A Model for Nonlinear Viscoelastic Mechanical Responses of Collagenous Soft Tissues

2005 ◽  
Vol 898 ◽  
Author(s):  
Michelle Oyen
Keyword(s):  
Stress Relaxation ◽  
Mechanical Behavior ◽  
Soft Tissues ◽  
Applied Strain ◽  
Monotonic Loading ◽  
Experimental Results ◽  
Strain Level ◽  
Time Dependent ◽  
Large Strains ◽  
Mechanical Responses

AbstractExperimental observations of the time-dependent mechanical responses of collagenous tissues have demonstrated behavior that deviates from standard treatments of linear or quasi-linear viscoelasticity. In particular, time-dependent deformation can be strongly coupled to strain level, and strain-rate independence can be observed under monotonic loading, even for a tissue with dramatic stress relaxation. It was postulated that this nonlinearity is fundamentally associated with gradual recruitment of individual collagen fibrils during applied mechanical loading. Based on previously observed experimental results for the time-dependent response of collagenous soft tissues, a model is developed to describe the mechanical behavior of these tissues under uniaxial loading. Tissue stresses, under applied strain-controlled loading, are assumed to be a sum of elastic and viscoelastic stress contributions. The relative contributions of elastic and viscoelastic stresses is assumed to vary with strain level, leading to strain- and time-dependent mechanical behavior. The model formulation is examined under conditions of monotonic loading at varying constant strain rates and stress-relaxation at different applied strain levels. The model is compared with experimental data for a membranous biological soft tissue, the amniotic sac, and is found to agree well with experimental results. The limiting behavior of the novel model, at large strains relative to the collagen recruitment, is consistent with the quasi-linear viscoelastic approach.

QUASI-LINEAR VISCOELASTIC MODELLING OF UNCURED PREPREGS UNDER COMPACTION

2021 ◽  
Author(s):  
SIDDHESH S. KULKARNI ◽  
KAMRAN A. KHAN ◽  
REHAN UMER
Keyword(s):  
Stress Relaxation ◽  
Relaxation Function ◽  
Soft Tissues ◽  
Volume Fraction ◽  
Time Dependent ◽  
Strain History ◽  
Manufacturing Processes ◽  
Fiber Volume ◽  
Consolidation Process ◽  
Thermoset Resin

Reinforcement compaction sometimes referred as consolidation process and is one of the key steps in various composite manufacturing processes such as autoclave and out-of-autoclave processing. The prepregs consist of semi-cured thermoset resin system impregnating the fibers. hence, the prepreg shows strong viscoelastic compaction response, which strongly depends on compaction speed and stress relaxation. modeling of time-dependent response is of utmost importance to understand the behavior of prepregs during different stages of composites manufacturing processes. The quasilinear viscoelastic (QLV) theory has been extensively used for the modeling of viscoelastic response of soft tissues in biomedical applications. In QLV approach, the stress relaxation can be expressed in terms of the nonlinear elastic function and the reduced relaxation function. The constitutive equation can be represented by a convolution integral of the nonlinear strain history, and reduced relaxation function. This study adopted a quasilinear viscoelastic modeling approach to describe the time dependent behavior of uncured-prepregs under compression. The model was modified to account for the compaction behavior of the prepreg under a compressive load. The deformation behavior of the prepreg is usually characterized by the fiber volume fraction, V . In this study, the material used was a 2/2 Twill weave glass prepreg (M26T) supplied by Hexcel® Industries USA. We performed a compaction experiment of the uncured prepreg at room temperature at different displacement rate and subsequent relaxation to describe the viscoelastic behavior of the prepreg. The model parameter calibration was performed using the trust-region-reflective algorithm in matlab to a selected number of test data. The calibrated model was then used to predict the rate dependent compaction and relaxation response of prepregs for different fiber volume fractions and strain rates.

