Instantaneous Elastic Response Research Articles

Rheology of growing axons

The growth of axons is a key process in neural system development, which relies upon a subtle balance between external mechanical forces and remodeling of cellular constituents. A key problem in the biophysics of axons is therefore to understand the overall response of the axon under stretch, which is often modeled phenomenologically using morphoelastic or viscoelastic models. Here, we develop a microscopic mixture model of growth and remodeling based on protein turnover and damage to obtain the macroscopic rheology of axonal shafts. First, we provide an estimate for the instantaneous elastic response of axons. Second, we predict that under moderate traction velocities, the axonal core behaves like a viscoelastic Maxwell material whose rheological parameters can be expressed in terms of the microscopic properties. Third, for larger velocities, we show that failure takes place due to extensive damage.

On the explicit dynamics implementation and validation of partitioned rate-type constitutive relation for dampers

We propose a simple 3D nonlinear rate-type constitutive relation with just three parameters for elastomeric dampers capable of emulating double-shear data in frequency and strain sweep mode. The nonlinear relation derived using two scalar functions, namely Helmholtz free energy and the rate of dissipation function [1], result in a partitioned constitutive relation: Cauchy stress tensor is described in terms of the left Cauchy-Green stretch tensor and a tensor describing instantaneous elastic response, and the evolution equation for the instantaneous elastic response is derived by maximizing the rate of dissipation function. A compressible version of this model is implemented in Abaqus® The constitutive relation and the implementation are validated by comparing with known semi-inverse solutions obtained by specializing rate-type relation to special deformations. Material parameters are obtained for dampers made of synthetic and natural rubber by fitting the predictions of the model with that of double shear data. By using the same parameters, three dimensional simulations of a cylindrical damper subjected to sinusoidal force akin to that of an unbalanced machinery predict different hysteresis curves in compression/tension and shear. To that end, we show that the non-linear 3 parameter model is one of the simple models that can be formulated within the thermodynamic framework which can predict the inherent non-linearity of the damper operating under combined harmonic loading situations. A robust implementation (VUMAT) of the developed model is included with the article. We believe that this can aid engineers in tailoring dampers for its controlled dissipation across multiple modes of deformation as well as academicians in adding more value by building and implementing sophisticated models within this framework.

Dynamic shearing resistance of hydroxyl-terminated polybutadiene (HTPB)

Hydroxyl-terminated polybutadiene (HTPB) is a widely used polymeric binder in polymer-bonded explosives (PBXs) and solid rocket propellants. Even though used in small fractions, the elastomeric binder absorbs much of the impact energy and therefore requires careful modeling of its mechanical behavior to accurately simulate the response of PBXs when they are subjected to large strains and strain rates. While the normal response of HTPB has been characterized under uniaxial stress and uniaxial strain loading, shear strength measurements under large pressures and large shear strain rates have not been made so far. Such measurements are critical for modeling localization and failure in PBXs and accurate prediction hotspot formation. In this study, pressure-shear plate impact (PSPI) experiments have been used to measure the shearing resistance of HTPB at different pressures. The shearing resistance of HTPB is found to be strongly pressure dependent. A quasi-linear viscoelastic model with pressure-dependent shear wave speeds and shearing resistance is used to describe the experimentally observed dynamic response of HTPB. The model consists of an instantaneous elastic response and viscoelastic relaxation of the elastic response.

Rheological model for rock-type materials under large deformations

In this paper the behaviour of rock-type materials is described with respect to the current configuration through rate-type constitutive equations, within the finite deformation framework, using the relative motion. The viscoplastic part of the constitutive equations concerns the long-time effects, i.e. the deformation by creep, while the instantaneous elastic response characterizes the short-time effect. The instantaneous elastic response expresses an appropriate objective time derivative of Cauchy stress tensor via the rate of strain, with the aid of fourth-order elastic stiffness tensor. Using mathematical arguments it follows that our new model extends, to finite strains, Cristescu’s rheological model Cristescu (1989)[2]. To solve boundary value problems for rock-type materials described by the proposed model, the appropriate variational equality for the velocity field, at a time t, is derived starting from the weak formulation of the incremental equilibrium problem. The rate form of the constitutive model is coupled with the variational equality, and serves to update the current state of the material.

