Time-dependent Material Behavior Research Articles

Modeling time-dependent deformation in concrete: A fractional calculus method with finite element implementation

This study presents a novel numerical method to simulate the time-dependent behavior of concrete materials. The deformation response of both traditional and fractional calculus (FC) viscoelastic models is analyzed by the proposed method, in which models’ one-dimensional constitutive relationships are extended to the three-dimensional form. By applying numerical and finite difference methods based on Caputo-type fractional integration, the stress-strain behavior of the FC viscoelastic model is discretized over the time scale. This method exhibits broad application prospects, and can be employed to represent various forms of viscoelastic models. For the concrete material, suitable FC viscoelastic models are developed. To facilitate practical engineering applications of the proposed model, a numerical solution algorithm is implemented in the finite element (FE) analysis through the User-defined Material Mechanical Behavior (UMAT) interface of the commercial FE software ABAQUS. Finally, FE results are compared with the experimental results from several concrete creep tests. The consistency between the FE results and experimental data confirms the effectiveness of the proposed model in describing concrete behavior. The proposed method and model provide theoretical and numerical support for a more profound understanding and simulation of the time-dependent deformation of RC specimens in practical engineering applications.

Data-driven rheological characterization of stress buildup and relaxation in thermal greases

Thermal greases, often used as thermal interface materials, are complex paste-like mixtures composed of a base polymer in which dense metallic (or ceramic) filler particles are dispersed to improve the heat transfer properties of the material. They have complex rheological properties that impact the performance of the thermal interface material over its lifetime. We perform rheological experiments on thermal greases and observe both stress relaxation and stress buildup regimes. This time-dependent rheological behavior of such complex fluid-like materials is not captured by steady shear-thinning models often used to describe these materials. We find that thixo-elasto-visco-plastic (TEVP) and nonlinear-elasto-visco-plastic (NEVP) constitutive models characterize the observed stress relaxation and buildup regimes, respectively. Specifically, we use the models within a data-driven approach based on physics-informed neural networks (PINNs). PINNs are used to solve the inverse problem of determining the rheological model parameters from the dynamic response in experiments. These training data are generated by startup flow experiments at different (constant) shear rates using a shear rheometer. We validate the “learned” models by comparing their predicted shear stress evolution to experiments under shear rates not used in the training datasets. We further validate the learned TEVP model by solving a forward problem numerically to determine the shear stress evolution for an input step-strain profile. Meanwhile, the NEVP model is further validated by comparison to a steady Herschel–Bulkley fit of the material’s flow curve.

Strain-rate dependence of mechanical characteristics of PLLA with different MW

Abstract Dynamic mechanical properties of polymers for biomedical applications are crucial parameters for development and engineering of new medical devices. Here, the time-dependent material behavior is a key factor for durability. Varying the strain rate is a convenient implementation of time-dependency for uniaxial testing. This study investigates time-dependence of Poly(L-Lactide) (PLLA) through uniaxial testing with different strain rates and PLLA with different molecular weight. The results show strain dependence for elongation at break and yield stress, Young’s modulus however is not rate dependent. An increase in elongation at break is also seen with increasing molecular weight of PLLA. Plastic strain increases significantly only for PLLA with an intermediate inherent viscosity. Results show distinct time dependencies regarding strain rate for PLLA with slightly different inherent viscosities. For stent-related mechanical material characteristics, higher molecular weight PLLA seems to be advantageous. This study only considers base materials, although appropriate thermal, mechanical as well as chemical post processing approaches for further adjustment of different properties have already been shown. A combination of the best possible base material and a suitable post-processing should be targeted.

