Strain-Rate Sensitive Constitutive Modeling of Anisotropic Visco-Hyperelastic Materials

2012 ◽  
Author(s):  
Sahand Ahsanizadeh ◽  
LePing Li
Keyword(s):  
Strain Rate ◽  
Evolution Equations ◽  
Mechanical Response ◽  
Viscoelastic Behavior ◽  
Biological Tissues ◽  
Internal Variables ◽  
Current Configuration ◽  
Hyperelastic Materials ◽  
History Of ◽  
Viscoelastic Constitutive Model

Integral-based formulations of viscoelasticity have been widely used to describe the mechanical behavior of soft biological tissues and polymers. However, it is suggested that they are not suitable to be used under high strain rates. On the other hand, strain-rate sensitive models with an explicit dependence on the strain-rate have been developed for a certain class of materials. They predict the viscoelastic behavior during ramp loading more accurately while fail to account for the relaxation response. In order to overcome these drawbacks, a viscoelastic constitutive model has been proposed in this study based on the concept of internal variables. While the behavior of elastic materials is uniquely determined by the current state of deformation or external variables, the mechanical response of inelastic materials are regulated also by internal variables. The internal variables are associated with the dissipative mechanisms in the material and along with the evolution equations introduce the effect of history of the deformation to the current configuration. The current study employs short-term and long-term internal variables to account for the viscoelastic response during loading and relaxation respectively.

scholarly journals Design and Demonstration of a Microbiaxial Optomechanical Device for Multiscale Characterization of Soft Biological Tissues with Two-Photon Microscopy

2011 ◽  
Vol 17 (2) ◽  
pp. 167-175 ◽  
Author(s):  
Joseph T. Keyes ◽  
Stacy M. Borowicz ◽  
Jacob H. Rader ◽  
Urs Utzinger ◽  
Mohamad Azhar ◽  
...  
Keyword(s):  
Mechanical Response ◽  
Tissue Sample ◽  
Imaging Techniques ◽  
High Stress ◽  
Viscoelastic Behavior ◽  
Biological Tissues ◽  
The Body ◽  
Two Photon ◽  
Biomechanical Response ◽  
Tissue Specimens

AbstractThe biomechanical response of tissues serves as a valuable marker in the prediction of disease and in understanding the related behavior of the body under various disease and age states. Alterations in the macroscopic biomechanical response of diseased tissues are well documented; however, a thorough understanding of the microstructural events that lead to these changes is poorly understood. In this article we introduce a novel microbiaxial optomechanical device that allows two-photon imaging techniques to be coupled with macromechanical stimulation in hydrated planar tissue specimens. This allows that the mechanical response of the microstructure can be quantified and related to the macroscopic response of the same tissue sample. This occurs without the need to fix tissue in strain states that could introduce a change in the microstructural configuration. We demonstrate the passive realignment of fibrous proteins under various types of loading, which demonstrates the ability of tissue microstructure to reinforce itself in periods of high stress. In addition, the collagen and elastin response of tissue during viscoelastic behavior is reported showing interstitial fluid movement and fiber realignment potentially responsible for the temporal behavior. We also demonstrate that nonhomogeneities in fiber strain exist over biaxial regions of assumed homogeneity.

Creep Analysis of Cr-Mo Steels Using a Dislocation Based Constitutive Modelling

2004 ◽  
Vol 449-452 ◽  
pp. 117-120 ◽  
Author(s):  
Hyoung Seop Kim ◽  
Min Hong Seo ◽  
Sun Ig Hong ◽  
Sung Ho Kim ◽  
Woo Seog Ryu
Keyword(s):  
Kinetic Equation ◽  
Dislocation Density ◽  
Metal Forming ◽  
Evolution Equations ◽  
Mechanical Response ◽  
Creep Behaviour ◽  
Constitutive Modelling ◽  
Internal Variables ◽  
Dislocation Glide ◽  
Creep Analysis

In order to analyze the creep behaviour of Cr-Mo steels, an elasto-viscoplastic constitutive model based on dislocation density considerations is described. A combination of a kinetic equation, which describes the mechanical response of a material at a given microstructure in terms of dislocation glide, and evolution equations for internal variables characterising the microstructure provide the constitutive equations of the model. Microstructural features of the material are implemented in the constitutive equation. The internal variables are associated with the total dislocation density. The model has a modular structure and can be adjusted to describe a particular type of materials behaviour and metal forming processes. In this paper, the predicted creep behaviour of Cr-Mo steels is compared with the experimental results.