A Microscale Collagen-Fibrin Interacting Network Model With Comparison to Experimental Results

2012 ◽  
Author(s):  
Jeffrey D. Hyypio ◽  
Mohammad F. Hadi ◽  
Victor K. Lai ◽  
Victor H. Barocas
Keyword(s):  
Mechanical Loading ◽  
Network Model ◽  
Computer Model ◽  
Soft Tissues ◽  
Uniaxial Extension ◽  
Tissue Mechanics ◽  
Experimental Results ◽  
Large Strains ◽  
Heterogeneous Nature ◽  
Engineered Tissue

Many native and bioengineered soft tissues are composed of two or more types of biopolymer networks that mechanically define and support the material [1]. Modeling the response of multi-network soft tissues to mechanical loading can be difficult due to the heterogeneous nature of these materials and the large strains (>1) involved. As tissues deform, the different biopolymer networks interact with one another and determine the overall stress-strain outcome for the tissue. Capturing this interaction could help improve the accuracy of a computer model to simulate the microscale behavior of soft tissues under load. We have developed a two-network model to reflect interactions between collagen and fibrin biopolymer networks loaded in uniaxial extension. The model can help improve our understanding of native and engineered tissue mechanics.

The Rate (Time)–Dependent Mechanical Behavior of the PMR-15 Thermoset Polymer at Temperatures in the 274–316 °C Range: Experiments and Modeling

2011 ◽  
Author(s):  
C. E. C. Ryther ◽  
M. B. Ruggles-Wrenn
Keyword(s):  
Strain Rate ◽  
Mechanical Behavior ◽  
Deformation Behavior ◽  
Inelastic Deformation ◽  
Monotonic Loading ◽  
Relaxation Behavior ◽  
Time Dependent ◽  
Experimental Program ◽  
Model Parameters ◽  
Thermoset Polymer

The inelastic deformation behavior of the PMR-15 neat resin, a high-temperature thermoset polymer, was investigated at temperatures in the 274–316 °C range. The experimental program was designed to explore the influence of strain rate on monotonic loading at various temperatures. In addition, the effects of prior strain rate on relaxation response and on creep behavior following strain controlled loading were examined at temperatures in the range of interest. Positive, nonlinear strain rate sensitivity is observed in monotonic loading at all temperatures investigated. Both relaxation behavior and creep are profoundly influenced by prior strain rate at all temperatures. The time-dependent mechanical behavior of the PMR-15 polymer is also strongly affected by temperature. The elastic modulus decreases and the departure from quasi-linear behavior is accelerated with increasing temperature. Stress levels in the region of inelastic flow decrease as the temperature increases. The relaxation behavior as well as the creep response is strongly influenced by temperature. The viscoplasticity theory based on overstress (VBO) is augmented to model the effects of temperature on the inelastic deformation behavior of PMR-15. VBO is a unified state variable theory with growth laws for three state variables: the equilibrium stress, the kinematic stress and the isotropic stress. Based on experimental findings several VBO model parameters are developed as functions of temperature. The augmented model is employed to predict the response of the material under both strain- and stress-controlled loading histories at temperatures in the range of interest. Comparison with experimental data demonstrates that the augmented VBO successfully predicts the inelastic deformation behavior of PMR-15 polymer under various loading histories at temperatures between 274 and 316 °C.

scholarly journals Study on the Time-Dependent Mechanical Behavior and Springback of Magnesium Alloy Sheet (AZ31B) in Warm Conditions

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3856
Author(s):  
Jae-Hyeong YU ◽  
Chang-Whan Lee
Keyword(s):  
Magnesium Alloy ◽  
Stress Relaxation ◽  
Dynamic Recrystallization ◽  
Mechanical Behavior ◽  
Alloy Sheet ◽  
Holding Time ◽  
Time Dependent ◽  
Die Set ◽  
Creep And Stress Relaxation ◽  
Springback Angle

In this study, the time-dependent mechanical behavior of the magnesium alloy sheet (AZ31B) was investigated through the creep and stress relaxation tests with respect to the temperature and pre-strain. The microstructure changes during creep and stress relaxation were investigated. As the tensile deformation increased in the material, twinning and dynamic recrystallization occurred, especially after the plastic instability. As a result, AZ31B showed lower resistance to creep and stress relaxation due to dynamic recrystallization. Additionally, time-dependent springback characteristics in the V- and L-bending processes concerning the holding time and different forming conditions were investigated. We analyzed changes of microstructure at each forming temperature and process. The uniaxial tensile creep test was conducted to compare the microstructures in various pre-strain conditions with those at the secondary creep stage. For the bending process, the change of the microstructure after the forming was compared to that with punch holding maintained for 1000 s after forming. Due to recrystallization, with the holding time in the die set of 60 s, the springback angle decreased by nearly 70%. Increased holding time in the die set resulted in a reduced springback angle.