Reliability of quasi-integrable Hamiltonian systems with coupled viscoelastic dampings driven by wideband noises

Viscoelasticity is the time-dependent anelastic behavior of materials, which means the response of a viscoelastic system to a stimulus depends on the instantaneous state and its history. For quasi-integrable Hamiltonian systems with coupled viscoelastic dampings driven by wideband noises, the key to estimate their reliability is how to handle the coupled viscoelastic dampings between different degrees of freedom. In the present paper, the contributions of the coupled viscoelastic dampings are decoupled into elastic restoring forces and viscous dampings by using the generalized harmonic balance technique, and the equivalent quasi-integrable Hamiltonian systems without coupled viscoelastic dampings are obtained. Then by using the stochastic averaging method, the averaged equations for all slowly varying processes of the equivalent systems in both non-resonant and internally resonant cases are derived, which retain the main dynamical characteristics of the equivalent systems. The lower-dimensional backward Kolmogorov (BK) equation for reliability and the Pontryagin equation for the mean first passage time of the equivalent systems are derived. Two examples are worked out in detail to illustrate the application of the proposed procedure. Comparisons of the results obtained by using the proposed method with those from the Monte Carlo simulations of original systems show that the proposed method is well applicable.

A practical biaxial time-dependent material model of PVDF-coated polyester fabrics for structural applications

The utilization of air-supported fabric structures as formwork to construct concrete shells has attracted increasing attention in recent decades. An example of such an airform is the air-supported structure at Dahaize, which consists of a cylindrical part and a hemispherical part, and is 66 m in diameter and 65 m in height. The precise forming analysis of large-span air-supported structures requires the use of a reasonable material model that considers the biaxial stress condition and the creep behavior of the fabric. In this paper, a practical approach to modeling the biaxial time-dependent material behavior of composite fabrics is proposed based on the uniaxial linear viscoelastic theory and the plane stress orthotropic assumption. The multi-Kelvin physical model is developed to the two-dimensional form for the simulation of biaxial creep compliances. Biaxial tensile and biaxial creep tests are conducted on PVDF-coated polyester fabrics to calibrate the material parameters. The experimental stress conditions were determined according to the pre-estimated actual membrane stress distribution. The established material model is employed for the forming analysis of the Dahaize airform under conditions of varying creep times. The simulation results agree well with the on-site measured data, and this validates the accuracy and efficiency of the proposed material model.

An Analytical Model to Evaluate Short- and Long-Term Performances of Post-Tensioned Concrete Box-Girder Bridges Rehabilitated by an Ultrahigh-Performance Concrete Overlay

Potentially unfavorable stress redistributions could occur in post-tensioned concrete box-girder bridges upon deck rehabilitation by an ultrahigh-performance concrete (UHPC) overlay. The reason for such redistributions is that the deck forms an integral part of the load-resisting mechanism so that deck rehabilitation, namely, the process of removing the deteriorated deck and casting a fresh UHPC overlay, may cause large stress redistributions in the box girder. In addition, the significantly different shrinkage behavior between the freshly cast UHPC deck overlay and the old existing concrete deck below would result in restrained stress in the UHPC–old concrete interface. Therefore, how to evaluate the stress redistributions and the potentially unfavorable stresses in the box girder resulting from construction operations and the incompatible shrinkage is a crucial issue. Here, we propose an analytical model to assess the short- and long-term performances of the concrete box girder during and after deck rehabilitation. The analytical model was verified by using finite-element models incorporating the staged construction simulation and time-dependent behavior of materials. The model can be easily established and calculated with a great amount of time-saving compared with finite-element modeling, and it applies to different types of post-tensioned concrete box-girder bridges. The analytical model involves the balancing-load concept and the age-adjusted effective modulus method (AEMM). The balancing-load concept in the short-term analysis is to account for the prestressing force, and the AEMM in the time-dependent analysis is an effective tool to determine how stresses and strains vary with time due to the creep and shrinkage of a UHPC deck overlay. A parametric study was then conducted based on the analytical model, which involved the thickness of the deck layer to be rehabilitated and the addition of steel reinforcement in the new UHPC deck overlay. Analysis results indicated that pronounced tensile stresses developed in the UHPC deck overlay, which resulted from the restraint of the free shrinkage of the UHPC overlay by the subjacent concrete deck. An increase in the thickness of the newly cast UHPC deck overlay resulted in a decrease of the tensile stress in the UHPC deck overlay, and a rehabilitation thickness of 3.8–5.1 cm (1.5–2.0 in.) was deemed appropriate for the selected bridge according to the analysis.