STRAIN RATE–DEPENDENT BEHAVIOR OF UNCURED RUBBER: EXPERIMENTAL INVESTIGATION AND CONSTITUTIVE MODELING

2022 ◽  
Author(s):  
Sanghyeub Kim ◽  
Thomas Berger ◽  
Michael Kaliske
Keyword(s):  
Strain Rate ◽  
Evolution Equations ◽  
Cyclic Creep ◽  
Tensile Tests ◽  
Internal Variables ◽  
Creep Tests ◽  
Rate Dependent ◽  
Nonlinear Viscosity ◽  
Dependent Behavior ◽  
Building Process

ABSTRACT The strain rate dependence of uncured rubber is investigated through a series of tensile tests (monotonic, multistep relaxation, cyclic creep tests) at different strain rates. In addition, loading/unloading tests in which the strain rate is varied every cycle are carried out to observe their dependence on the deformation history. A strain rate–dependent viscoelastic–viscoplastic constitutive model is proposed with the nonlinear viscosity and process-dependent recovery properties observed in the test results. Those properties are implemented by introducing evolution equations for additional internal variables. The identified material parameters capture the experiments qualitatively well. The proposed model is also evaluated by finite element simulations of the building process of a tire, followed by the in-molding.

Constitutive Formulation for Numerical Analysis of Visco-Hyperelastic Damage Phenomena in Soft Biological Tissues

2006 ◽  
Author(s):  
Arturo N. Natali ◽  
Emanuele L. Carniel ◽  
Piero G. Pavan ◽  
Alessio Gasparetto ◽  
Franz G. Sander ◽  
...  
Keyword(s):  
Strain Rate ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Constitutive Models ◽  
Experimental Tests ◽  
Biological Tissues ◽  
Tissue Response ◽  
Time Dependent ◽  
Soft Biological Tissues ◽  
Constitutive Formulation

Soft biological tissues show a strongly non linear and time-dependent mechanical response and undergo large strains under physiological loads. The microstructural arrangement determines specific anisotropic macroscopic properties that must be considered within a constitutive formulation. The characterization of the mechanical behaviour of soft tissues entails the definition of constitutive models capable of accounting for geometric and material non linearity. In the model presented here a hyperelastic anisotropic formulation is adopted as the basis for the development of constitutive models for soft tissues and can be properly arranged for the investigation of 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. This 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. This makes it possible to perform numerical analyses of the mechanical response considering time-dependent effects and damage phenomena. The experimental tests develop investigated tissue response for different strain rate conditions, accounting for stretch situations capable of inducing damage phenomena. The reliability of the formulation is evaluated by a comparison with the results of experimental tests performed on pig periodontal ligament.

scholarly journals Influence of strain rate on the mechanical response of nanostructured coppers elaborated by SPD and SPS

2021 ◽  
Vol 250 ◽  
pp. 03014
Author(s):  
Hervé Couque ◽  
Yuri Khoptiar ◽  
Frédéric Bernard ◽  
Itamar Gutman ◽  
Florian Bussiere ◽  
...  
Keyword(s):  
Strain Rate ◽  
Uniaxial Compression ◽  
Mechanical Response ◽  
Tensile Tests ◽  
Strain Rates ◽  
Static Compression ◽  
Plasma Sintering ◽  
History Of ◽  
Spark Plasma ◽  
Nanostructured Copper

