Interrelation of creep and relaxation: a modeling approach for ligaments

Experimental data (Thornton et al., 1997) show that relaxation proceeds more rapidly (a greater slope on a log-log scale) than creep in ligament, a fact not explained by linear viscoelasticity. An interrelation between creep and relaxation is therefore developed for ligaments based on a single-integral nonlinear superposition model. This interrelation differs from the convolution relation obtained by Laplace transforms for linear materials. We demonstrate via continuum concepts of nonlinear viscoelasticity that such a difference in rate between creep and relaxation phenomenologically occurs when the nonlinearity is of a strain-stiffening type, i.e., the stress-strain curve is concave up as observed in ligament. We also show that it is inconsistent to assume a Fung-type constitutive law (Fung, 1972) for both creep and relaxation. Using the published data of Thornton et al. (1997), the nonlinear interrelation developed herein predicts creep behavior from relaxation data well (R > or = 0.998). Although data are limited and the causal mechanisms associated with viscoelastic tissue behavior are complex, continuum concepts demonstrated here appear capable of interrelating creep and relaxation with fidelity.     

离体心舰顺应性综合评定的实验研究

采用精度高、稳定性好的标准等长收缩灌流装置,从数学和弹性力学角度计算、分析正常及缺氧状态下大鼠乳头肌的应力-应变、应力松弛和蠕变三种生物物理特性的变化。以前者反映顺应性的静态变化,尝试以后二者反映顺应性的动态变化。结果表明,缺氧状态下,不仅心肌的静态顺应性降低(应力—应变曲线明显左移),其动态顺应性也明显降低(应力松驰及蠕变的程度和速度明显降低)。结果提示,本实验方法可用于不同状态下离体心肌顺应性的综合评定。     

Required test duration for group comparisons in ligament viscoelasticity: a statistical approach

The goal of this study was to determine the duration of time that ligaments from a study group need to be loaded in order to adequately determine their collective viscoelastic behavior. Rat ligaments were subjected either to creep or stress relaxation for 1,000 s or stress relaxation for 10,000 s to compare estimates of viscoelastic behavior for different test durations. Stresses versus time (relaxation) or strains versus time (creep) were fit with power law models (tbeta where beta is the rate of creep or relaxation on a log-log scale). Time intervals were separated by logarithmic decade and analyzed using a Random Coefficients approach to compute residual specimen error as a function of the number of decades of data analyzed. Standard Regression was also used for comparison. Results show that by testing for 相似文献   

A dual optimization method for the material parameter identification of a biphasic poroviscoelastic hydrogel: Potential application to hypercompliant soft tissues

A dual-indentation creep and stress relaxation methodology was developed and validated for the material characterization of very soft biological tissue within the framework of the biphasic poroviscoelastic (BPVE) constitutive model. Agarose hydrogel, a generic porous medium with mobile fluid, served as a mechanical tissue analogue for validation of the experimental procedure. Indentation creep and stress relaxation tests with a solid plane-ended cylindrical indenter were performed at identical sites on a gel sample with dimensions large enough with respect to indenter size in order to satisfy an infinite layer assumption. A finite element (FE) formulation coupled to a global optimization algorithm was utilized to simultaneously curve-fit the creep and stress relaxation data and extract the BPVE model parameters for the agarose gel. A numerical analysis with artificial data was conducted to validate the uniqueness of the computational procedure. The BPVE model was able to successfully cross-predict both creep and stress relaxation behavior for each pair of experiments with a single unique set of material parameters. Optimized elastic moduli were consistent with those reported in the literature for agarose gel. With the incorporation of appropriately-sized indenters to satisfy more stringent geometric constraints, this simple yet powerful indentation methodology can provide a straightforward means by which to obtain the BPVE model parameters of biological soft tissues that are difficult to manipulate (such as brain and adipose) while maintaining a realistic in situ loading environment.     