Experimental investigation of the primary and secondary creep behaviour of shale gas reservoir rocks from deep sections of the Cooper Basin

This paper investigates the mechanical properties of shale gas reservoir rocks from deep sections of the Cooper Basin with a focus on the creep deformation at high stress and temperature conditions. Rock samples are collected from depths greater than 3000 m in Nappamerri Trough of the Cooper Basin and a series of deformation as well as creep tests were carried out using a triaxial apparatus under simulated reservoir pressure and temperature conditions. Creep tests were conducted at different axial stresses for different durations. The results of this study show that temperature and differential axial stress (a difference between axial stress and confining stress) have significant bearing on the shales' mechanical properties, including creep deformation behaviour. A number of models developed by different authors were used to analyse the experimental data (creep deformation). It has been found that none of these models can adequately describe the creep behaviour of shale gas reservoir rocks from deep sections of the Cooper Basin. In this study we have revised the power-law model and incorporated Arrhenius factor (equation) to account for temperature effect on creep behaviour of shale gas reservoir rocks. The revised power-law model is used to simulate wellbore deformation of the Roseneath, Barnett and Eagle-ford shales at the Cooper Basin temperature and pressure conditions. The results show that the Barnett exhibits little viscoelastic deformation over time while Eagle-ford exhibited twice and Roseneath 180% as much as its instantaneous elastic response over a 24 h period.

Viscoelastic properties of shock wave exposed brain tissue subjected to unconfined compression experiments

Traumatic brain injuries (TBI) affect millions of people each year. While research has been dedicated to determining the mechanical properties of the uninjured brain, there has been a lack of investigation on the mechanical properties of the brain after experiencing a primary blast-induced TBI. In this paper, whole porcine brains were exposed to a shock wave to simulate blast-induced TBI. First, ten (10) brains were subjected to unconfined compression experiments immediately following shock wave exposure. In addition, 22 brains exposed to a shock wave were placed in saline solution and refrigerated between 30 minutes and 6.0 hours before undergoing unconfined compression experiments. This study aimed to investigate the effect of a time delay on the viscoelastic properties in the event that an experiment cannot be completed immediately. Samples from both soaked and freshly extracted brains were subjected to compressive rates of 5, 50, and 500 mm/min during the unconfined compression experiments. The fractional Zener (FZ) viscoelastic model was applied to obtain the brain's material properties. The length of time in the solution statistically influenced three of the four FZ coefficients, E0 (instantaneous elastic response), τ0 (relaxation time), and α (fractional order). Further, the compressive rate statistically influenced τ0 and α.

A model on the viscoelastic behavior of sewn knitted fabrics

Purpose Knitted fabrics have been widely used in a wide range of applications such as apparel industry. Since these fabrics are continuously subjected to the long-term tensile stresses or tensile creep in real conditions, investigation of viscoelastic behavior of sewn knitted fabrics would be important especially at the seamed area. The paper aims to discuss this issue. Design/methodology/approach A lockstitch machine was used to produce sewn samples by knitted fabric. Factors such as stitch per inch (SPI), thread tension and thread type were variables of the model. Tensile creep tests under constant load of 200 N were conducted, and creep compliance parameter D(t) of samples was obtained as a response variable. A successive residual method (SRM) was also used to characterize viscoelastic properties of sewn-seamed fabrics. Findings The instantaneous elastic responses of the seamed samples were less than those of the neat fabric (fabric with no seam). An increase in sewing thread strength increases the instantaneous elastic response of the sample. SPI and thread tension have an optimum value to increase E0. High tenacity polyester thread, due to its higher elastic modulus, caused a larger E0 than polyester/cotton thread in sewn knitted fabric. Characteristics of seam including sewing thread type, SPI and sewing tension have significant influence on T0. Sewn-seamed fabric by high modulus thread shows less viscous strain T0 than the neat fabric (fabric with no seam). Viscous strain T0 decreases as SPI changes from 8 to 4 and/or 12. SPI and thread tension have an optimum value to increase the viscous strain T0. E1 is the same for optimum seamed fabric and fabric sample but T1 is about two times greater for seamed fabric. Retarded time for creep recovery increases by sewing process but characteristics of seam have significant influence on E1 and T1. All sewn knitted fabric samples used in this study could be described by Burger’s model, which is a Maxwell model paralleled with a Kelvin one. Originality/value This paper is going to use a different method named successive residuals to model the creep behavior of seamed knitted fabric. On the whole, this paper paved a way to obtain viscoelastic constants of sewn-seamed knitted fabrics based on different sewing parameters such as the modulus of elasticity of the sewing thread, SPI and sewing thread tension.