The influence of strain rate on the mechanical response of two different nanostructured pure coppers was investigated under uniaxial compression. The first nanostructured copper was elaborated by powder metallurgy using the Spark Plasma Sintering (SPS) process. The second nanostructured copper was elaborated by Severe Plastic Deformation (SPD). Conventional characterizations were conducted with quasi-static compression and tensile tests, hardness tests and, with microstructure analysis. The effect of strain rate was evaluated under uniaxial compression at strain rates varying from 10-4 to 10+4 s-1. The high strain rate data were generated with a direct Hopkinson impact technique. The increase of strength with strain rates was analysed and discussed from the Scanning Electron Microscope observations and grain size distribution. The mechanical properties are consequently dependent on the metallurgical history of these samples prepared according to two different routes.

A microsphere-based remodelling formulation for anisotropic biological tissues

2009 ◽  
Vol 367 (1902) ◽  
pp. 3499-3523 ◽  
Author(s):  
Andreas Menzel ◽  
Tobias Waffenschmidt
Keyword(s):  
Evolution Equations ◽  
Three Dimensional ◽  
Biological Tissues ◽  
Internal Variables ◽  
Chain Model ◽  
Chain Molecules ◽  
Numerical Studies ◽  
Algorithmic Treatment ◽  
The One ◽  
Unit Vectors

Biological tissues possess the ability to adapt according to the respective local loading conditions, which results in growth and remodelling phenomena. The main goal of this work is the development of a new remodelling approach that, on the one hand, reflects the alignment of fibrous soft biological tissue with respect to representative loading directions. On the other hand, the continuum approach proposed is based on a sound micro-mechanically motivated formulation. To be specific, use of a worm-like chain model is made to describe the behaviour of long-chain molecules as present in, for instance, collageneous tissues. The extension of such a one-dimensional constitutive equation to the three-dimensional macroscopic level is performed by means of a microsphere formulation. Inherent with the algorithmic treatment of this type of modelling approach, a finite number of unit vectors is considered for the numerical integration over the domain of the unit sphere. As a key aspect of this contribution, remodelling is incorporated by setting up evolution equations for the referential orientations of these integration directions. Accordingly, the unit vectors considered now allow interpretation as internal variables, which characterize the material’s anisotropic properties. Several numerical studies underline the applicability of the model that, moreover, nicely fits into iterative finite element formulations so that general boundary value problems can be solved.

Mechanical Response of Brain Stem in Compression and the Differential Scanning Calorimetry and FTIR Analyses

2016 ◽  
Vol 83 (9) ◽  
Author(s):  
Wei Zhang ◽  
Run-run Zhang ◽  
Liang-liang Feng ◽  
Yang Li ◽  
Fan Wu ◽  
...  
Keyword(s):  
Differential Scanning Calorimetry ◽  
Strain Rate ◽  
Brain Stem ◽  
Mechanical Response ◽  
Viscoelastic Behavior ◽  
Transitional Region ◽  
Rate Dependency ◽  
Scanning Calorimetry ◽  
Polar Functional Groups ◽  
The Brain

The stress–strain curves of brain stem in uniaxial compression demonstrate strain rate dependency and can be characterized with three regions: initial toe region, transitional region, and high strain region, suggesting strong viscoelastic behavior. To investigate the origin of this viscoelasticity at microscale, differential scanning calorimetry (DSC) and Fourier transform infrared (FTIR) spectra of brain stem tissue were recorded and analyzed. The emergence of endotherm thermal domains in DSC indicates that the conformation change of biomolecules can absorb and dissipate energy, explaining the viscous behavior of the brain stem. FTIR analyses indicate that the presence of polar functional groups such as amide, phosphate, and carboxyl groups in the biomolecules takes responsibility for the viscous performance of brain stem. Ogden, Fung, and Gent models were adopted to fit the experimental data, and Ogden model is the most apt one in capturing the stiffening of the brain stem with the increasing strain rate.

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.

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