential calculation of additional displacements of the nodes, which are due to the residual forces. The proposed approach for increasing the accuracy of determination of creep deformations at each step provides using the fourth-order Runge-Kutta method instead of the Euler method. Results. Based on the Lagrange variational principle, expressions are obtained for the stiffness matrix and the vector of additional dummy loads due to creep. The method developed by the authors is implemented in the form of a program in the MATLAB environment. Calculation examples are given for parabolic arches simply supported at the ends without an intermediate hinge and with an intermediate hinge in the middle of the span under the action of a uniformly distributed load. The results obtained are compared in the viscoelastic and viscoelastic formulation. The reliability of the results is validated through the calculation in the elastic formulation in the ANSYS software package. Discussion and Conclusions. For the arches considered, it is found that even with a load close to the instant critical, the growth of time travel is limited. Thus, the nature of their work under creep conditions differs drastically from the nature of the deformation of compressed rods.

Predictive Mechanistic Model of Creep Response of Single-Layered Pressure-Sensitive Adhesive (PSA) Joints.

This paper explores the uniaxial tensile creep response of acrylic-based pressure-sensitive adhesive (PSA), which exhibits a unique multi-phase creep response that does not have the classical steady-state region due to multiple transitions caused by several competing mechanisms: (i) cavity nucleation and growth in the interior of the adhesive material of the PSA system, as well as at the interfaces between the PSA and the substrate; (ii) fibrillation of the bulk adhesive, and (iii) interfacial mechanical locking between the adhesive and the bonding substrate. This results in multiple regimes of strain hardening and strain softening, evidenced by multiple regions of steady-state creep, separated by strong transitions in the creep rates. This complex, multi-phase, nonlinear creep response cannot be described by conventional creep constitutive models commonly used for polymers in commercial finite element codes. Accordingly, based on the empirical uniaxial tensile creep response and the mechanisms behind it, a new mechanistic model was proposed. This is capable of quantitatively capturing the characteristic features of the multiphase creep response of single-layered PSA joints as a function of viscoelastic bulk properties and free energy of the PSA material, substrate surface roughness, and interfacial surface energy between the adhesive and substrate. This is the first paper to present the modeling approach for capturing unique multi-phase creep behavior of PSA joint under tensile loading.

A new simplified method for calculating short-term and long-term consolidation settlements of multi-layered soils considering creep limit

The long-term consolidation settlement of soft soils under infrastructures is seriously concerned in coastal areas. In practice, soft soil ground is usually composed of multiple layers with different properties, and the effect of soil creep is nonnegligible. However, in conventional consolidation analysis, creep is seldom included during the “primary” consolidation. With conventional creep model, creep strain will reach infinity with time, which is unreasonable in the long-term view. In this study, a new simplified method based on Hypothesis B is presented to calculate both short-term and long-term consolidation settlements of multi-layered soils exhibiting non-linear creep. There are three main characteristics for this new simplified method: (a) the consolidation analysis for multi-layered soil is conducted using spectral method; (b) a nonlinear creep function with creep limit is incorporated to calculate both short-term and long-term creep settlements; (c) the “primary” consolidation and creep are calculated independently and combined with an empirical parameter α together with the consolidation degree U for correcting the creep settlement. Finite element analysis with a self-developed Elastic Visco-Plastic (EVP) constitutive model considering creep limit was also carried out. Verifications by field cases and finite element simulation demonstrate the efficiency and accuracy of the new simplified method in calculating the long-term settlements of soft soil ground under varied engineering conditions. Influences of major parameters selection in the calculation of the new simplified method are also discussed.

The Nonlinear Creep Behaviors of Sandstone Under the Different Confining Pressures Based on NMR Technology

The Nonlinear Creep Behaviors of Sandstone Under the Different Confining Pressures Based on NMR Technology

A novel nonlinear creep model based on damage characteristics of mudstone strength parameters.