A Rheological Model of Sandstones considering Response to Thermal Treatment

Time‐dependent rheological response of geomaterials to thermal treatment is a crucial issue in geothermal energy utilization and deep mineral mining. This response, however, has not yet been fully considered in the existing rheological constitutive models for sandstones. In order to experimentally investigate such responses and establish the associated rheological constitutive model, this study considers the sandstone specimens which have been thermally treated under different temperatures. The triaxial rheological test in conjunction with the scanning electron microscope is employed in the investigation to observe the mechanically and macro‐/micromorphologically rheological response. Investigation results show that the thermal treatment induces microcracks and microdefects, and subsequently, they propagate during the creep. As a consequence, the heterogeneous deformation occurs, and macrocracks are present, leading to the irregular fluctuation and mutation in strain over time. A higher temperature contributes to a more severe structure damage and in turn reduces the intactness of sandstones and elevates the rheological response. The investigation allows successful establishment of a three‐dimensional constitutive equation considering the instantaneous elastic response to thermal treatment. Based on the equation, a nonlinear visco‐elastoplastic rheological constitutive model is developed for sandstones. Comparison with three existing rheological models shows that the model developed in this study could well represent the rheological process of the thermally treated sandstones.

The Instantaneous Elastic Response in Compression and Tension in Porcine Brain

The Instantaneous Elastic Response in Compression and Tension in Porcine Brain

The Instantaneous Elastic Response in Compression and Tension in Porcine Brain

The Instantaneous Elastic Response in Compression and Tension in Porcine Brain

Simple model for time-dependent bond transfer in pretensioned concrete using draw-in data

Time evolution of prestress loss and bond transfer length holds vital information concerning long-term performance of pretensioned prestressed concrete. In this paper, it is proposed to utilize long-term measurements of strand draw-in to extract this time-varying information, which could be more effectively obtained than concrete or strand surface strain measurements. Theoretical investigations combined with numerical studies of experimental data are carried out for this purpose. This study builds on Guyon’s boundary value problem (BVP) model which quantifies draw-in for instantaneous elastic response. A one-dimensional linear viscoelastic standard solid model is employed to model the creep of concrete, which is a simple but effective model of the time-dependent response of concrete. Guyon’s BVP model is generalized to include time dependence and then combined with an existing initial value problem (IVP) model for post-tensioned concrete leading to a new mixed model for time-dependent prestress loss and bond transfer in pretensioned concrete.Analysis is undertaken in this study to (i) quantify long-term prestress loss and bond-transfer behaviors by applying the proposed model and directly utilizing measured draw-in time history data, (ii) validate the proposed quantitative analysis by using scaled pretensioned concrete beams with different types of aggregates and strengths of concrete - among other factors, and (iii) offer discussion of future work. For example, introducing concrete drying shrinkage into the proposed simple model seems promising and is necessary to provide an improved representation of the time-dependent behavior of prestressed concrete.

A micromechanical model of rate and state friction: 2. Effect of shear and normal stress changes

AbstractIn this paper we analyze the influence of shear and normal stress changes on frictional properties. This problem is fundamental as, for instance, sudden stress changes are naturally induced on active faults by nearby earthquakes. As any stress changes can be seen as resulting from a succession of infinitesimal stress steps, the role of sudden stress changes is crucial to our understanding of fault dynamics. Laboratory experiments carried out by Linker and Dieterich (1992) and Nagata et al. (2012), considering steps in normal and shear stress, respectively, show an instantaneous response of the state variable (a proxy for the evolution of contact surface in our model) to a sudden stress change. We interpret this response as being due to an (instantaneous) elastic response of the plastic and elastic contacts. We assume that the anelastic response of the plastic contacts is frozen during sudden stress changes. The contacts, which were driven by plasticity before the stress change, are elastically accommodated during the sudden variation of the load. On the contrary, when the loading is slowly varying, elastic deformation of plastic contacts can be neglected. Our model is able to explain the evolution law for the state variable reported by Linker and Dieterich (1992).

Quasi-linear viscoelastic properties of the human medial patello-femoral ligament

The evaluation of viscoelastic properties of human medial patello-femoral ligament is fundamental to understand its physiological function and contribution as stabilizer for the selection of the methods of repair and reconstruction and for the development of scaffolds with adequate mechanical properties. In this work, 12 human specimens were tested to evaluate the time- and history-dependent non linear viscoelastic properties of human medial patello-femoral ligament using the quasi-linear viscoelastic (QLV) theory formulated by Fung et al. (1972) and modified by Abramowitch and Woo (2004). The five constant of the QLV theory, used to describe the instantaneous elastic response and the reduced relaxation function on stress relaxation experiments, were successfully evaluated. It was found that the constant A was 1.21±0.96MPa and the dimensionless constant B was 26.03±4.16. The magnitude of viscous response, the constant C, was 0.11±0.02 and the initial and late relaxation time constants τ1 and τ2 were 6.32±1.76s and 903.47±504.73s respectively. The total stress relaxation was 32.7±4.7%. To validate our results, the obtained constants were used to evaluate peak stresses from a cyclic stress relaxation test on three different specimens. The theoretically predicted values fit the experimental ones demonstrating that the QLV theory could be used to evaluate the viscoelastic properties of the human medial patello-femoral ligament.

