Time-dependent Material Properties Research Articles

First- and Second-Order Forces in the Asymmetric Dynamical Casimir Effect for a Single δ − δ′ Mirror

Here, we consider an asymmetric δ−δ′ mirror undergoing time-dependent interactions with a massless scalar field in 1 + 1 dimensions. Using fluctuation-dissipation theory for a mirror in vacuum, we compute the force on a moving δ−δ′ mirror with time-dependent material properties. We investigate the first-order forces arising from the two distinct fluctuation sources and calculate the linear susceptibility in each case. We then plot the resulting forces. At the second order, we also find the independent contributions to the total force as well as the force that arises from the interference phenomena between the two fluctuation sources.

Time-dependant effects on curved precast segmentally constructed balanced cantilever bridges

Excessive long-term deflections and diagonal cracking in the webs are two commonly reported issues in segmentally constructed balanced cantilever bridges. The design of superstructure in such bridges is rather complicated due to the staged construction, secondary restraint forces, and time-dependent effects such as shrinkage, creep, and steel relaxation. The influence of these factors significantly increases by the curvature of the bridge on plan, to the point where it can result in the failure of the bridge if special considerations are not made. In this study, stepwise numerical analyses of a curved pre-cast construction of a balanced cantilever bridge with time-dependent material properties are carried out. The results show the effects of time-dependent losses, especially creep, on deflections during cantilevering and in long-term. It is shown that the curvature of the bridge due to long-term effects can increase the transverse moments in segments that adversely affect the principal tensile stresses, which can lead to diagonal cracking in the web of the segments.

Rheology and yield stress evolution of highly flowable cementitious grouting materials: Mechanisms and modeling

To study the rheological properties of grouting materials, the effects of sand-binder ratio, water-binder ratio, and rest time on the rheological model and parameters were studied through rheological tests. Through the cryo-scanning electron microscopy test to observe the structural build-up process of microstructures with rest time, the particle size test to measure the size distribution variation of flocculated structures over rest time, and the low-field nuclear magnetic resonance test to measure the change of water content in the slurry, the evolution mechanism of yield stress was studied. The results showed that the rheological model was consistent with Herschel–Bulkley model (H–B model). The yield stress increased with time. The growth of network flocculated structures and the decrease in the lubrication effect of water caused an increase in the aggregate particles–cement paste interaction stress. Therefore, the yield stress of the grouting materials increased over time. Considering the combined influences of the flocculation effect, hydration reaction, and the aggregate particles–cement paste interaction, a new evolution model was proposed to better describe the evolution law of yield stress with time. The results could provide a basis for the study on flow diffusion of grouting materials and an in-depth understanding of the time-dependent rheological properties of cement-based materials containing aggregate particles.

Sequence-specific insights into the time-dependent material properties of biomolecular condensates

Sequence-specific insights into the time-dependent material properties of biomolecular condensates

Material properties of nonpregnant and pregnant human uterine layers

The uterus has critical biomechanical functions in pregnancy and undergoes dramatic material growth and remodeling from implantation to parturition. The intrinsic material properties of the human uterus and how they evolve in pregnancy are poorly understood. To address this knowledge gap and assess the heterogeneity of these tissues, the time-dependent material properties of all human uterine layers were measured with nanoindentation. The endometrium-decidua layer was found to be the least stiff, most viscous, and least permeable layer of the human uterus in nonpregnant and third-trimester pregnant tissues. In pregnancy, the endometrium-decidua becomes stiffer and less viscous with no material property changes observed in the myometrium or perimetrium. Additionally, uterine material properties did not significantly differ between third-trimester pregnant tissues with and without placenta accreta. The foundational data generated by this study will facilitate the development of physiologically accurate models of the human uterus to investigate gynecologic and obstetric disorders.

Acoustic scattering from spatiotemporally modulated domains

Acoustic and elastic metamaterials with space- and time-dependent material properties have received significant attention recently as a means to realize systems that induce nonreciprocal wave propagation in the bulk or enable frequency and mode conversion of fields scattered from metasurfaces. A previous study derived a nonreciprocal Green’s function for flexural waves in a one- and two-dimensional finite plate with a spatiotemporal modulation of the Young’s modulus [Goldsberry et al., J. Acoust. Soc. Am. 150(4), 2021]. In this work, we generalize the nonreciprocal Green’s function approach to the acoustic case of scattering from an inhomogeneity whose properties are general functions of space and time. Canonical geometries where the analytical solution is known for the unmodulated case will be investigated. Computations of the scattered field directivity pattern will then be carried out as a function of the modulation parameters to determine cases that yield a large degree of control over the scattered field directivity pattern for each generated frequency harmonic. [Work supported by ONR.]

