Mechanics of Biomacromolecular Networks Containing Folded Domains

The force-extension behavior of single modular biomacromolecules is known to exhibit a characteristic repeating pattern of a nonlinear rise in force with imposed displacement to a peak, followed by a significant force drop upon reaching the peak. This “saw-tooth” pattern is a result of stretch-induced unfolding of modules along the molecular chain and is speculated to play a governing role in the function of biological materials and structures. In this paper, constitutive models for the large strain deformation of networks of modular macromolecules are developed building directly from statistical mechanics based models of the single molecule force-extension behavior. The proposed two-dimensional network model has applicability to biological membrane skeletons and the three-dimensional network model emulates cytoskeletal networks, natural fibers, and soft biological tissues. Simulations of the uniaxial and multiaxial stress-strain behavior of these networks illustrate the macroscopic membrane and solid stretching conditions which activate unfolding in these microstructures. The models simultaneously track the evolution in underlying microstructural features with different macroscopic stretching conditions, including the evolution in molecular orientation and the forces acting on the constituent molecular chains and junctions. The effect of network pretension on the stress-strain behavior and the macroscopic stress and strain conditions which trigger unfolding are presented. The implications of the predicted stress-strain behaviors on a variety of biological materials are discussed.

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Protein Forced Unfolding and Its Effects on the Finite Deformation Stress-Strain Behavior of Biomacromolecular Solids

MRS Proceedings ◽

10.1557/proc-874-l4.3 ◽

2005 ◽

Vol 874 ◽

Cited By ~ 3

Author(s):

H. Jerry Qi ◽

Christine Ortiz ◽

Mary C. Boyce

Keyword(s):

Constitutive Model ◽

Single Molecule ◽

Biological Networks ◽

Finite Deformation ◽

State Theory ◽

Force Extension ◽

Stress Strain ◽

Strain Behavior ◽

Mechanics Model ◽

Deformation Stress

AbstractMany proteins have been experimentally observed to exhibit a force-extension behavior with a characteristic repeating pattern of a nonlinear rise in force with imposed displacement to a peak, followed by a significant force drop upon reaching the peak (a “saw-tooth” profile) due to successive unfolding of modules during extension. This behavior is speculated to play a governing role in biological and mechanical functions of natural materials and biological networks composed of assemblies of such protein molecules. In this paper, a constitutive model for the finite deformation stress-strain behavior of crosslinked networks of modular macromolecules is developed. The force-extension behavior of the individual modular macromolecule is represented using the Freely Jointed Chain (FJC) statistical mechanics model together with a two-state theory to capture unfolding. The single molecule behavior is then incorporated into a formal continuum mechanics framework to construct a constitutive model. Simulations illustrate a relatively smooth “yield”-like stress-strain behavior of these materials due to activate unfolding in these microstructures.

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Percolation of collagen stress in a random network model of the alveolar wall

Scientific Reports ◽

10.1038/s41598-021-95911-w ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Dylan T. Casey ◽

Samer Bou Jawde ◽

Jacob Herrmann ◽

Vitor Mori ◽

J. Matthew Mahoney ◽

...

Keyword(s):

Connective Tissue ◽

Network Model ◽

Random Network ◽

Collagen Fibers ◽

Tissue Mechanics ◽

Alveolar Wall ◽

Stress Strain ◽

Fiber Network ◽

Strain Behavior ◽

Nonlinear Stress

AbstractFibrotic diseases are characterized by progressive and often irreversible scarring of connective tissue in various organs, leading to substantial changes in tissue mechanics largely as a result of alterations in collagen structure. This is particularly important in the lung because its bulk modulus is so critical to the volume changes that take place during breathing. Nevertheless, it remains unclear how fibrotic abnormalities in the mechanical properties of pulmonary connective tissue can be linked to the stiffening of its individual collagen fibers. To address this question, we developed a network model of randomly oriented collagen and elastin fibers to represent pulmonary alveolar wall tissue. We show that the stress–strain behavior of this model arises via the interactions of collagen and elastin fiber networks and is critically dependent on the relative fiber stiffnesses of the individual collagen and elastin fibers themselves. We also show that the progression from linear to nonlinear stress–strain behavior of the model is associated with the percolation of stress across the collagen fiber network, but that the location of the percolation threshold is influenced by the waviness of collagen fibers.

