Time-dependent Mechanical Response Research Articles

Fracture properties of mixed mode I-II cracks in concrete after sustained loading

To investigate the fracture properties of mixed mode I-II cracks in concrete after sustained loading, the basic creep tests were conducted on concrete beams with five initial mode mixity ratios under three-point bending (TPB) loading or four-point shearing (FPS) loading, two sustained load levels, 80 % of the initial cracking load and the initial cracking load, for a period of 90 days. After creep tests, the specimens were unloaded and immediately loaded up to failure under the quasi-static TPB/FPS loading. Meanwhile, the entire crack propagation process was monitored using the digital image correlation technique. The numerical simulations based on the Norton-Bailey creep model were conducted to capture the time-dependent mechanical response of concrete under sustained loading. The experimental and numerical results showed that the pre-crack did not initiate in the creep tests unless the applied sustained loading exceeded the initial cracking load observed under quasi-static loading. It can be attributed to the viscoelastic characteristics of the concrete, which caused a decrease in the average stress around the pre-crack tip. A load increment was necessary to compensate for the reduced stress, resulting in an increase in the initial cracking load and the crack resistance of the structures. Moreover, sustained loading showed no significant effect on the peak load, fracture angle, initial cracking angle and crack propagation path. It suggests that sustained loading primarily induced a viscoelastic response of the concrete around the pre-crack tip rather than promoting extensive crack growth. Therefore, it is reasonable to approximate crack propagation paths of the concrete after sustained loading by considering the paths observed under quasi-static loading.

A numerical multi-scale method for analyzing the rate-dependent and inelastic response of short fiber reinforced polymers: Modeling framework and experimental validation

This research presents a numerical multi-scale approach that efficiently addresses the inelastic and time-dependent mechanical response of short fiber reinforced polymers (SFRPs) under monotonic loading conditions by linking the mechanical analysis from microscale analysis to a continuum model. To do so, first, the mechanical performance of a recently suggested unit cell, considering the intrinsic mechanical characteristics of both fiber and matrix, is studied to address the inelastic and rate-dependent mechanical behavior of completely aligned SFRPs. Then, the evaluated mechanical response is linked to the Hill's plasticity and two-layer viscoplastic (TLVP) models to represent the anisotropic mechanical response of SFRPs. Furthermore, an easy-to-use multi-step homogenization process is considered to numerically incorporate the influence of fiber misalignments. Finally, the suggested multi-scale technique is thoroughly validated at different strain rates, by using experimental observations of short fiber composites with high volume fraction and direct FE simulations of RVEs with complex microstructures.

Enhancing nanoscale viscoelasticity characterization in bimodal atomic force microscopy.

Polymeric, soft, and biological materials exhibit viscoelasticity, which is a time dependent mechanical response to deformation. Material viscoelasticity emerges from the movement of a material's constituent molecules at the nano- and microscale in response to applied deformation. Therefore, viscoelastic properties depend on the speed at which a material is deformed. Recent technological advances, especially in atomic force microscopy (AFM), have provided tools to measure and map material viscoelasticity with nanoscale resolution. However, to obtain additional information about the viscoelastic behavior of a material from such measurements, theoretical grounding during data analysis is required. For example, commercially available bimodal AFM imaging maps two different viscoelastic properties of a sample, the storage modulus, E', and loss tangent, tan δ, with each property being measured by a different resonance frequency of the AFM cantilever. While such techniques provide high resolution maps of E' and tan δ, the different measurement frequencies make it difficult to calculate key viscoelastic properties of the sample such as: the model of viscoelasticity that describes the sample, the loss modulus, E'', at either frequency, elasticity E, viscosity η, and characteristic response times τ. To overcome this difficulty, we present a new data analysis procedure derived from linear viscoelasticity theory. This procedure is applied and validated by performing amplitude modulation-frequency modulation (AM-FM) AFM, a commercially available bimodal imaging technique, on a styrene-butadiene rubber (SBR) with known mechanical behavior. The new analysis procedure correctly identified the type of viscoelasticity exhibited by the SBR and accurately calculated SBR E, η, and τ, providing a useful means of enhancing the amount of information gained about a sample's nanoscale viscoelastic properties from bimodal AFM measurements. Additionally, being derived from fundamental models of linear viscoelasticity, the procedure can be employed for any technique where different viscoelastic properties are measured at different and discrete frequencies with applied deformations in the linear viscoelastic regime of a sample.