Thixomolding of Magnesium - Efficient Process Industrialization by Combining a Digital Twin and Systematic Casting Trials

Besides the realization of the technical specification of a casting, aspects such as resource minimization, cost awareness and robustness of the defined quality requirements are taking major priority, especially in the current global economic situation. Lightweight design, in that respect, is a central topic far beyond the automotive industry and characterizes in particular the ongoing research and development of innovative magnesium cast components. As a resource-efficient alternative to traditional die casting, magnesium-thixomolding offers the benefit of low energy consumption and eschews the necessity of protective gases. The identification of significant influencing factors between process settings, shear and time dependent material properties of semi-solid magnesium, the machine capabilities and the resulting casting quality are the basis for effective product and process design of magnesium thixomolding. Obtaining this knowledge is only possible through methodical process analysis and systematic design of experiments. YIZUMI Germany, together with MAGMA, demonstrates the methodical evaluation of a reliable process window for an AZ91D magnesium “box” component, using a demo mold on a UN1250MGII thixomolding machine. The work shows how a systematic combination of virtual and real casting experiments is used to identify a concrete process layout and generate important knowledge on process variations, robustness as well as control limits. In particular, the comparison of virtual and real casting experiments using statistical methods generates a comprehensive understanding of the impact and limits of different process variables, such as fraction solid, mold temperature and injection speeds. Furthermore it is possible to predict the influence of the gating and component design on the process. The methodological use of qualified casting simulation enables the development of an optimized component design and the determination of a suitable process window with minimized economic or productive risks long before the first component is manufactured – a step towards more resource efficiency and sustainability!

A chemo-viscoelastic model and a numerical scheme to study stress-diffusion interactions in Lithium ion battery electrode particles

A mathematical model and an associated numerical framework is developed for an isotropic viscoelastic electrode particle. The ensuing differential equations are solved using FEM with the help of an open source C++ library (deal.ii). The developed model is then used to understand the effects of time dependent material property (stress relaxation function) on the stress distribution of a viscoelastic electrode particle under potentiostatic boundary conditions. In contrast to a purely elastic particle, it is observed that the radial stresses become compressive and tangential stresses tensile towards the outer end of the particle. On varying the values of the characteristic time constant (τ), it is observed that stress relaxes faster for lower values of τ when compared to larger ones. Furthermore, the interactions between stress evolution, stress relaxation function, and diffusion is studied by varying τ and the electrode particle size. The study reveals that viscoelastic effects are apparent for a range of τ depending on the particle size. Thus, the interactions between the rate of diffusion, which varies with particle sizes, and τ affect the stress relaxation function, resulting in a complex mechanical response.

One-Step Hybrid Bending/Diffusion Bonding Process and Analysis of the Bonding Characteristics of Titanium Alloy Sheets.

A one-step hybrid bending/diffusion bonding process (HB/DBP) was developed for application to Ti-6Al-4V sheets to effectively improve buy-to-fly (BTF) ratio of aircraft parts, integrating sequential diffusion bonding followed by a bending process. The resulting bonding characteristics of these titanium alloy sheets were analyzed. Microstructural analysis and mechanical lap shear tests were performed to estimate the bonding quality. Additionally, bonding ratio, thickness strain, and shear strength were evaluated in relation to pressure under increasing temperature. When the applied pressure was lower than 0.5 MPa, early failure occurred at the joint of the specimens. However, when high pressure was applied, early failure occurred near the joint. To discuss the phenomenon, time-dependent viscoplastic material properties were characterized, and a numerical simulation analysis was performed. Viscoplastic deformation was observed around the bending area, which caused weakness around the bond under high-pressure conditions. A prototype of a Y-shaped heat shield was manufactured and the buy-to-fly ratio was effectively improved using the newly developed process. This study demonstrates the potential of applying the developed process for producing aircraft parts and the importance of viscoplastic behavior for the analysis of final product reliability.

Time-Dependent Material Properties of Aging Biomolecular Condensates from Different Viscoelasticity Measurements in Molecular Dynamics Simulations.