Nonlinear viscoelastic material property estimation of lower extremity residual limb tissues

Axisymmetric nonlinear finite-element analysis was used to simulate force-relaxation and creep data obtained during in vivo indentation of the residual limb soft tissues of six individuals with trans-tibial amputation [1]. The finite-element models facilitated estimation of an appropriate set of nonlinear viscoelastic material coefficients of extended James-Green-Simpson material formulation for bulk soft tissue at discrete, clinically relevant test locations. The results indicate that over 90% of the experimental data can be simulated using the two-term viscoelastic Prony series extension of James-Green-Simpson material formulation. This phenomenological material formulation could not, however, predict the creep response from relaxation experiments, nor the relaxation response from creep experiments [2-5]. The estimated material coefficients varied with test location and subject indicating that these coefficients cannot be readily extrapolated to other sites or individuals.     

人角膜的生物力学特性

以人角膜为研究对象,通过建立一套规范、系统的实验方法,揭示人角膜的生物力学特性。对人角膜标本进行了单轴拉伸实验,测定了其极限强度、应力最大时的变形能及其变形能密度;循环加载实验表明应力－应变的滞后环随加载次数的增加而逐渐减小,应力－应变曲线在应力为０．１５ＭＰａ以上时能用幂指数拟合;应力松弛实验测定了应力松弛谱各参数;蠕变实验表明归一化蠕变数据和时间对数呈线性关系     

Simulation of creep in non-homogenous samples of human cortical bone

Characterising the mechanisms causing viscoelastic mechanical properties of human cortical bone, as well as understanding sources of variation, is important in predicting response of the bone to creep and fatigue loads. Any better understanding, when incorporated into simulations including finite element analysis, would assist bioengineers, clinicians and biomedical scientists. In this study, we used an empirically verified model of creep strain accumulation, in a simulation of 10 non-homogeneous samples, which were created from micro-CT scans of human cortical bone of the femur midshaft obtained from a 74-year-old female cadaver. These non-homogeneous samples incorporate the presence of Haversian canals and resorption cavities. The influence of inhomogeneity on the response and variation in the samples in both creep and stress relaxation tests are examined. The relationship between steady-state creep rate, applied loads (stress relaxation and creep tests) and microstructure, that is bone apparent porosity, is obtained. These relations may provide insight into damage accumulation of whole human bones and be relevant to studies on osteoporosis.     

Simulation of creep in non-homogenous samples of human cortical bone

Characterising the mechanisms causing viscoelastic mechanical properties of human cortical bone, as well as understanding sources of variation, is important in predicting response of the bone to creep and fatigue loads. Any better understanding, when incorporated into simulations including finite element analysis, would assist bioengineers, clinicians and biomedical scientists. In this study, we used an empirically verified model of creep strain accumulation, in a simulation of 10 non-homogeneous samples, which were created from micro-CT scans of human cortical bone of the femur midshaft obtained from a 74-year-old female cadaver. These non-homogeneous samples incorporate the presence of Haversian canals and resorption cavities. The influence of inhomogeneity on the response and variation in the samples in both creep and stress relaxation tests are examined. The relationship between steady-state creep rate, applied loads (stress relaxation and creep tests) and microstructure, that is bone apparent porosity, is obtained. These relations may provide insight into damage accumulation of whole human bones and be relevant to studies on osteoporosis.     

A comparison of deconvolution techniques for stress relaxation

Stress relaxation (or equivalently creep) allows a large range of the relaxation (retardation) spectrum of materials to be examined, particularly at lower frequencies. However, higher frequency components of the relaxation curves (typically of the order of Hertz) are attenuated due to the finite time taken to strain the specimen. This higher frequency information can be recovered by deconvolution of the stress and strain during the loading period. This paper examines the use of three separate deconvolution techniques: numerical (Fourier) deconvolution, semi-analytical deconvolution using a theoretical form of the strain, and deconvolution by a linear approximation method. Both theoretical data (where the exact form of the relaxation function is known) and experimental data were used to assess the accuracy and applicability of the deconvolution methods. All of the deconvolution techniques produced a consistent improvement in the higher frequency data up to the frequencies of the order of Hertz, with the linear approximation method showing better resolution in high-frequency analysis of the theoretical data. When the different deconvolution techniques were applied to experimental data, similar results were found for all three deconvolution techniques. Deconvolution of the stress and strain during loading is a simple and practical method for the recovery of higher frequency data from stress-relaxation experiments.     