Implementation of a surrogate model for a novel path‐based finite element simulation for additive manufacturing processes in construction

AbstractAdditive manufacturing in large‐scale construction is an ongoing research topic that shows significant potential to overcome the challenges in terms of efficient material usage and process automation in construction. A large challenge in deposition based additive manufacturing processes of concrete material is to ensure the structural stability while printing. Due to the weak material properties of the fresh concrete, it has to be ensured that during the printing process the not fully cured printed structure is able to carry its own weight. This requires process stabilization and a proper process control to prevent a collapse of the structure. Therefore, a numerical model of the printing process that takes into account the time dependent material behavior of the applied concrete as well as the printing path and the process parameters is necessary to support the process planning. Within the framework of project B04 of the collaborative research center TRR277 – Additive Manufacturing in Construction, a novel path‐based finite element simulation was developed in which the simulated geometry is constructed directly from the printing trajectory. Additionally, this approach allows the time‐dependent material properties of fresh concrete to be modeled directly and efficiently into the mesh of the printed structure. Since the computation of large scale printing processes with finite element simulations is quite expensive, there exists a need for a much faster computational model. In this contribution, the implementation of a surrogate model based on a neural network and its deployment to optimize the interlayer waiting time is presented.

Time-dependent behaviour of industrial granular materials under vibration: Modelling and phenomenology.

Several industrial and fundamental studies focus on the consolidation of granular materials as this covers many technological fields. When a granular material is shaken, it densifies. The energy needed to compact or decompact a powder column is of great interest in handling, filling and transport operations. This work studies the dynamic behaviour of four industrial granular materials–wheat flour, sericite, microcrystalline cellulose and glass beads–when submitted to vertical vibration using a particle damper. The effect of the vibration wave was studied by varying two dimensionless parameters: the relative acceleration, Γ and relative frequency, Ω including the relaxation time between periods. Our results show that despite the cohesiveness of the samples, their compaction dynamics occurs in at least two-compaction steps that a succession of stretched exponentials can model, denoted herein as a generalised KWW model. Also the absence of a relaxation time between periods leads to fluidisation during the first periods of vibration.The Fluidisation phenomena–the convective movement, granular jets, bubbling and slugging–appear to enhance particle reorganisation giving rise to higher packing fractions depending on the nature of the grains and operational conditions. A classification of the observed behaviours is proposed and related to the compaction kinetics.

Printing quality control of cement-based materials under flow and rest conditions

Time-dependent rheological properties of cement-based materials have a significant impact on 3D printing processes, where multiple rheological requirements should be met. A proper high rate of structural build-up is recommended to ensure the buildability and stability of printed elements. However, the loss of workability may occur rapidly, resulting in a significant reduction in print quality. Workability and buildability requirements usually interfere due to the time-dependent rheological behavior of cement-based materials under flow and rest conditions. This research aims to highlight the effects of time-dependent behavior on the printability of cement-based materials. The coupling mechanisms of microstructure development at rest and under shearing conditions are discussed. A new thixotropy index is proposed to quantify the printability window of cement-based materials based on their structuration rates. An experimental study was conducted on printable mortars incorporating a viscosity-modifying agent (VMA) to assess printing quality as a function of the degree of thixotropy. Different types of stability failures were captured and discussed.

Foreword to the special issue on new developments in structural stability.

Foreword to the special issue on new developments in structural stability.

Mechanical Response of Epoxy Resin-Flax Fiber Composites Subjected to Repeated Loading and Creep Recovery Tests.