Biomolecular condensates are important contributors to the internal organization of the cell material. While initially described as liquid-like droplets, the term biomolecular condensates is now used to describe a diversity of condensed phase assemblies with material properties extending from low to high viscous liquids, gels, and even glasses. Because the material properties of condensates are determined by the intrinsic behavior of their molecules, characterizing such properties is integral to rationalizing the molecular mechanisms that dictate their functions and roles in health and disease. Here, we apply and compare three distinct computational methods to measure the viscoelasticity of biomolecular condensates in molecular simulations. These methods are the Green-Kubo (GK) relation, the oscillatory shear (OS) technique, and the bead tracking (BT) method. We find that, although all of these methods provide consistent results for the viscosity of the condensates, the GK and OS techniques outperform the BT method in terms of computational efficiency and statistical uncertainty. We thus apply the GK and OS techniques for a set of 12 different protein/RNA systems using a sequence-dependent coarse-grained model. Our results reveal a strong correlation between condensate viscosity and density, as well as with protein/RNA length and the number of stickers vs spacers in the amino acid protein sequence. Moreover, we couple the GK and the OS technique to nonequilibrium molecular dynamics simulations that mimic the progressive liquid-to-gel transition of protein condensates due to the accumulation of interprotein β-sheets. We compare the behavior of three different protein condensates, i.e., those formed by either hnRNPA1, FUS, or TDP-43 proteins, whose liquid-to-gel transitions are associated with the onset of amyotrophic lateral sclerosis and frontotemporal dementia. We find that both the GK and OS techniques successfully predict the transition from functional liquid-like behavior to kinetically arrested states once the network of interprotein β-sheets has percolated through the condensates. Overall, our work provides a comparison of different modeling rheological techniques to assess the viscosity of biomolecular condensates, a critical magnitude that provides information on the behavior of biomolecules inside condensates.

A finite porous-viscoelastic model capturing mechanical behavior of human cervix under multi-step spherical indentation

The cervix is a soft tissue exhibiting time-dependent behavior under mechanical loads. The cervix is a vital mechanical barrier to protect the growing fetus. The remodeling of the cervical tissue, characterized by an increase in time-dependent material properties, is necessary for a safe parturition. The failure of its mechanical function and accelerated tissue remodeling is hypothesized to lead to preterm birth, which is birth before 37 weeks of gestation. To understand the mechanism of the time-dependent behavior of the cervix under compressive states, we employ a porous-viscoelastic material model to describe a set of spherical indentation tests performed on nonpregnant and term pregnant tissue. A genetic algorithm-based inverse finite element analysis is used to fit the force-relaxation data by optimizing the material parameters, and the statistical analysis of the optimized material parameters is conducted on different sample groups. The force response is captured well using the porous-viscoelastic model. The indentation force-relaxation of the cervix is explained by the porous effects and the intrinsic viscoelastic properties of the extracellular matrix (ECM) microstructure. The hydraulic permeability obtained from the inverse finite element analysis agrees with the trend of the value directly measured previously by our group. The nonpregnant samples are found significantly more permeable than the pregnant samples. Within nonpregnant samples, the posterior internal os is found significantly less permeable than the anterior and posterior external os. The proposed model exhibits the superior capability to capture the force-relaxation response of the cervix under indentation, as compared to the conventional quasi-linear viscoelastic framework (range of r2 of the porous-viscoelastic model 0.88–0.98 vs. quasi-linear model: 0.67–0.89). As a constitutive model with a relatively simple form, the porous-viscoelastic framework has the potential to be used to understand disease mechanisms of premature cervical remodeling, model contact of the cervix with biomedical devices, and interpret force readings from novel in-vivo measurement tools such as an aspiration device.

Domain-specific modulatory effects of phosphomimetic substitutions on liquid-liquid phase separation of tau protein

Aggregation of tau is one of the major pathogenic events in Alzheimer's disease and several other neurodegenerative disorders. Recent reports demonstrated that tau can condense into liquid droplets that undergo time-dependent transition to a solid-like state, suggesting that liquid condensates may be on the pathway to pathological aggregation of tau. While hyperphosphorylation is a key feature of tau isolated from brains of patients with Alzheimer's disease and other tauopathies, the mechanistic role of phosphorylation in tau liquid-liquid phase separation (LLPS) remains largely unexplored. In an attempt to bridge this gap, here we performed systematic studies by introducing phosphomimetic substitutions of Ser/Thr residues with negatively charged Asp/Glu residues in different regions of the protein. Our data indicate that the phosphorylation patterns that increase the polarization of charge distribution in full-length tau (tau441) promote protein LLPS, whereas those that decrease charge polarization have an opposite effect. Overall, this study further supports the notion that tau LLPS is driven by attractive intermolecular electrostatic interactions between the oppositely charged domains. We also show that the phosphomimetic tau variants with low intrinsic propensity for LLPS can be efficiently recruited to droplets formed by the variants with high LLPS propensity. Furthermore, the present data demonstrate that phosphomimetic substitutions have a major effect on time-dependent material properties of tau droplets, generally slowing down their aging. The latter effect is most dramatic for the tau variant with substitutions within the repeat domain, which correlates with the decreased fibrillation rate of this variant.