Mudstone interlayer is a weak layer in rock engineering. When it is subjected to continuous stress higher than its damage threshold, due to the dislocation of particles in mudstone crystals and the expansion of cracks, mudstone strength is gradually damaged and deteriorated and the strain gradually increases, thus accelerating the phenomenon of creep damage. In order to describe the characteristics of the whole process of mudstone aging deformation, based on the damage evolution of strength parameters (cohesion and internal friction coefficient) with stress and time in mudstone creep tests, a novel damage nonlinear viscoelastoplastic body (D-NVPB) is proposed through improving traditional plastic element. D-NVPB describes the nonlinear characteristics of the accelerated creep stage of mudstone. With the element combination method, D-NVPB is connected with the Burgers model in series to form a new nonlinear damage creep model (D-NVEP model). The analysis results of creep characteristics theoretically verified the rationality of the model in describing the instantaneous elasticity, viscoelasticity, and nonlinear viscoplastic characteristics of the complete creep curve of mudstone. With the data obtained in the uniaxial compression creep test of mudstone under the action of a stress level of 14 MPa, based on the Levenberg-Marquardt nonlinear least squares method, the fitting calculation was performed through piecewise fitting and overall fitting. The correlation coefficient was 0.9909, which verified the applicability of the model. The obtained model parameters by the identification were used to predict the mudstone creep curve under the stress levels of 13 MPa and 15 MPa. The good prediction results further verified the feasibility of the model. Compared with the traditional creep model, the D-NVEP model can better describe the nonlinear characteristics of the accelerated creep stage and quantitatively display the strength damage evolution process of rock in the creep failure process.

Tensile creep mechanical behavior of periodontal ligament: A hyper-viscoelastic constitutive model

ObjectiveIn orthodontic treatment, the biomechanical response of periodontal ligament (PDL) induces tooth movement. Coupling modeling of PDL can effectively reflect its biomechanical response. The nonlinear creep mechanical behavior of PDL was studied by uniaxial tensile creep test and a new hyper-viscoelastic constitutive model. Two coupling modeling methods with limitations were excluded. MethodsPDL specimens were prepared from the central incisors of pig mandible. The theoretical step function was replaced by static loading with a total loading time of 1 s. The creep loading with the constant stresses of 0.05, 0.1, and 0.15 MPa was selected and kept unchanged for 1000 s. The instantaneous hyperelastic mechanical behavior and time-dependent nonlinear viscoelastic mechanical behavior of PDL were characterized by coupled instantaneous third-order Ogden hyperelastic and time-dependent nonlinear creep models. ResultsThe results showed that the instantaneous elastic curve of PDL increases in the form of hyperelastic index. The creep strain and creep compliance curves increase rapidly before 200s, and then increase slowly in steady state. The creep strain increased with an increase in the constant stress; conversely, the creep compliance decreased with an increase in the constant stress. The results showed that the experimental data were highly consistent with the hyper-viscoelastic constitutive model (R2>0.97). SignificanceWe normalize the framework of hyper-viscoelastic coupling modeling (Instantaneous hyperelastic model + time-dependent nonlinear viscoelastic model). Which can be extended to other nonlinear viscoelastic biomaterials.

Nonlinear Creep Model for Rocks Considering Damage Evolution Based on the Modified Nishihara Model

In general, the microdefects in rocks obey Weibull distribution. Based on the laws of statistics of microdefects in rocks, the relationship between the damage and the strain is established. Moreover, by considering characteristics of the viscoelastic–plastic and the damage evolution in rocks, a nonlinear creep model for rocks considering damage evolution is proposed to predict the creep behaviors of rocks based on the modified Nishihara model. In the proposed model, a dashpot element and a nonlinear viscoplastic body are added into the classical Nishihara model to simulate the accelerating creep stage of soft rocks. Moreover, the damage of rocks is considered in the process of creep. The effects of the shape parameter, the scale parameter, the peak stress, the peak strain, and the confining stress on the damage are investigated using the proposed method. The novel model is suitable to predict the creep behaviors of hard rocks and soft rocks simultaneously, and the difficulty to simulate the accelerating creep stage using the traditional creep model is overcome. To verify the robustness and precision of the proposed model, the creep behaviors of granite, coal, and red sandstone at different stresses are investigated. The predicted creep behaviors of soft and hard rocks using the proposed method are in good agreement with the experimental data, especially for the nonlinear accelerating creep stage.