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Development of High Strength Linepipe With Excellent Deformability

24th International Conference on Offshore Mechanics and Arctic Engineering: Volume 3 ◽

10.1115/omae2005-67149 ◽

2005 ◽

Cited By ~ 10

Author(s):

Mitsuhiro Okatsu ◽

Toyohisa Shinmiya ◽

Nobuyuki Ishikawa ◽

Shigeru Endo ◽

Joe Kondo

Keyword(s):

Large Strain ◽

Thermal Strain ◽

Strain Curve ◽

High Strength ◽

Stress Strain ◽

Microstructural Characteristics ◽

Seismic Region ◽

Strain Behavior ◽

Different Types ◽

High Deformability

Extensive studies to develop high deformability linepipe have been conducted. In case of linepipes laid at seismic region, higher resistance to buckling against large strain induced by earthquake related ground movements are required. In order to improve the deformability of pipes, two different types of microstructural control technologies were proposed, base on theoretical and analytical studies on the effect of microstructural characteristics on stress-strain behavior. Grade X65 to X100 linepipes with ferrite-bainite microstructure were manufactured by optimizing the microstructural characteristics. Grade X80 linepipe with bainitic microstructure containing dispersed fine M-A constituents particles was also developed by applying new conceptual TMCP process. Deformability of developed linepipes with two different types of microstructure were evaluated by axial compression test, and all the developed linepipes showed superior resistance to buckling comparing with conventional pipes. Tensile properties after thermal coating of developed high deformability pipe was also investigate. It was shown that increase in yield strength by thermal strain aging was minimized and round-house type stress-strain curve was maintained for the linepipe manufactured by new conceptional TMCP process.

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Mathematical modeling and simulations for large-strain J-shaped diagrams of soft biological tissues

10.1101/275206 ◽

2018 ◽

Author(s):

K. Mitsuhashi ◽

S. Ghosh ◽

H. Koibuchi

Keyword(s):

Degrees Of Freedom ◽

Large Strain ◽

Finsler Geometry ◽

Biological Tissues ◽

Strain Diagram ◽

Stress Strain ◽

Soft Biological Tissues ◽

Stress Region ◽

Animal Skin ◽

2D And 3D

Herein, we study stress-strain diagrams of soft biological tissues such as animal skin, muscles and arteries by Finsler geometry (FG) modeling. The stress-strain diagram of these biological materials is always J-shaped and is composed of toe, heel, linear and failure regions. In the toe region, the stress is zero, and the length of this zero-stress region becomes very large (≃ 150%) in, for example, certain arteries. In this paper, we study long-toe diagrams using two-dimensional (2D) and 3D FG modeling techniques and Monte Carlo (MC) simulations. We find that except for the failure region, large-strain J-shaped diagrams are successfully reproduced by the FG models. This implies that the complex J-shaped curves originate from the interaction between the directional and positional degrees of freedom of polymeric molecules, as implemented in the FG model.

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Structural Constitutive Characterization of the Vocal Fold: Modeling the Fibrous and the Interstitial Matrix Proteins

Advances in Bioengineering ◽

10.1115/imece2004-61298 ◽

2004 ◽

Cited By ~ 1

Author(s):

Roger W. Chan ◽

Thomas H. Siegmund ◽

Kai Zhang ◽

Neeraj Tirunagari ◽

Min Fu

Keyword(s):

Vocal Fold ◽

Sound Production ◽

Large Strain ◽

Stress Strain ◽

Strain Behavior ◽

Nonlinear Viscoelastic ◽

Nonlinear Stress ◽

Deep Layers ◽

Biomechanical Stimuli

The extracellular matrix (ECM) of the human vocal fold is a highly specialized soft connective tissue with a layered microstructure that is optimally tuned for vibration and sound production in response to a unique set of biomechanical stimuli in vivo, including oscillation at amplitudes up to 3–4 mm at magnitudes of acceleration > 200g and at high frequencies (> 100Hz). The vocal fold ECM, commonly called the lamina propria or mucosa, consists of biomacromolecules of two major classes distributed in different densities: (1) fibrous proteins including collagen and elastin fibers that are denser in the deep layers of the ECM, and (2) interstitial proteins like glycosaminoglycans and structural glycoproteins that are scattered throughout the entire ECM [1,2]. Nonlinear viscoelastic response of the vocal fold ECM under different loading conditions has been reported, including strain rate-dependence and hysteresis of tensile stress-strain curves, and nonlinear stress-strain behavior under large-strain shear [3,4].