Flax fiber-reinforced plastics have an innate eco-friendly nature due to the fiber reinforcement and reduced energy requirements in fabrication when compared to current fiber reinforced composite materials. They possess a complex time-dependent material behavior, which is investigated in the present paper. A composite material with flax fiber reinforcement on the load direction, embedded in an epoxy resin matrix, was studied. The procedures used were tensile tests, repeated loading-recovery, and creep-recovery tests, which were meant to expose the components of the response with respect to stress level and load duration. The results showed an elastic bi-linear behavior, a yield point at approximately 20% of the ultimate tensile stress, and tensile moduli of 35.9 GPa and 26.3 GPa, before and after yield. This is coupled with significant non-linear viscoelastic and, after yield, viscoplastic components, accounting for up to 14% of the strain response. The behavior is inherited from both the matrix and the fiber reinforcement and is attributed to the amorphous nature of the matrix combined with the microstructural re-organization of the fiber under load, which are partially reversible.

Time-dependent hydrophobic characterisation of granular materials synthesised with commercial chemical agents

The impact of hydrophobicity on unsaturated granular materials is important because suction is a function of the degree of saturation as well as the surface tension and contact angle of the water menisci. In this study, coatings have been applied on the surfaces of a quartzitic sand at different concentrations following synthesis with eight commercial chemical agents and dimethyldichlorosilane (DMDCS) to induce hydrophobicity. Contact angle (CA) measurements and water drop penetration time (WDPT) tests have been carried out at different time intervals to investigate the hydrophobicity and its persistence. Scanning electron microscope (SEM)-energy dispersive X-ray spectroscopy (EDS) was performed to evaluate the resulting chemical composition of the sand. Results demonstrate that synthesis at high concentration (5%) caused fluctuations in CA and WDPT measurements within the first 24h. Except for one commercial chemical agent, the maximum CAs reached by the remaining agents after 24h were comparable to DMDCS (CA=119°). However, the critical concentration needed to achieve these CAs differed significantly: the lowest critical concentration amongst the commercial chemical agents was 0.2% whereas with DMDCS, the critical concentration was 0.0053%. The resulting surface properties of the synthesised granular materials with the commercial chemical agents showed increases in carbon content whereas with DMDCS, no change was recorded compared to the untreated sand. In addition to illustrating the efficacy of commercial chemical agents in inducing hydrophobicity in granular materials, this study has provided insights into the timedependent hydrophobic behaviour of granular materials following synthesis.

Time-dependent hyper-viscoelastic parameter identification of human articular cartilage and substitute materials

Numerical simulations are a valuable tool to understand which processes during mechanical stimulations of hydrogels for cartilage replacement influence the behavior of chondrocytes and contribute to the success or failure of these materials as implants. Such simulations critically rely on the correct prediction of the material response through appropriate material models and corresponding parameters. In this study, we identify hyper-viscoelastic material parameters for numerical simulations in COMSOL Multiphysics® v. 5.6 for human articular cartilage and two replacement materials, the commercially available ChondroFillerliquid and oxidized alginate gelatin (ADA-GEL) hydrogels. We incorporate the realistic experimental boundary conditions into an inverse parameter identification scheme based on data from multiple loading modes simultaneously, including cyclic compression-tension and stress relaxation experiments. We provide individual parameter sets for the unconditioned and conditioned responses and discuss how viscoelastic effects are related to the materials’ microstructure. ADA-GEL and ChondroFillerliquid exhibit faster stress relaxation than cartilage with lower relaxation time constants, while cartilage has the largest viscoelastic stress contribution. The elastic response predominates in ADA-GEL and ChondroFillerliquid, while the viscoelastic response predominates in cartilage. These results will help to simulate mechanical stimulations, support the development of suitable materials with distinct mechanical properties in the future and provide parameters and insight into the time-dependent material behavior of human articular cartilage.