Multiscale simulation of inelastic creep deformation for geological rocks

Subsurface geological formations provide giant capacities for large-scale (TWh) storage of renewable energy, once this energy (e.g. from solar and wind power plants) is converted to green gases, e.g. hydrogen. The critical aspects of developing this technology to full-scale will involve estimation of storage capacity, safety, and efficiency of a subsurface formation. Geological formations are often highly heterogeneous and, when utilized for cyclic energy storage, entail complex nonlinear rock deformation physics. In this work, we present a novel computational framework to study rock deformation under cyclic loading, in presence of nonlinear time-dependent creep physics. Both classical and relaxation creep methodologies are employed to analyze the variation of the total strain in the specimen over time. Implicit time-integration scheme is employed to preserve numerical stability, due to the nonlinear process. Once the computational framework is consistently defined using finite element method on the fine scale, a multiscale strategy is developed to represent the nonlinear deformation not only at fine but also coarser scales. This is achieved by developing locally computed finite element basis functions at coarse scale. The developed multiscale method also allows for iterative error reduction to any desired level, after being paired with a fine-scale smoother. Numerical test cases are studied to investigate various aspects of the developed computational workflow, from benchmarking with experiments to analysing the impact of nonlinear deformation for a field-scale relevant environment. Results indicate the applicability of the developed multiscale method in order to employ nonlinear physics in their laboratory-based scale of relevance (i.e., fine scale), yet perform field-relevant simulations. The developed simulator is made publicly available at https://gitlab.tudelft.nl/ADMIRE_Public/mechanics.

Powerful calibration strategy for the two-layer viscoplastic model

An efficient numerical integration scheme is proposed for the uniaxial loading of the two-layer viscoplastic (TLVP) model, which is a built-in material model in the commercial finite element software Abaqus. The particular version of the TLVP model under investigation is governed by linear isotropic plastic hardening rule with time-hardening nonlinear creep law. The new integration scheme can be easily implemented in any programming environment leading to a fast and robust tool to obtain the stress response in uniaxial loading for a given input strain history. The accuracy of the proposed algorithm is demonstrated and validated by comparing the results obtained with it to those calculated by Abaqus. A new calibration software with a graphical user interface is developed, which can fit the material parameters to the experimental data with arbitrary strain history in a uniaxial loading case. The new software is freely available to download from the webpage of the authors, and it is free to use for research purposes. The excellent performance of the new program is demonstrated by fitting the material parameters to three distinct experimental data sets.

MODELLING OF TIME-DEPENDENT BEHAVIOUR OF PARTICULATE THERMOSET POLYMERS

A preliminary study of a numerical model describing the behaviour of polymer-based composites is presented. The numerical model consists of three main parts. The first is the microplane M4 model, which is the main part of the model and is used to simulate elastoplastic behaviour and damage. The second part consists of a generalized Maxwell model, which adds the effect of linear creep of the material to the calculation. The last part is a free volume model that extends the linear creep to the nonlinear creep. The creep is calculated on the deviatoric part of the normal stress of each microplane, which allows the model to capture the polymer behaviour adequately without adjusting the free volume of the model.