In vivo creep and stress relaxation experiments to determine the wall extensibility and yield threshold for the sporangiophores of phycomyces

The pressure probe was used to conduct in vivo creep and in vivo stress relaxation experiments on the sporangiophores of Phycomyces blakesleeanus. The in vivo creep and in vivo stress relaxation methods are compared with respect to their utility for determining the irreversible wall extensibility and the yield threshold. The results of the in vivo stress relaxation experiments demonstrate that the growth usually does not cease when the external water supply is removed, and the turgor pressure does not decay for hours afterwards. A successful stress relaxation experiment requires that the cell enlargement rate (growth rate) be zero during the turgor pressure decay. In a few experiments, the growth rate was zero during the turgor pressure decay. However, in general only the yield threshold could be determined.

In vivo creep experiments proved to be easier to conduct and more useful in determining values for both the irreversible wall extensibility and the yield threshold. The results of the in vivo creep experiments demonstrate that small steps-up in turgor pressure, generally <0.02 MPa, elicit increases in growth rate as predicted by the growth equations and the augmented growth equations. The irreversible wall extensibility and the yield threshold were determined from these results. The results also demonstrate that steps-up in turgor pressure larger than 0.02 MPa, produce a different response; a decrease in growth rate. The decreased growth rate behavior is related to the magnitude of the step-up, and in general, larger steps-up in turgor pressure produce larger decreases in growth rate and longer periods of decreased growth rate. Qualitatively, this growth behavior is very similar to the “stretch response” previously reported by Dennison and Roth (1967).

     

Unconfined compression of hydrated viscoelastic tissues: a biphasic poroviscoelastic analysis

A biphasic poroviscoelastic theory was used to analyze the unconfined compression creep and stress relaxation of a hydrated viscoelastic tissue. The intrinsic shear properties of the tissue matrix was described by an integral-type viscoelastic constitutive law while the intrinsic bulk property of the matrix was assumed to be linearly elastic. Parametric data were presented to show how the two major energy dissipative mechanisms, namely the interstitial fluid flow and the intrinsic matrix viscoelasticity, may each contribute to the apparent viscoelastic behavior of the whole tissue under unconfined compression. The hydraulic permeability of the tissue was found to enter in only as a scaling factor for time.     

A computer simulation of the creep process of the cell wall using stress relaxation parameters

The stress relaxation of the cell wall of pea plants was measured and viscoelastic parameters were obtained according to the stress-relaxation analysis developed by Yamamoto et al. (Plant & Cell Physiol. 1970). The creep process of the cell wall was simulated by a numerical integration using stress-relaxation parameters, because the direct conversion of the stress relaxation process to the creep is impractical. In the conversion, a personal computer was programmed for the Maxwell viscoelastic model with a compiler language. Cell wall creep was measured with a specially constituted apparatus and compared with that calculated by the simulation process. The results suggested that the creep can be reproduced by a computer simulation using the stress-relaxation parameters. Both creep and stress-relaxation properties of plant cell walls can be analyzed by using a single model.     

Biomechanical and viscoelastic properties of skin,SMAS, and composite flaps as they pertain to rhytidectomy