Experimental determination of cyclically stabilized material properties of the Mo-based alloy MHC in stress-relieved condition from room temperature to 1400 °C

The aim of the current study was the determination of the time-dependent visco-plastic material behavior of the molybdenum alloy MHC (Molybdenum-Hafnium-Carbon) in stress-relieved condition with cyclic strain-controlled low cycle fatigue experiments at room temperature, 800 °C and 1400 °C. To ensure high data quality, a servohydraulic testing machine modified with a vacuum chamber was utilized to avoid material oxidation. The long-time strain-controlled experiments were conducted with a laser extensometer with high accuracy up to the highest applied test temperature of 1400 °C. The determined data were appropriate to generate cyclic stress-strain curves, strain-Wöhler curves, and their descriptive parameters. Furthermore, the strain rate dependency of the cyclic stress response and the stress relaxation behavior of the cyclically stabilized material were also investigated at the mentioned temperatures. The current study indicates that MHC in stress-relieved condition has a softening ability during cyclic loading, especially at 800 °C and 1400 °C. The strain rate sensitivity of the stress amplitude for the case of cyclic stabilization shows similar behavior as described in the literature for the case of monotonously increasing loading conditions, with a minimum at 800 °C. An interesting effect was identified in relaxation tests with loading at different strain rates. A kind of rebound effect was observed at the highest utilized strain rate of 10−2 s−1, which disappears with decreasing strain rate. Elastic strain proportions can be converted into plastic strain proportions during the application of the slow strain rate.

Structural identification via the inference of the stochastic volatility model conditioned on the time-dependent bridge deflection

The time-dependent deflection data collected by a structural health monitoring (SHM) system contains information indicating the damage accumulation of prestressed concrete bridges (PSCBs). However, for this information to be used, the results must be fully translated into reliable metrics. Model-based structural identification (SI) targeting the time-dependent deflection of PSCBs is affected by time-dependent material behavior such as creep and shrinkage as well as the unknown path of structural deterioration, which should be considered in a stochastic volatility model (SVM). This paper presents an inference framework for an SVM conditioned on the time-dependent deflection of PSCBs. In this framework, the augmented state space includes the full ranges of the unobserved state variables affecting the time-dependent deflection of PSCBs, namely, structural rigidity, creep, shrinkage, prestress level and dead load level, along with the volatility parameters associated with the deterioration path of structural rigidity, which is modeled via the Wiener process. Exploiting the latent structure of the SVM, a cyclic Markov chain Monte Carlo (MCMC) sampler is proposed to draw samples from the joint posterior distribution of the unobserved state variables and volatility parameters. In an illustrative example, two-year continuous deflection monitoring data of an existing bridge are utilized as the target information for inference. The updated model can indicate the accumulated damage of the case bridge over the monitoring period. The proposed SI framework is able to support accurate probabilistic analysis of the time-dependent deflection of PSCB.

Time-variant reliability analysis of underground structures against delayed failure based on the probability density evolution method

The unpredictable delayed failure of underground tunnels may occur after excavation due to the time-dependent behavior of surrounding rock mass, which brings a new consideration to the reliability evaluation of underground structures. In this study, a time-variant reliability analysis procedure via the probability density evolution method (PDEM) is proposed for underground tunnels against delayed failure. The creep-damage theory is introduced to model the time-dependent behavior of rock materials. A new energy-based stability criterion is developed to identify the structural delayed failure. By applying the PDEM with the absorbing boundary condition, the time-varying reliability of underground structures can be obtained. The proposed procedure is applied to a case study involving the deep tunnel with uncertain material parameters. Numerical results demonstrate that the inherent variability of rock properties could result in the large fluctuation of structural delayed responses, which has a significant influence on the time-varying reliability of the tunnels.

An extended gradient-enhanced damage-plasticity model for concrete considering nonlinear creep and failure due to creep

For high stress levels, the dependence of the creep strain rate of concrete on the acting stress is nonlinear. Furthermore, very high stress levels may lead to a critical growth of microcracks resulting in material failure. For the lifetime assessment of creep sensitive concrete structures by means of numerical simulations, the realistic description of nonlinear creep is crucial. However, many concrete models are formulated for either nonlinear time-independent material behavior, or time-dependent material behavior, restricted to linear creep. This is the motivation for extending a damage-plasticity model, aiming at a unified and computationally efficient approach for representing the highly nonlinear time-dependent material behavior of concrete. Well established approaches for modeling the evolution of material properties, inelastic deformation, damage, creep and shrinkage serve as basis for considering nonlinear creep and material failure due to high sustained acting stress. The extended material model for concrete is validated by comprehensive experimental results from the literature.