A Stochastic Model Based on Fiber Breakage and Matrix Creep for the Stress-Rupture Failure of Unidirectional Continuous Fiber Composites 2. Non-linear Matrix Creep Effects

Stress rupture (sometimes called creep-rupture) is a time-dependent failure mode occurring in unidirectional fiber composites under high tensile loads sustained over long times (e. g., many years), resulting in highly variable lifetimes and where failure has catastrophic consequences. Stress-rupture is of particular concern in such structures as composite overwrapped pressure vessels (COPVs), tension members in infrastructure applications (suspended roofs, post-tensioned bridge cables) and high angular velocity rotors (e.g., flywheels, centrifuges, and propellers). At the micromechanical level, stress rupture begins with the failure of some individual fibers at random flaws, followed by local load-transfer to neighboring intact fibers through shear stresses in the matrix. Over time, the matrix between the fibers creeps in shear, which causes lengthening of local fiber overload zones around previous fiber breaks, resulting in even more fiber breaks, and eventually, formation clusters of fiber breaks of various sizes, one of which eventually grows to a catastrophically unstable size. Most previous models are direct extension of classic stochastic breakdown models for a single fiber, and do not reflect the micromechanical detail, particularly in terms of the creep behavior of the matrix. These models may be adequate for interpreting experimental, composite stress rupture data under a constant load in service; however, they are of highly questionable accuracy under more complex loading profiles, especially ones that initially include a brief “proof test” at a “proof load” of up to 1.5 times the chosen service load. Such models typically predict an improved reliability for proof-test survivors that is higher than the reliability without such a proof test. In our previous work relevant to carbon fiber/epoxy composite structures we showed that damage occurs in the form of a large number of fiber breaks that would not otherwise occur, and in many important circumstances the net effect is reduced reliability over time, if the proof stress is too high. The current paper continues our previous work by revising the model for matrix creep to include non-linear creep whereby power-law creep behavior occurs not only in time but also in shear stress level and with differing exponents. This model, thus, admits two additional parameters, one determining the sensitivity of shear creep rate to shear stress level, and another that acts as a threshold shear stress level reminiscent of a yield stress in the plastic limit, which the model also admits. The new model predicts very similar behavior to that seen in the previous model under linear viscoelastic behavior of the matrix, except that it allows for a threshold shear stress. This threshold allows consideration of behavior under near plastic matrix yielding or even matrix shear failure, the consequence of which is a large increase in the length-scale of load transfer around fiber breaks, and thus, a significant reduction in composite strength and increase in variability. Derivations of length-scales resulting from non-linear matrix creep are provided as Appendices in the Supplementary Material.

A fixed-stress split strategy for two-phase flow in heterogeneous poroelastic media overlain by viscoelastic rock salt layers

We propose a new computational model for two-phase immiscible flow in a poroelastic medium overlain by a saline formation displaying creep behavior with viscous strain ruled by a nonlinear dependence of power-law type on the deviatoric stress. Within the framework of the fixed-stress split algorithm, hinged upon freezing the total mean stress in the flow equations, hydrodynamics and geomechanics subsystems are solved by mixed finite element methods whereas the hyperbolic equation for the water saturation is formulated in terms of the Lagrangian porosity and solved adopting an operator splitting fractional-step method combined with a higher-order non-oscillatory finite volume central scheme. Within this typical multi-physics setting, the sequential formulation allows greater flexibility in the choice of the meshes for the subsystems, particularly for the geomechanics module, which can be solved in the extended domain including the adjacent impervious formations (over-, under- and side-burdens). Considering the upper interface of the rock salt dictated by the profile of saline dome geobodies, whose impermeability property precludes hydraulic communication between adjacent formations, the initial in situ undrained state is also modeled by invoking Skempton’s coefficient along with the characterization of the undrained bulk and shear modulus. By constructing a robust evolving algorithm between the discrete counterparts of the three subsystems in the reservoir, in conjunction with an iterative scheme underlying the mixed method for the nonlinear creep problem in the rock salt, numerical simulations of a water-flooding problem in secondary oil recovery are performed for different realizations of the input random fields. Numerical results illustrate the influence of viscoelastic effects in the cap rock upon subsidence, reservoir compaction, finger grow and breakthrough curves. Comparisons with the performance of traditional one-way formulation are also presented.

Finite Element Method-Based Simulation Creep Behavior of Viscoelastic Carbon-Fiber Composite.