Previous studies have focused on biomechanical and viscoelastic properties of the superficial musculoaponeurotic system (SMAS) flap and the skin flap lifted in traditional rhytidectomy procedures. The authors compared these two layers with the composite rhytidectomy flap to explain their clinical observations that the composite dissection allows greater tension and lateral pull to be placed on the facial and cervical flaps, with less long-term stress-relaxation and tissue creep. Eight fresh cadavers were dissected by elevating flaps on one side of the face and neck as skin and SMAS flaps and on the other side as a standard composite rhytidectomy flap. The tissue samples were tested for breaking strength, tissue tearing force, stress-relaxation, and tissue creep. For breaking strength, uniform samples were pulled at a rate of 1 inch per minute, and the stress required to rupture the tissues was measured. Tissue tearing force was measured by attaching a 3-0 suture to the tissues and pulling at the same rate as that used for breaking strength. The force required to tear the suture out of the tissues was then measured. Stress-relaxation was assessed by tensing the uniformly sized strips of tissue to 80 percent of their breaking strength, and the amount of tissue relaxation was measured at 1-minute intervals for a total of 5 minutes. This measurement is expressed as the percentage of tissue relaxation per minute. Tissue creep was assessed by using a 3-0 suture and calibrated pressure gauge attached to the facial flaps. The constant tension applied to the flaps was 80 percent of the tissue tearing force. The distance crept was measured in millimeters after 2 and 3 minutes of constant tension. Breaking strength measurements demonstrated significantly greater breaking strength of skin and composite flaps as compared with SMAS flaps (p < 0.05). No significant difference was noted between skin and composite flaps. However, tissue tearing force demonstrated that the composite flaps were able to withstand a significantly greater force as compared with both skin and SMAS flaps (p < 0.05). Stress-relaxation analysis revealed the skin flaps to have the highest degree of stress-relaxation over each of five 1-minute intervals. In contrast, the SMAS and composite flaps demonstrated a significantly lower degree of stress-relaxation over the five 1-minute intervals (p < 0.05). There was no difference noted between the SMAS flaps and composite flaps with regard to stress-relaxation. Tissue creep correlated with the stress-relaxation data. The skin flaps demonstrated the greatest degree of tissue creep, which was significantly greater than that noted for the SMAS flaps or composite flaps (p < 0.05). Comparison of facial flaps with cervical flaps revealed that cervical skin, SMAS, and composite flaps tolerated significantly greater tissue tearing forces and demonstrated significantly greater tissue creep as compared with facial skin, SMAS, and composite flaps (p < 0.05). These biomechanical studies on facial and cervical rhytidectomy flaps indicate that the skin and composite flaps are substantially stronger than the SMAS flap, allowing significantly greater tension to be applied for repositioning of the flap and surrounding subcutaneous tissues. The authors confirmed that the SMAS layer exhibits significantly less stress-relaxation and creep as compared with the skin flap, a property that has led aesthetic surgeons to incorporate the SMAS into the face lift procedure. On the basis of the authors' findings in this study, it seems that that composite flap, although composed of both the skin and SMAS, acquires the viscoelastic properties of the SMAS layer, demonstrating significantly less stress-relaxation and tissue creep as compared with the skin flap. This finding may play a role in maintaining long-term results after rhytidectomy. In addition, it is noteworthy that the cervical flaps, despite their increased strength, demonstrate significantly greater tissue creep as compared with facial flaps, suggesting earlier relaxation of the neck as compared with the face after rhytidectomy.     

The apparent viscoelastic behavior of articular cartilage--the contributions from the intrinsic matrix viscoelasticity and interstitial fluid flows

Articular cartilage was modeled rheologically as a biphasic poroviscoelastic material. A specific integral-type linear viscoelastic model was used to describe the constitutive relation of the collagen-proteoglycan matrix in shear. For bulk deformation, the matrix was assumed either to be linearly elastic, or viscoelastic with an identical reduced relaxation spectrum as in shear. The interstitial fluid was considered to be incompressible and inviscid. The creep and the rate-controlled stress-relaxation experiments on articular cartilage under confined compression were analyzed using this model. Using the material data available in the literature, it was concluded that both the interstitial fluid flow and the intrinsic matrix viscoelasticity contribute significantly to the apparent viscoelastic behavior of this tissue under confined compression.     

Using wood creep data to discuss the contribution of cell-wall reinforcing material

Longitudinal four-point creep bending tests were performed on small clear-wood spruce specimens having various microfibrillar angles. Cell-wall compliance was deduced from macroscopic data by accounting for porosity. Time-dependent compliance was converted into complex compliance and rigidity using the value and the slope of the compliance versus logarithm of time. Complex rigidity plots of all specimens, for the time range 10(3)-10(6) s, could be superimposed by a horizontal shift depending on the microfibrillar angle. The shape of complex trajectories allowed a decomposition of the cell-wall relaxation modulus as the sum of an elastic contribution function of the microfibrillar angle and a time-dependent term unrelated to it, and suggested a discussion on the contribution of the various cell-wall layers to the observed relaxation process.     