Time-dependent frictional properties of granular materials used in analogue modelling: implications for mimicking fault healing during reactivation and inversion

Abstract. Analogue models are often used to model long-term geological processes such as mountain building or basin inversion. Most of these models use granular materials such as sand or glass beads to simulate the brittle behaviour of the crust. In granular material, deformation is localised in shear bands, which act as an analogue to natural fault zones and detachments. Shear bands, also known as faults, are permanent anomalies in the granular package and are often reactivated during a test run. This is due to their lower strength compared to the undeformed material. When the fault movement stops, time-dependent healing immediately begins to increase the strength of the fault. Faults that have been inactive for a long time therefore have a higher strength than younger faults. This time-dependent healing, also called time consolidation, can therefore affect the structure of an analogue model as the strength of the fault changes over time. Time consolidation is a well-known mechanism in granular mechanics, but it is poorly described for analogue materials and on the timescales of typical analogue models. In this study, we estimate the healing rate of different analogue materials and evaluate the impact on the reactivation potential of analogue faults. We find that healing rates are generally less than 3 % per 10-fold increase in holding time, which is comparable to natural fault zones. We qualitatively compare the frictional properties of the materials with grain characteristics and find a weak correlation of healing rates with sphericity and friction with an average quality score. Accordingly, in models where there are predefined faults or reactivation is forced by blocks, the stability range of the fault angles that can be reactivated can decrease by up to 7∘ over the duration of 12 h. The stress required to reactivate an existing fault can double in the same time, which can favour the development of new faults. In a basin inversion scenario, normal faults cannot be inverted because of the strong misorientation, so time consolidation plays little additional role for such models.

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.

Non-reciprocal wave propagation in time-modulated elastic lattices with inerters

Non-reciprocal wave propagation in acoustic and elastic media has received much attention of researchers in recent years. This phenomenon can be achieved by breaking the reciprocity through space- and/or time-dependent constitutive material properties, which is an important step in overcoming the limitations of conventional acoustic- and phononic-like mechanical lattices. A special class of mechanical metamaterials with non-reciprocal wave transmission are latices with time-modulated mass and stiffness properties. Here, we investigate the non-reciprocity in elastic locally resonant and phononic-like one-dimensional lattices with inerter elements where mass and stiffness properties are simultaneously modulated through inerters and springs as harmonic functions of time. By considering the Bloch theorem and Fourier expansions, the frequency-band structures are determined for each configuration while asymmetric band gaps are found by using the weighting and threshold method. The reduction in frequency due to introduced inerters was observed in both phononic and locally resonant metamaterials. Dynamic analysis of finite-length lattices by the finite difference method revealed a uni-directional wave propagation. Special attention is given to phononic-like lattice based on a discrete-continuous system of multiple coupled beams. Moreover, the existence of edge modes in the discrete phononic lattice is confirmed through the bulk-edge correspondence and their time evolution quantified by the topologically invariant Chern number. The proposed methodology used to investigate non-reciprocal wave transmission in one-dimensional inerter-based lattices can be extended to study more complex two-dimensional lattices.

Comparison of in vivo visco-hyperelastic properties of uterine suspensory tissue in women with and without pelvic organ prolapse

The uterine suspensory tissue (UST) complex includes the cardinal (CL) and uterosacral “ligaments” (USL), which are mesentery-like structures that play a role in resisting pelvic organ prolapse (POP). Since there is no information on the time-dependent material properties of the whole structure in situ and in vivo, we developed and tested an intraoperative technique to quantify in vivo whether there is a significant difference in visco-hyperelastic behavior of the CL and USL between women with and without POP. Thirteen women with POP (cases) and four controls scheduled for surgery were selected from an ongoing POP study. Immediately prior to surgery, a computer-controlled linear servo-actuator with a series force transducer applied a continuous, caudally directed traction force while simultaneously recording the resulting cervical displacement in the same direction. After applying an initial 1.1 N preload, a ramp rate of 4 mm/s was used to apply a maximum force of 17.8 N in three “ramp-and-hold” test trials. A simplified bilateral four-cable biomechanical model was used to identify the material behavior of each ligament. For this, the initial cross-section areas of the CL and USL were measured on 3-T magnetic resonance image-based 3D models from each subject. The time-dependent strain energy function of CL/USL was defined with a three-parameter hyperelastic Mooney–Rivlin material model and a two-term Prony series in relaxation form. When cases were compared with controls, the estimated time-dependent material constants of CL and USL did not differ significantly. These are the first measurements that compare the in vivo and in situ visco-hyperelastic response of the tissues comprising the CL and USL to loading in women with and without prolapse. Larger sample sizes would help improve the precision of intergroup differences.