Experimental Investigation on the Penetrability Mechanism of Gel Slug During Well Completion Processes.

Reservoir formation damage is an essential problem which troubled oil and gas well production, a smart packer is a promising technology to maintain sustainable development for the oil and gas fields. Currently, the "gel valve" technology has been proved to be feasible with gel slug to seal casing and descend the completion pipe string, while the systemic performance of ideal gel is still not clear. In the underbalanced completion stage with the gel valve, the downward completion string needs to penetrate the gel slug to form an oil and gas passage in the wellbore. The penetration of rod string to gel is a dynamic process. The gel-casing structure often shows a time-dependent mechanical response, which is different from the static response. In the process of penetration, the interaction force between the rod and gel is not only related to the properties of the interface between gel and string but also affected by the moving speed, rod diameter, and thickness of the gel. The dynamic penetration experiment was carried out to determine the penetrating force varied with depth. The research showed that the force curve was mainly composed of three parts, the rising curve of elastic deformation, decline curve for the surface worn out, and another curve of the rod wear into. By changing the rod diameter, gel thickness, and penetration speed, the change rules of forces in each stage were further analyzed, which would provide a scientific basis for a well completion design with a gel valve.

Characterizing site-specific mechanical properties of knee cartilage with indentation-relaxation maps and machine learning

Knee cartilage experiences site-specific focal lesion and degeneration, which is likely associated with tissue inhomogeneity and nonuniform mechanical stimuli in the joint, for which a complete picture remains to be depicted. The present study aimed to develop a methodology to quantify knee cartilage inhomogeneity using porcine knee specimens. Automated indentation-relaxation and needle probing were performed on fully intact cartilage to obtain data that essentially represent continuous distributions of cartilage properties in the knee. Machine learning was then introduced to approximate the tissue inhomogeneity with several regions via clusters of indentation locations, and finite element modeling was used to obtain poromechanical properties for each region using indentation-relaxation and thickness data. Significant region dependence was established from the full time-dependent mechanical response. Seventeen regions, or clusters, were found to best approximate the site-specific poromechanical properties of articular cartilage for femoral groove, lateral and medial condyles and tibial plateaus, after up to eight clusters were tested for each of the five cartilage sections. The region partitions recommended, and tissue properties acquired would facilitate implementation of tissue inhomogeneity in future applications, e.g., contact modeling of the knee joint. The results obtained from 14 porcine knees revealed interesting region differences, for example, the two condyles have the same effective stiffness when responding to slowly applied mechanical loadings but substantially lower stiffness in the medial condyle when responding to fast loadings. This mechanical behavior may be associated with the fact that medial femoral cartilage is more prone to focal lesions than the lateral one.

Compressive Mechanical Behavior of Partially Oxidized Polyvinyl Alcohol Hydrogels for Cartilage Tissue Repair.

Polyvinyl alcohol (PVA) hydrogels are extensively used as scaffolds for tissue engineering, although their biodegradation properties have not been optimized yet. To overcome this limitation, partially oxidized PVA has been developed by means of different oxidizing agents, obtaining scaffolds with improved biodegradability. The oxidation reaction also allows tuning the mechanical properties, which are essential for effective use in vivo. In this work, the compressive mechanical behavior of native and partially oxidized PVA hydrogels is investigated, to evaluate the effect of different oxidizing agents, i.e., potassium permanganate, bromine, and iodine. For this purpose, PVA hydrogels are tested by means of indentation tests, also considering the time-dependent mechanical response. Indentation results show that the oxidation reduces the compressive stiffness from about 2.3 N/mm for native PVA to 1.1 ÷ 1.4 N/mm for oxidized PVA. During the consolidation, PVA hydrogels exhibit a force reduction of about 40% and this behavior is unaffected by the oxidizing treatment. A poroviscoelastic constitutive model is developed to describe the time-dependent mechanical response, accounting for the viscoelastic polymer matrix properties and the flow of water molecules within the matrix during long-term compression. This model allows to estimate the long-term Young's modulus of PVA hydrogels in drained conditions (66 kPa for native PVA and 34-42 kPa for oxidized PVA) and can be exploited to evaluate their performances under compressive stress in vivo, as in the case of cartilage tissue engineering.