A Visco-Hyperelastic-Damage Constitutive Model for the Analysis of the Biomechanical Response of the Periodontal Ligament

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Arturo N. Natali ◽  
Emanuele L. Carniel ◽  
Piero G. Pavan ◽  
Franz G. Sander ◽  
Christina Dorow ◽  
...  
Keyword(s):  
Strain Rate ◽  
Periodontal Ligament ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Experimental Testing ◽  
Constitutive Models ◽  
Biological Tissues ◽  
Time Dependent ◽  
Large Strains ◽  
Free Energy Function

The periodontal ligament (PDL), as other soft biological tissues, shows a strongly non-linear and time-dependent mechanical response and can undergo large strains under physiological loads. Therefore, the characterization of the mechanical behavior of soft tissues entails the definition of constitutive models capable of accounting for geometric and material non-linearity. The microstructural arrangement determines specific anisotropic properties. A hyperelastic anisotropic formulation is adopted as the basis for the development of constitutive models for the PDL and properly arranged for investigating the viscous and damage phenomena as well to interpret significant aspects pertaining to ordinary and degenerative conditions. Visco-hyperelastic models are used to analyze the time-dependent mechanical response, while elasto-damage models account for the stiffness and strength decrease that can develop under significant loading or degenerative conditions. Experimental testing points out that damage response is affected by the strain rate associated with loading, showing a decrease in the damage limits as the strain rate increases. These phenomena can be investigated by means of a model capable of accounting for damage phenomena in relation to viscous effects. The visco-hyperelastic-damage model developed is defined on the basis of a Helmholtz free energy function depending on the strain-damage history. In particular, a specific damage criterion is formulated in order to evaluate the influence of the strain rate on damage. The model can be implemented in a general purpose finite element code. The accuracy of the formulation is evaluated by using results of experimental tests performed on animal model, accounting for different strain rates and for strain states capable of inducing damage phenomena. The comparison shows a good agreement between numerical results and experimental data.

The Rate (Time)-Dependent Mechanical Behavior of the PMR-15 Thermoset Polymer at Temperatures in the 274–316 °C Range: Experiments and Modeling

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
C. E. C. Ryther ◽  
M. B. Ruggles-Wrenn
Keyword(s):  
Strain Rate ◽  
Mechanical Behavior ◽  
Deformation Behavior ◽  
Inelastic Deformation ◽  
Monotonic Loading ◽  
Relaxation Behavior ◽  
Time Dependent ◽  
Experimental Program ◽  
Model Parameters ◽  
Thermoset Polymer

The inelastic deformation behavior of the PMR-15 neat resin, a high-temperature thermoset polymer, was investigated at temperatures in the 274–316 °C range. The experimental program was designed to explore the influence of strain rate on monotonic loading at various temperatures. In addition, the effects of prior strain rate on relaxation response and on creep behavior following strain-controlled loading were examined at temperatures in the range of interest. Positive, nonlinear strain rate sensitivity is observed in monotonic loading at all temperatures investigated. Both relaxation behavior and creep are profoundly influenced by prior strain rate at all temperatures. The time-dependent mechanical behavior of the PMR-15 polymer is also strongly affected by temperature. The elastic modulus decreases and the departure from quasi-linear behavior is accelerated with increasing temperature. Stress levels in the region of inelastic flow decrease as the temperature increases. The relaxation behavior as well as the creep response is strongly influenced by temperature. The viscoplasticity theory based on overstress for polymers (VBOP) is augmented to model the effects of temperature on the inelastic deformation behavior of PMR-15. VBOP is a unified state variable theory with growth laws for three state variables: the equilibrium stress, the kinematic stress, and the isotropic stress. Based on the experimental findings several VBOP model parameters are developed as functions of temperature. The augmented model is employed to predict the response of the material under both strain- and stress-controlled loading histories at temperatures in the range of interest. Comparison with experimental data demonstrates that the augmented VBOP successfully predicts the inelastic deformation behavior of PMR-15 polymer under various loading histories at temperatures between 274 and 316 °C.