The orthotropic viscoelastic behavior of aortic elastin

In this paper, we studied the viscoelastic behaviors of isolated aortic elastin using combined modeling and experimental approaches. Biaxial stress relaxation and creep experiments were performed to study the time-dependent behavior of elastin. Experimental results reveal that stress relaxation preconditioning is necessary in order to obtain repeatable stress relaxation responses. Elastin exhibits less stress relaxation than intact or decellularized aorta. The rate of stress relaxation of intact and decellularized aorta is linearly dependent on the initial stress levels. The rate of stress relaxation for elastin increases linearly at stress levels below about 60 kPa; however, the rate changes very slightly at higher initial stress levels. Experimental results also show that creep response is negligible for elastin, and the intact or decellularized aorta. A quasi-linear viscoelasticity model was incorporated into a statistical mechanics based eight-chain microstructural model at the fiber level to simulate the orthotropic viscoelastic behavior of elastin. A user material subroutine was developed for finite element analysis. Results demonstrate that this model is suitable to capture both the orthotropic hyperelasticity and viscoelasticity of elastin.     

Linear viscoelasticity - bone volume fraction relationships of bovine trabecular bone

Trabecular bone has been previously recognized as time-dependent (viscoelastic) material, but the relationships of its viscoelastic behaviour with bone volume fraction (BV/TV) have not been investigated so far. Therefore, the aim of the present study was to quantify the time-dependent viscoelastic behaviour of trabecular bone and relate it to BV/TV. Uniaxial compressive creep experiments were performed on cylindrical bovine trabecular bone samples (\(\textit{n}\,{=}\,13\)) at loads corresponding to physiological strain level of 2000 \({\upmu }{\upvarepsilon }\). We assumed that the bone behaves in a linear viscoelastic manner at this low strain level and the corresponding linear viscoelastic parameters were estimated by fitting a generalized Kelvin–Voigt rheological model to the experimental creep strain response. Strong and significant power law relationships (\(r^2\,{=}\,0.73,\ p\,{<}\,0.001\)) were found between time-dependent creep compliance function and BV/TV of the bone. These BV/TV-based material properties can be used in finite element models involving trabecular bone to predict time-dependent response. For users’ convenience, the creep compliance functions were also converted to relaxation functions by using numerical interconversion methods and similar power law relationships were reported between time-dependent relaxation modulus function and BV/TV.     

Nonlinear viscoelastic, thermodynamically consistent, models for biological soft tissue

The mechanical behavior of most biological soft tissue is nonlinear viscoelastic rather than elastic. Many of the models previously proposed for soft tissue involve ad hoc systems of springs and dashpots or require measurement of time-dependent constitutive coefficient functions. The model proposed here is a system of evolution differential equations, which are determined by the long-term behavior of the material as represented by an energy function of the type used for elasticity. The necessary empirical data is time independent and therefore easier to obtain. These evolution equations, which represent non-equilibrium, transient responses such as creep, stress relaxation, or variable loading, are derived from a maximum energy dissipation principle, which supplements the second law of thermodynamics. The evolution model can represent both creep and stress relaxation, depending on the choice of control variables, because of the assumption that a unique long-term manifold exists for both processes. It succeeds, with one set of material constants, in reproducing the loading-unloading hysteresis for soft tissue. The models are thermodynamically consistent so that, given data, they may be extended to the temperature-dependent behavior of biological tissue, such as the change in temperature during uniaxial loading. The Holzapfel et al. three-dimensional two-layer elastic model for healthy artery tissue is shown to generate evolution equations by this construction for biaxial loading of a flat specimen. A simplified version of the Shah-Humphrey model for the elastodynamical behavior of a saccular aneurysm is extended to viscoelastic behavior.     

The effect of auxin on stress relaxation in isolated Avena coleoptiles

In order to characterize further the mechanical properties of coleoptile cell walls, stress relaxation measurements were made on methanol-boiled sections of Avena coleoptiles. Relaxation was measured both in mechanically conditioned specimens and in specimens which had not been previously extended. In both cases the relaxation was proportional to log time. Mechanical conditioning increased the relaxation modules and decreased the relative rate of relaxation. In contrast, pretreatment of the live coleoptiles with indoleacetic acid reduced the relaxation modulus and the absolute rate of relaxation but did not affect the relative rate of relaxation. Essentially similar pictures of the mechanical properties of coleoptile walls are obtained from stress relaxation and creep tests; the wall behaves as a nonlinear viscoelastic material.