Usually, a polymer composite with a viscoelastic response matrix has a creep behavior. To predict this phenomenon, a good knowledge of the properties and mechanical constants of the material becomes important. Schapery’s equation represents a basic relation to study the nonlinear viscoelastic creep behavior of composite reinforced with carbon fiber (matrix made by polyethrtethrtketone (PEEK) and epoxy resin). The finite element method (FEM) is a classic, well known and powerful tool to determine the overall engineering constants. The method is applied to a fiber one-directional composite for two different applications: carbon fibers T800 reinforcing an epoxy matrix Fibredux 6376C and carbon fibers of the type IM6 reinforcing a thermoplastic material APC2. More cases have been considered. The experimental results provide a validation of the proposed method and a good agreement between theoretical and experimental results.

Fractional robust adaptive decoupled control for attenuating creep, hysteresis and cross coupling in a parallel piezostage

Parallel micropositioning piezostages are widely used in the micro-/nano-manipulation applications, but also subject to the nonlinear disturbances, like hysteresis, creep and cross-coupling effects. In this paper, a new fractional robust adaptive decoupled control (FRADC) is synthesized for a six-axis parallel micropositioning piezostage to improve the positioning accuracy. The proposed FRADC contains three intuitional terms: (1) a decoupling term that alleviates the coupled motions among different axes, making the controller implementation more convenient and efficient; (2) a feedforward compensation term based on a fractional normalized Bouc-Wen (FONBW) model, compensating for the rate-dependent hysteresis effect induced by the piezoelectric actuators; (3) a feedback model reference adaptive control (MRAC) term with fractional proportional-plus-integral-type updating rules that suppresses the creep effect, parameters uncertainty and external disturbances, further enhancing the robustness and positioning accuracy. The stability of the closed-loop system is analyzed in theory. The effectiveness of the proposed FRADC is experimentally validated by comparing with the standalone inverse-FONBW-based feedforward control, the standalone feedback fractional MRAC, and the traditional integer-order control methods. Results demonstrate that the proposed FRADC can guarantee higher positioning accuracy for the piezostage system in wider control bandwidth.

A Viscoelastic-Plastic Constitutive Model of Creep in Clay Based on Improved Nonlinear Elements

A Triaxial creep experiment was performed with Chengdu clay. The results demonstrate that the deformation of clay includes instantaneous elastic strain, attenuated creep deformation, steady creep deformation, and accelerated creep deformation. In view of the nonlinear properties of creep, an improved nonlinear viscous element describing attenuating creep and an improved fractional order viscous element describing accelerating creep are established, and a one-dimensional nonlinear fractional order five-element creep model is developed with the two improved elements. The model can theoretically describe the entire process of creep. The nonlinear fractional order five-element model and the traditional five-element model were employed to verify the creep test. Compared with the traditional five-element creep model, the nonlinear fractional order creep model more faithfully reproduces the experimental data and more accurately describes the deformation trend in each stage, especially the accelerated creep stage.

Non-linear creep damage model of sandstone under freeze-thaw cycle

To study rock damage characteristics under long-term freeze-thaw cycles and loads, rock freeze-thaw and creep damage factors were defined based on nuclear magnetic resonance porosity and volume strain, respectively. The damage factor is introduced into the basic rheological element, and the non-linear creep damage constitutive model and freeze-thaw rock equation are established to describe non-linear creep characteristics under a constant load. Simultaneously, the creep test of freeze-thaw rock under step loading is performed. Based on the test data, the applicability and accuracy of the creep damage freeze-thaw rock model are analyzed and verified. The results show that freeze-thaw cycles result in continuous rock pore structure damage and deterioration, and nuclear magnetic resonance porosity enhancement. The constant load induces increasing rock plastic deformation, volume, and creep aging damage. As the loading stress increases, the instantaneous rock elastic parameters increase, and the rheological elastic and viscosity parameters decrease. Furthermore, the damage degradation of freeze-thaw cycles weakens the rock viscoplasticity, resulting in a rapid decrease in the viscosity parameter with an increase in freeze-thaw cycles. Generally, the continuous damage of the rock is degraded, and the long-term strength decreases continuously.