Strain-Level Dependent Nonequilibrium Anisotropic Viscoelasticity: Application to the Abdominal Muscle

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Marcos Latorre ◽  
Francisco J. Montáns
Keyword(s):  
Soft Tissues ◽  
Viscoelastic Behavior ◽  
Abdominal Muscle ◽  
Strain Level ◽  
Large Strains ◽  
Fully Nonlinear ◽  
Material Parameters ◽  
Viscoelastic Models ◽  
Linear Viscoelastic ◽  
Relaxation Curves

Soft connective tissues sustain large strains of viscoelastic nature. The rate-independent component is frequently modeled by means of anisotropic hyperelastic models. The rate-dependent component is usually modeled through linear rheological models or quasi-linear viscoelastic (QLV) models. These viscoelastic models are unable, in general, to capture the strain-level dependency of the viscoelastic properties present in many viscoelastic tissues. In linear viscoelastic models, strain-level dependency is frequently accounted for by including the dependence of multipliers of Prony series on strains through additional evolution laws, but the determination of the material parameters is a difficult task and the obtained accuracy is usually not sufficient. In this work, we introduce a model for fully nonlinear viscoelasticity in which the instantaneous and quasi-static behaviors are exactly captured and the relaxation curves are predicted to a high accuracy. The model is based on a fully nonlinear standard rheological model and does not necessitate optimization algorithms to obtain material parameters. Furthermore, in contrast to most models used in modeling the viscoelastic behavior of soft tissues, it is valid for the large deviations from thermodynamic equilibrium typically observed in soft tissues.

scholarly journals Time-Dependent Response of a Recycled C&D Material-Geotextile Interface under Direct Shear Mode

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3070
Author(s):  
Fernanda Bessa Ferreira ◽  
Paulo M. Pereira ◽  
Castorina Silva Vieira ◽  
Maria de Lurdes Lopes
Keyword(s):  
Shear Stress ◽  
Stress Relaxation ◽  
Shear Displacement ◽  
Time Dependent ◽  
Shear Behaviour ◽  
Displacement Rate ◽  
Shear Mode ◽  
Direct Shear ◽  
Constant Displacement ◽  
Shear Box

Geosynthetic-reinforced soil structures have been used extensively in recent decades due to their significant advantages over more conventional earth retaining structures, including the cost-effectiveness, reduced construction time, and possibility of using locally-available lower quality soils and/or waste materials, such as recycled construction and demolition (C&D) wastes. The time-dependent shear behaviour at the interfaces between the geosynthetic and the backfill is an important factor affecting the overall long-term performance of such structures, and thereby should be properly understood. In this study, an innovative multistage direct shear test procedure is introduced to characterise the time-dependent response of the interface between a high-strength geotextile and a recycled C&D material. After a prescribed shear displacement is reached, the shear box is kept stationary for a specific period of time, after which the test proceeds again, at a constant displacement rate, until the peak and large-displacement shear strengths are mobilised. The shear stress-shear displacement curves from the proposed multistage tests exhibited a progressive decrease in shear stress with time (stress relaxation) during the period in which the shear box was restrained from any movement, which was more pronounced under lower normal stress values. Regardless of the prior interface shear displacement and duration of the stress relaxation stage, the peak and residual shear strength parameters of the C&D material-geotextile interface remained similar to those obtained from the conventional (benchmark) tests carried out under constant displacement rate.

Random Forces Resulting From Internal Two-Phase Flow on Bends and Tees

2006 ◽  
Author(s):  
E. de Langre ◽  
J. L. Riverin ◽  
M. J. Pettigrew
Keyword(s):  
Two Phase Flow ◽  
Experimental Results ◽  
Time Dependent ◽  
Phase Flow ◽  
Water Mixture ◽  
Dimensionless Form ◽  
Two Phase ◽  
Practical Applications ◽  
Random Forces

The time dependent forces resulting from a two-phase air-water mixture flowing in an elbow and a tee are measured. Their magnitudes as well as their spectral contents are analyzed. Comparison is made with previous experimental results on similar systems. For practical applications a dimensionless form is proposed to relate the characteristics of these forces to the parameters defining the flow and the geometry of the piping.

Sign in / Sign up

Export Citation Format

Share Document