Predicting effect of fibers on thermal gelation of methylcellulose using Bayesian optimization

Understanding of the viscoelastic behavior of a polymer is a prerequisite for its thermomechanical processing beyond laboratory scale. Utilizing rheological characterization is a powerful tool to comprehend the complex nature and time-dependent properties of macromolecular materials. Nevertheless, it consumes time as rheometry involves iterating experiments under several conditions to visualize the non-linear behavior of materials under varying conditions. The work hereunder examines the rheology of cellulosic aqueous suspensions prepared using cellulose fibers as the dispersed phase (Refcell and Storacell) and methylcellulose (MC) as the polymeric matrix. Interfacial phenomena between MC and cellulose fibers arise in particle laden systems with supramolecular structures formed by non-covalent interactions. Therefore, this study elucidates the rheological evolution of these interactions as a function of temperature and fiber concentration. This study displays how researchers may reduce the number of rheological experiments and save time utilizing a novel method based on a Bayesian optimization with Gaussian processes.

Novel Modeling of Heat and Moisture Diffusion in Adhesive Joints

Abstract A novel two-dimensional shear stress-heat and moisture diffusion model is proposed for adhesive single-lap joints. Spatial and time-dependent material properties are derived from coupled partial differential equations governing moisture diffusion and heat transfer through the exposed adhesive edges. Constituting differential equations are numerically solved for the shear stress distribution in the bonded area. Several diffusion scenarios and boundary conditions are analyzed. Significant improvements are achieved in the prediction of the shear stress distribution in the adhesive layer when compared to the one-dimensional models in the literature. Scenarios of moisture diffusion generate stress gradients through the bondline, while the relatively fast internal thermal conductivity reduces temperature differentials within the joint. Moisture diffusion in the adhesive layer is significantly accelerated at high temperatures. The results of the proposed model show reasonable agreement with a three-dimensional finite element analysis.

Characterization of transient rheological behavior of soft materials using ferrofluid droplets

Physical material properties, such as elasticity, viscosity, or viscoelasticity, can be characterized by using rheometers or stick-type solenoid electromagnets. In this work, we developed a magnet measurement setup based on a Helmholtz arrangement of electromagnets. While applying homogeneous magnet fields to ferrofluid droplets inside a soft material of interest, the deformations of the ellipsoidal deformed droplets were measured. Kelvin-Voigt models and corresponding analytical descriptions were used to calculate the values of viscosity and Young’s modulus of materials under test. For calibration purposes of the developed setup, glycerin/water mixtures and methylcellulose/water solutions were characterized as viscous and polyacrylamide gels as elastic materials, respectively. In addition, the interfacial tensions were calculated with respect to the magnetic Bond number from the droplet deformations. For the first time, the transient rheological behavior of viscoelastic material was measured using the method of ferrofluid droplet deformation. When polyacrylamide gel with a shear modulus of 230 Pa was evacuated for less than 40 min during preparation, it showed a strong time-depending viscoelastic behavior several minutes after starting the measurements. Here, Young’s modulus increased up to the value of elastic behavior, whereas the values for viscosity decreased to a baseline. The developed setup can favorably be used in future applications to investigate local and also time-dependent rheological properties of soft materials.

Nonreciprocal acoustic scattering from an elastic plate with spatiotemporally modulated material properties

Acoustic and elastic metamaterials with space- and time-dependent material properties have received great attention recently as a means to realize nonreciprocal wave propagation. The nonreciprocal behavior of propagating waves in a spatiotemporally modulated infinite medium is usually characterized by directional bandgaps present in the frequency-wavenumber spectrum. However, less attention has been given to acoustic scattering from spatiotemporally modulated media. In this work, we consider nonreciprocal reflection and transmission from a spatiotemporally modulated, infinite elastic plate excited by a plane wave at oblique incidence. A semi-analytical approach is developed that considers the coupling between the acoustic waves and the displacement of the plate. The reflection and transmission response of the plate for each generated frequency harmonic as a function of the incident angle are reported. Finally, we find conditions on the modulation parameters that yield a large degree of nonreciprocity. The present analysis leads to potential applications in acoustic communications, such as directional wave sensing.