Dynamic Covalent Hydrogels: Strong yet Dynamic.

Hydrogels are crosslinked polymer networks with time-dependent mechanical response. The overall mechanical properties are correlated with the dynamics of the crosslinks. Generally, hydrogels crosslinked by permanent chemical crosslinks are strong but static, while hydrogels crosslinked by physical interactions are weak but dynamic. It is highly desirable to create synthetic hydrogels that possess strong mechanical stability yet remain dynamic for various applications, such as drug delivery cargos, tissue engineering scaffolds, and shape-memory materials. Recently, with the introduction of dynamic covalent chemistry, the seemingly conflicting mechanical properties, i.e., stability and dynamics, have been successfully combined in the same hydrogels. Dynamic covalent bonds are mechanically stable yet still capable of exchanging, dissociating, or switching in response to external stimuli, empowering the hydrogels with self-healing properties, injectability and suitability for postprocessing and additive manufacturing. Here in this review, we first summarize the common dynamic covalent bonds used in hydrogel networks based on various chemical reaction mechanisms and the mechanical strength of these bonds at the single molecule level. Next, we discuss how dynamic covalent chemistry makes hydrogel materials more dynamic from the materials perspective. Furthermore, we highlight the challenges and future perspectives of dynamic covalent hydrogels.

A MODIFIED FINITE ELEMENT MODEL OF A POROVISCOELASTIC INTERVERTEBRAL DISC

The intervertebral disc (IVD) is the soft tissue between the vertebral bodies, which is responsible for transmitting multi-directional loads through the spine and to allow relative motion between the vertebral bodies. The IVD is composed of three distinct tissues, including the nucleus pulposus, annulus fibrosus, and the cartilaginous endplates. Each of these tissues has a characteristic composition and structure which provide them with unique mechanical properties. Among these, nucleus pulposus and annulus fibrosus due to their intricate time-dependent mechanical response has always been the topic of interest for the researchers. Here, we aimed at establishing a patient-specific 3D finite element (FE) model of human IVD based on the poroviscoelastic constitutive law. The main objective was to use the data of tensile stress-relaxation tests on the annulus and nucleus regions to find the poroviscoelastic material constitutive law. The model assumed that the disc is a two-phase body consisting of a water-saturated solid matrix. To do that, the available data in the literature was used as the primary material properties of our model. Thereafter, a set of compressive and tensile loadings was applied on the established patient-specific model of the IVD and the FE results of the poroviscoelastic model were compared to the experimental data. This allowed us to determine a new set of revised parameter values for the poroviscoelastic model which will have practical implications for any future FE studies.

Insights into the Microstructural Origin of Brain Viscoelasticity

Mechanical aspects play an important role in brain development, function, and disease. Therefore, continuum-mechanics-based computational models are a valuable tool to advance our understanding of mechanics-related physiological and pathological processes in the brain. Currently, mainly phenomenological material models are used to predict the behavior of brain tissue numerically. The model parameters often lack physical interpretation and only provide adequate estimates for brain regions which have a similar microstructure and age as those used for calibration. These issues can be overcome by establishing advanced constitutive models that are microstructurally motivated and account for regional heterogeneities through microstructural parameters.In this work, we perform simultaneous compressive mechanical loadings and microstructural analyses of porcine brain tissue to identify the microstructural mechanisms that underlie the macroscopic nonlinear and time-dependent mechanical response. Based on experimental insights into the link between macroscopic mechanics and cellular rearrangements, we propose a microstructure-informed finite viscoelastic constitutive model for brain tissue. We determine a relaxation time constant from cellular displacement curves and introduce hyperelastic model parameters as linear functions of the cell density, as determined through histological staining of the tested samples. The model is calibrated using a combination of cyclic loadings and stress relaxation experiments in compression. The presented considerations constitute an important step towards microstructure-based viscoelastic constitutive models for brain tissue, which may eventually allow us to capture regional material heterogeneities and predict how microstructural changes during development, aging, and disease affect macroscopic tissue mechanics.