English

In this study, we develop a Galerkin-type finite element (FE) solution to assess the creep deformation of fracture surfaces. These surfaces are treated as comparatively compliant rocks which are separated by a comparatively stiff proppant pack. Viscoelastic properties of fracture surfaces are assessed by the temperature and deformation dependent modulus. The key challenge is to appropriately develop the creep and the relaxation functions which are continuous spectrum material functions and are unique for each model. Time dependent mechanical properties are connected through an instantaneous elastic response and coupled by way of nonlinear and convolution integral relationships. Coupling is achieved by way of convolution integrals computed using the full-time history of the material functions. As a novel numerical procedure, we apply a more computationally efficient algorithm to use discrete-spectrum approximation to the creep and relaxation functions, thus, allowing for adjustment of the energy dissipativity of the model in a consistently low computation-time. The proposed approach is novel and is the only approach in the literature (to the best of authors’ knowledge) that considers the conductivity in an intended reservoir at the level of proppants. It will be demonstrated that the proposed model can be used for the assessment of fracture conductivity under short or long-term loading conditions when rock material properties can be determined. Key words: Finite element method, reservoir engineering, numerical model, fractured reservoir.

Poroelastic behaviour of the degenerating human intervertebral disc: a ten-day study in a loaded disc culture system.

The intervertebral disc (IVD) allows flexibility to the vertebral column, and transfers the predominant axial loads during daily activities. Its axial biomechanical behaviour is poroelastic, due to the water-binding and releasing capacity of the nucleus pulposus. Degeneration of the intervertebral disc presumably affects both the instantaneous elastic response to the load on the IVD and the subsequent interstitial flow of fluid. This study aims to quantify the poroelastic behaviour of the IVD and its change with degeneration, as defined by the magnetic resonance imaging-based Pfirrmann Score (PS). For a period of ten days, 36 human lumbar IVDs were loaded with a simulated physiological axial loading regime, while deformation was monitored. The IVDs responded to the loads with instantaneous elastic and slow poroelastic axial deformation. Several mechanical parameters changed throughout the first five days of the experiment, until the IVDs settled into a dynamic equilibrium. In this equilibrium, degeneration was significantly related to a decrease in disc height loss during the daytime high load phase (ρ=-0.49), and to a decrease in the rate of this deformation during the final half hour of each day (ρ=-0.53). These properties were related to the nucleus glycosaminoglycan/hydroxyproline (GAG/HYP) ratio, rather than GAG content alone, indicating that remodelling of the extracellular matrix reduces poroelastic properties of the IVD. This implies that the degenerated discs have a reduced capacity to bind water and/or a reduced resistance against fluid flow. The resulting loss in hydrostatic pressure may further change cell behaviour in the nucleus pulposus.

On a variant of the Maxwell and Oldroyd-B models within the context of a thermodynamic basis

In this paper we develop models within a thermodynamic standpoint that are very similar in form to the classical Maxwell and Oldroyd-B models but differ from them in one important aspect, the manner in which they unload instantaneously from the deformed configuration. As long as the response is not instantaneous, the models that are derived cannot be differentiated from the Maxwell and Oldroyd-B models, respectively. The models can be viewed within the context of materials whose natural configuration evolves, the evolution being determined by the maximization of the rate of entropy production of the material. However, the underpinnings to develop the model are quite different from an earlier development by Rajagopal and Srinivasa [8] in that while the total response of the viscoelastic fluid satisfies the constraint of an incompressible material, the energy storage mechanism associated with the elastic response is allowed to be that for a compressible elastic solid and the dissipative mechanism associated with the viscous response allowed to be that for a compressible fluid, the total deformation however being isochoric. The analysis calls for a careful evaluation of firmly held customs in viscoelasticity wherein it is assumed that it is possible to subject a material to a purely instantaneous elastic response without any dissipation whatsoever. Finally, while the model developed by Rajagopal and Srinivasa [8] arises from the linearization of the non-linear elastic response that they chose and leads to a model wherein the instantaneous elastic response is isochoric, here we develop the model within the context of a different non-linear elastic response that need not be linearized but the instantaneous elastic response not necessarily being isochoric.