An n-sided polygonal selective smoothed finite element method for nearly incompressible visco-hyperelastic soft materials

In this article, an n-sided polygonal smoothed finite element (nSFEM) is formulated for dynamic analyses of nonlinear problems of visco-hyperelastic materials undergoing large deformations. Two types of smoothing domains are constructed for mesh of n-sided polygonal elements. Using the gradient smoothing technique, the calculation of the strain-displacement matrix requires only the shape function values rather than the derivatives of shape function. The simple averaging point interpolation technique is used to calculate the values of the shape functions on the boundary of different smoothing domains. The Total Lagrangian formulation is used to deal with the nonlinear dynamic analysis of soft materials with finite strain. The polygonal FEM with Wachspress coordinate is also implemented for comparison. To overcome volumetric locking, selective smoothing domain scheme is used to calculate the smoothing nodal internal force. To analyze the time-dependent mechanical behavior of soft materials, a constitutive update algorithm for explicit time-integration is implemented based on the generalized Maxwell visco-hyperelastic model. A number of numerical examples are presented to demonstrate the high precision and super convergence, and robustness of the present nS-FEM for incompressible visco-hyperelastic problems.

Analysis of the tensile creep performance of warp-knitted fabrics in technical applications in view of fabric structure

Creep is one of the time-dependent mechanical behavior of textile materials, which can effect on the appearance and performance of the fabrics in various applications from garment to technical applications such as tensile structures and geotextiles. In the present study, the effect of fabric structure and loading direction on the creep behavior of two bar warp-knitted fabrics (Tricot, Reverse Locknit, 3 needle Sharkskin, 4 needle Sharkskin and Queen’s cord) have been investigated. According to the results, the fabric structure and loading direction have outstanding influence on the creep of the fabrics. The creep of the fabric in the course direction decreases by increasing the length of underlaps in the back-guide bar, meanwhile increases in the wale direction. Moreover, Tricot and Revers Locknit structures demonstrated more creep in the course direction, whilst sharkskin 3, sharkskin 4 and Queen’s cord structures exhibited higher creep values in the wale direction. Moreover, among considered fabric structures, Reverse Locknit with level of orthotropy near to1, revealed almost isotropic viscoelastic properties.

Characterizing and Engineering Biomimetic Materials for Viscoelastic Mechanotransduction Studies.

The mechanical behavior of soft tissue extracellular matrix is time dependent. Moreover, it evolves over time due to physiological processes as well as aging and disease. Measuring and quantifying the time-dependent mechanical behavior of soft tissues and materials pose a challenge, not only because of their labile and hydrated nature but also because of the lack of a common definition of terms and understanding of models for characterizing viscoelasticity. Here, we review the most important measurement techniques and models used to determine the viscoelastic properties of soft hydrated materials—or hydrogels—underlining the difference between viscoelastic behavior and the properties and descriptors used to quantify viscoelasticity. We then discuss the principal factors, which determine tissue viscoelasticity in vivo and summarize what we currently know about cell response to time-dependent materials, outlining fundamental factors that have to be considered when interpreting results. Particular attention is given to the relationship between the different time scales involved (mechanical, cellular and observation time scales), as well as scaling principles, all of which must be considered when designing viscoelastic materials and performing experiments for biomechanics or mechanobiology applications. From this overview, key considerations and directions for furthering insights and applications in the emergent field of cell viscoelastic mechanotransduction are provided.Impact statementOur tissues are viscoelastic: they respond to mechanical stresses and strains in a time-dependent manner. Their mechanical behavior also evolves over time due to growth, aging, remodeling and disease. Understanding cell response to time-dependent and time-evolving mechanical cues is important for a better comprehension of a wide number of pathophysiological processes and for the design of biomimetic substrates, which can be used as physiologically relevant in vitro models and in regenerative medicine applications. This review highlights the importance of a more rigorous approach toward viscoelastic material design and testing for cell mechanobiology studies, which embrace the entire spectrum of elasto- and viscotransduction.