Protocols for studying the time-dependent mechanical response of viscoelastic materials using spherical indentation stress-strain curves

Spherical nanoindentation has been used successfully to extract meaningful indentation stress-strain curves in hard materials such as metals and ceramics. These methods have not yet been applied on viscoelastic-viscoplastic polymer samples. This study explores the potential of the current spherical nanoindentation analysis protocols in extracting indentation stress-strain curves and viscoelastic properties on samples exhibiting time-dependent material response at room temperature. These new protocols were tested on polymethyl methacrylate, polycarbonate, and low-density polyethylene. The properties extracted under different loading rates and indenter tip sizes conditions were observed to be consistent. It is further demonstrated that it is possible to recover the compression stress-strain curves for polymethyl methacrylate and low-density polyethylene from the measured indentation stress-strain curves. This study establishes some of the foundations needed for the development of protocols needed to reliably investigate the local time-dependent mechanical response of materials using spherical nanoindentation.

Anomalous tensile response of bacterial cellulose nanopaper at intermediate strain rates

Nanocellulose network in the form of cellulose nanopaper is an important material structure and its time-dependent mechanical response is crucial in many of its potential applications. In this work, we report the influences of grammage and strain rate on the tensile response of bacterial cellulose (BC) nanopaper. BC nanopaper with grammages of 20, 40, 60 and 80 g m−2 were tested in tension at strain rates ranging from 0.1% s−1 to 50% s−1. At strain rates le 2.5% s−1, both the tensile modulus and strength of the BC nanopapers stayed constant at ~ 14 GPa and ~ 120 MPa, respectively. At higher strain rates of 25% s−1 and 50% s−1 however, the tensile properties of the BC nanopapers decreased significantly. This observed anomalous tensile response of BC nanopaper is attributed to inertial effect, in which some of the curled BC nanofibres within the nanopaper structure do not have enough time to uncurl before failure at such high strain rates. Our measurements further showed that BC nanopaper showed little deformation under creep, with a secondary creep rate of only ~ 10–6 s−1. This stems from the highly crystalline nature of BC, as well as the large number of contact or physical crosslinking points between adjacent BC nanofibres, further reducing the mobility of the BC nanofibres in the nanopaper structure.

Time-dependent Mechanical Response at the Nanoscale

Modern nanofabrication processes on metals, polymers, and ceramics often require deforming these materials at strain rates ranging ~101 – 107 s–1. Therefore, there is a need to develop an appropriate methodology capable of measuring and predicting the effects of these deformation rates on the final mechanical response of the nanomaterial being processed. Here we report an experimental study of the indentation response of three materials with different nature and mechanical properties, but with known time-dependent mechanical responses. These materials allow validation of the findings under a wide variety of conditions. One metal (Pb), and two polymers (PMMA and PS), were indented at the sub-20 nm scale using commercial atomic force microscopy (AFM) probes. Based on our experimental findings, we also propose an analytical model for creeping solids in which their nanoscale mechanical behavior is completely described by two components: an elastic component (characterized by the Hertz contact model) and a time-dependent component (characterized by a power-law model). The proposed experimental protocol is easy to implement, and the analytical model can be extended to a large variety of materials. The ability to characterize the time-dependence of the mechanical response of different materials at the nanoscale will enable a better estimation of the effect of manufacturing processes on the properties and performance of nanomaterials.

Elasto-viscoplastic modeling of subsidence above gas fields in the Adriatic Sea

Abstract. From the analysis of GPS monitoring data collected above gas fields in the Adriatic Sea, in a few cases subsidence responses have been observed not to directly correlate with the production trend. Such behavior, already described in the literature, may be due to several physical phenomena, ranging from simple delayed aquifer depletion to a much more complex time-dependent mechanical response of subsurface geomaterials to fluid withdrawal. In order to accurately reproduce it and therefore to be able to provide reliable forecasts, in the last years Eni has enriched its 3D finite element geomechanical modeling workflow by adopting an advanced constitutive model (Vermeer and Neher, 1999), which also considers the viscous component of the deformation. While the numerical implementation of such methodology has already been validated at laboratory scale and tested on synthetic hydrocarbon fields, the work herein presents its first application to a real gas field in the Adriatic Sea where the phenomenon has been observed. The results show that the model is capable to reproduce very accurately both GPS data and other available measurements. It is worth remarking that initial runs, characterized by the use of model parameter values directly obtained from the interpretation of mechanical laboratory tests, already provided very good results and only minor tuning operations have been required to perfect the model outcomes. Ongoing R&D projects are focused on a regional scale characterization of the Adriatic Sea basin in the framework of the Vermeer and Neher model approach.