Mechanical responses of the periodontal ligament based on an exponential hyperelastic model: a combined experimental and finite element method

The V–W exponential hyperelastic model is adopted to describe the instantaneous elastic response of the periodontal ligament (PDL). The general theoretical framework of constitutive modeling is described based on nonlinear continuum mechanics, and the elasticity tensor used to develop UMAT subroutine is formulated. Nanoindentation experiment is performed to characterize mechanical properties of an adult pig PDL specimen. Then the experiment is simulated by using the finite element (FE) analysis. Meanwhile, the optimized material parameters are identified by the inverse FE method. The good agreement between the simulated results and experimental data demonstrates that the V–W model is capable of describing the mechanical behavior of the PDL. Therefore, the model and its implementation into FE code are validated. By using the model, we simulate the tooth movement under orthodontic loading to predict the mechanical responses of the PDL. The results show that local concentrations of stress and strain in the PDL are found.

Effects of immediate vs. delayed massage-like loading on skeletal muscle viscoelastic properties following eccentric exercise

BackgroundThis study compared immediate versus delayed massage-like compressive loading on skeletal muscle viscoelastic properties following eccentric exercise. MethodsEighteen rabbits were surgically instrumented with peroneal nerve cuffs for stimulation of the tibialis anterior muscle. Rabbits were randomly assigned to a massage loading protocol applied immediately post exercise (n=6), commencing 48h post exercise (n=6), or exercised no-massage control (n=6). Viscoelastic properties were evaluated in vivo by performing a stress-relaxation test pre- and post-exercise and daily pre- and post-massage for four consecutive days of massage loading. A quasi-linear viscoelastic approach modeled the instantaneous elastic response (AG0), fast (g1p) and slow (g2p) relaxation coefficients, and the corresponding relaxation time constants τ1 and τ2. FindingsExercise increased AG0 in all groups (P<0.05). After adjusting for the three multiple comparisons, recovery of AG0 was not significant in the immediate (P=0.021) or delayed (P=0.048) group compared to the control group following four days of massage. However, within-day (pre- to post-massage) analysis revealed a decrease in AG0 in both massage groups. Following exercise, g1p increased and g2p and τ1 decreased for all groups (P<0.05). Exercise had no effect on τ2 (P>0.05). After four days of massage, there was no significant recovery of the relaxation parameters for either massage loading group compared to the control group. InterpretationOur findings suggest that massage loading following eccentric exercise has a greater effect on reducing muscle stiffness, estimated by AG0, within-day rather than affecting recovery over multiple days. Massage loading also has little effect on the relaxation response.

Power Law and Stretched Exponential Responses in Composite Solids

Clay, rocks, concrete and other composite solids show evidence of a hierarchical structure. A fractal tree of nested viscoelastic boxes is proposed to describe the elastic after-effects in these composite solids. A generalized fractal transmission line approach is developed to relate the strain and stress responses. Power law for strain, under an applied stress step, is derived. The exponent in the power law is obtained as a well-defined function of the branching numbers and scaling parameters of the viscoelastic hierarchy. Then, a composite solid with both instantaneous (linear) elastic strain response and power law type (linear) elastic after-effect for an applied stress step, is considered. The stretched exponential stress relaxation to an applied strain step is derived as an approximation. For the same composite solid, the stretch parameter of the stretched exponential and the exponent of the power law result to be equal to each other.

Effect of storage methods on indentation-based material properties of abdominal organs

To investigate the possible changes in material properties of cadaveric abdominal organs due to the preservation methods, the indentation data obtained from porcine abdominal organs (kidney, liver, and spleen) preserved by cooling and freezing are analyzed statistically in this study. Indentation tests were first conducted on fresh specimens. One half of the specimens of each organ were then frozen (preserved at - 12 degrees C), and the other half of the specimens were cooled (preserved at 4 degrees C). All preserved specimens were retested after 20 days. Force and displacement data recorded during indentation were analyzed using a quasi-linear viscoelastic model. The results show that both cooling and freezing storage increased the kidney stiffness. In contrast, both storage methods decreased the stiffness of the spleen specimens. While cooling increased the liver stiffness, no significant changes of the instantaneous elastic response were observed in the liver specimens preserved by freezing. The liver and spleen's reduced relaxation responses and the liver's instantaneous elastic response were significantly different when comparing between cooling and freezing effects after 20 days of preservation. This study showed that both cooling and freezing storage methods significantly changed the material properties of abdominal organs, especially the instantaneous elastic response. More research is needed in investigating the effect of preservation on failure properties and mechanical properties under large deformation.