A thermodynamically-consistent phenomenological viscoplastic model for hydrogels

Today, hydrogels have a plethora of biomedical and biotechnological applications such as controlled drug delivery, tissue engineering and wound dressing. These materials possess high stretchability and are able to undergo large deformation. Hydrogels deform nonlinearly under the influence of external loads because of their nonlinear elasticity, plasticity and viscosity, which are manifestations of the interactions between the solvent and the cross-linked polymeric chains at different length and time scales. This paper attempts to model the mechanical behavior of hydrogels through a thermodynamically-consistent phenomenologically-motivated viscoplastic approach. Uniaxial compressive tests are conducted on cross-linked polyvinyl alcohol hydrogels with varying amounts of a chemical cross-linker (Gluteraldehyde) to check the validity of the model developed. Creep tests are carried out to understand the time-dependent mechanical response of the hydrogels. The results obtained from the theoretical model are found to be in close agreement with experimental observations.

Crystallinity dependency of the time-dependent mechanical response of polyethylene: application in total disc replacement.

Degeneration of the intervertebral disc (IVD) is a leading source of chronic low back pain or neck pain, and represents the main cause of long-term disability worldwide. In the aim to relieve pain, total disc replacement (TDR) is a valuable surgical treatment option, but the expected benefit strongly depends on the prosthesis itself. The present contribution is focused on the synthetic mimic of the native IVD in the aim to optimally restore its functional anatomy and biomechanics, and especially its time-dependency. Semi-crystalline polyethylene (PE) materials covering a wide spectrum of the crystallinity are used to propose new designs of TDR. The influence of the crystallinity on various features of the time-dependent mechanical response of the PE materials is reported over a large strain range by means of dynamic mechanical thermo-analysis and video-controlled tensile mechanical tests. The connection of the stiffness and the yield strength with the microstructure is reported in the aim to propose a model predicting the crystallinity dependency of the response variation with the frequency. New designs of TDR are proposed and implemented into an accurate computational model of a cervical spine segment in order to simulate the biomechanical response under physiological conditions. Predicted in-silico motions are found in excellent agreement with experimental data extracted from published in-vitro studies under compression and different neck movements, namely, rotation, flexion/extension and lateral bending. The simulation results are also criticized by analyzing the local stresses and the predicted biomechanical responses provided by the different prosthetic solutions in terms of time-dependency manifested by the hysteretic behavior under a cyclic movement and the frequency effect.

Time-dependent mechanical response of paper during web-fed high-speed inkjet printing

Abstract The influence of wetting and drying during high-speed inkjet (HSI) printing on the time-dependent mechanical behavior of commercial HSI papers was investigated using a custom-built C-Impact tensile tester. In HSI printing the water based ink solvent penetrates into the paper while the colorants adhere onto the surface. We found that water strongly affected paper stiffness and strength already 0.1 s after wetting. Creep compliance and paper strain at a typical HSI printing input tension of 180 N/m are varying strongly during the different process steps of HSI printing. In order to achieve a good color registration and print quality, we thus recommend that the web tension should be dynamically controlled in each process step to prevent straining after wetting or shrinkage during drying.

Static and time-dependent mechanical response of organic matrix of bone

Bone derives its mechanical strength from the complex arrangement of collagen fibrils (type-I primarily) reinforced with hydroxy-apatite (HAp) mineral crystals in extra- and intra-fibrillar compartments. This study demonstrates a novel approach to obtain organic matrix of bone through its demineralization as well as mechanically characterize it at small length scales using static and dynamic indentation techniques. Sample surface preparation protocol used in the present work maintained the surface integrity of demineralized bone samples which resulted sample surface of roughness (RMS) magnitude of approximately 14 nm (averaged over 1 × 1 μm2 area duly verified by atomic force microscope (AFM)). Elemental composition analysis via energy dispersive X-ray spectroscopy (EDX) (for probed depth upto 2 μm) confirmed the complete removal of HAp mineral from bone samples during their demineralization using EDTA leaving collagen molecule assemblies unaffected as represented by Second Harmonic Generation (SHG) imaging. The modulus magnitudes of organic matrix obtained using from quasistatic as well as dynamic indentations (at constant frequency of 30 Hz) as ∼2.6 GPa and 4.5 GPa respectively, demonstrated the influence of loading rate on the estimated mechanical properties. For indentation depth to surface roughness ratio greater than ∼5:1, interestingly, measured material properties of organic matrix were found to depend on increasing magnitude of indentation depth of up to ∼500 nm value which probed from few collagen fibrils to next level of hierarchy i.e. collagen fibers. These findings are very useful to accurately determine the elastic and visco-elastic response of organic matrices of mineralized tissues for various applications including tissue engineering, bio-mimetics, etc.

Post-fire failure mechanisms of seawater-accelerated weathering composites for coastal and marine structures

This paper is the first to examine the mechanical characteristics and the failure mechanisms of seawater-accelerated weathering GFRP composites followed by low intensity fire/heat damage. This work was done to understand how environmental conditions in a marine environment affected mechanical properties before and after low intensity fire damage. E-glass/vinylester composite specimens of angle-ply [±45°/mat]2s and cross-ply [0/90°]3s used in marine and offshore applications were exposed and tested. The effect of fire-induced damage under low heat fluxes (10, 20, and 30 kW/m2) on strength and modulus before and after 120 days of seawater exposure (freeze-thaw cycling in saline solution) is experimentally investigated. A total of 162 samples were tested for shear, tension, and compression. The fabric architectures and seawater exposure influence the post-fire residual properties. A time-dependent mechanical response (pre/post fire exposure) is also presented.

Concrete creep and shrinkage effect in adhesive anchors subjected to sustained loads

The safe design of fastening systems requires an accurate understanding of all time-dependent phenomena that may lead to damage or even failure during its service life of typically 50 years. Generally, safety and serviceability requirements are ensured through rigorous experimental testing during the approval phase. In the case of time-dependent phenomena, or more specifically the behavior under sustained load, the common practice of directly testing all critical service conditions fails. The long-term response can only be approximated e.g. by short-term structural system tests that are extrapolated to the full life-time utilising empirical models as required by current guidelines. These are based on the assumption of uniformly distributed bond stress along the anchor, attribute all creep deformations to the adhesive mortar, neglect the concrete creep contribution, and assume a stationary creep process represented by a power-law. Generally, it can be assumed that reliable predictions of the time-dependent behavior of complex systems can only be obtained by models that are derived from a systematic investigation of all involved factors and their interaction. In this study, specifically the effect of concrete creep and shrinkage on the long-term behavior of adhesive anchor systems, based on extensive experimental data and numerical analyses, is investigated. A state-of-the-art computational framework is applied which can explicitly model the underlying physical and chemical mechanisms at early age and beyond. The well-established Lattice Discrete Particle Model (LDPM) describes the time-dependent mechanical response of the structure considering the local maturity of concrete, temperature, and moisture content. After calibration and validation of the numerical framework, structural deformations owing to concrete creep, bond stress redistributions over time, and the gradual development of damage at higher load levels are discussed.

Superplastic Creep of Metal Nanowires from Rate-Dependent Plasticity Transition.

Understanding the time-dependent mechanical behavior of nanomaterials such as nanowires is essential to predict their reliability in nanomechanical devices. This understanding is typically obtained using creep tests, which are the most fundamental loading mechanism by which the time-dependent deformation of materials is characterized. However, due to existing challenges facing both experimentalists and theorists, the time-dependent mechanical response of nanowires is not well-understood. Here, we use atomistic simulations that can access experimental time scales to examine the creep of single-crystal face-centered cubic metal (Cu, Ag, Pt) nanowires. We report that both Cu and Ag nanowires show significantly increased ductility and superplasticity under low creep stresses, where the superplasticity is driven by a rate-dependent transition in defect nucleation from twinning to trailing partial dislocations at the micro- or millisecond time scale. The transition in the deformation mechanism also governs a corresponding transition in the stress-dependent creep time at the microsecond (Ag) and millisecond (Cu) time scales. Overall, this work demonstrates the necessity of accessing time scales that far exceed those seen in conventional atomistic modeling for accurate insights into the time-dependent mechanical behavior and properties of nanomaterials.