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Durometer Hardness and the Stress-Strain Behavior of Elastomeric Materials

Rubber Chemistry and Technology ◽

10.5254/1.3547752 ◽

2003 ◽

Vol 76 (2) ◽

pp. 419-435 ◽

Cited By ~ 73

Author(s):

H. J. Qi ◽

K. Joyce ◽

M. C. Boyce

Keyword(s):

Constitutive Model ◽

Hardness Test ◽

Hardness Measurement ◽

Biological Tissues ◽

Stress Strain ◽

Strain Behavior ◽

Initial Modulus ◽

Nonlinear Stress ◽

Simulation Results ◽

D Values

Abstract The Durometer hardness test is one of the most commonly used measurements to qualitatively assess and compare the mechanical behavior of elastomeric and elastomeric-like materials. This paper presents nonlinear finite element simulations of hardness tests which act to provide a mapping of measured Durometer Shore A and D values to the stress-strain behavior of elastomers. In the simulations, the nonlinear stress-strain behavior of the elastomers is first represented using the Gaussian (neo-Hookean) constitutive model. The predictive capability of the simulations is verified by comparison of calculated conversions of Shore A to Shore D values with the guideline conversion chart in ASTM D2240. The simulation results are then used to determine the relationship between the neo-Hookean elastic modulus and Shore A and Shore D values. The simulation results show the elastomer to undergo locally large deformations during hardness testing. In order to assess the potential role of the limiting extensibility of the elastomer on the hardness measurement, simulations are conducted where the elastomer is represented by the non-Gaussian Arruda-Boyce constitutive model. The limiting extensibility is found to predict a higher hardness value for a material with a given initial modulus. This effect is pronounced as the limiting extensibility decreases to less than 5 and eliminates the one-to-one mapping of hardness to modulus. However, the durometer hardness test still can be used as a reasonable approximation of the initial neo-Hookean modulus unless the limiting extensibility is known to be small as is the case in many materials, such as some elastomers and most soft biological tissues.

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Stress-Strain Behavior of Natural Rubber Vulcanized in the Swollen State

Rubber Chemistry and Technology ◽

10.5254/1.3544790 ◽

1971 ◽

Vol 44 (3) ◽

pp. 744-749 ◽

Cited By ~ 3

Author(s):

Colin Price ◽

G. Allen ◽

F. de Candia ◽

M. C. Kirkham ◽

A. Subramaniam

Keyword(s):

Statistical Theory ◽

Natural Rubber ◽

Theory Of Elasticity ◽

Elastic Behavior ◽

Force Extension ◽

Stress Strain ◽

Strain Behavior

Abstract Samples of natural rubber were vulcanized in the presence of n-decane, decalin and o-chlorobenzene. The diluents were then removed, and the force-extension characteristics of the samples studied over the range 1.1<α<2.0. The elastic behavior of the solution-vulcanized elastomers appear to be in much closer agreement with the statistical theory of elasticity than is the case for vulcanizates prepared in the dry state.

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Constitutive Modeling of the Stress-Stretch Behavior of Biological Membranes Containing Folded Domains

MRS Proceedings ◽

10.1557/proc-0898-l14-05 ◽

2005 ◽

Vol 898 ◽

Cited By ~ 1

Author(s):

Melis Arslan ◽

Mary C. Boyce ◽

Hang J. Qi ◽

Christine Ortiz

Keyword(s):

Strain Rates ◽

Macroscopic Strain ◽

Continuum Approach ◽

Force Extension ◽

Stress Strain ◽

Strain Behavior ◽

A Chain ◽

Chain Force ◽

Spectrin Network ◽

Different Levels

AbstractThe mechanical behavior of the red blood cell membrane is governed by the lipid bilayer which resists changes in surface area and the underlying spectrin network which resists changes in shape. The spectrin network can be modeled as an idealized triangulated network. Each spectrin chain consists of folded domains along the length of the chain which can unfold during stretching of the chain. A domain will completely unfold under the application of a chain force of20to35 pNdepending on the rate of imposed chain stretch. During macroscopic stretch of a network, individual chains within the network will experience different levels of chain stretch since the network chains will collectively stretch and rotate to accommodate the imposed stretch. Hence, the stretch on any individual chain will depend on the magnitude and state of macroscopic strain. A microstructurally informed continuum level constitutive model is developed which tracks individual chain deformation behavior as a function of macroscopic strain and also determines the overall macroscopic network stress-strain behavior. Using the introduced continuum approach and statistical mechanics based models of individual chain force-extension behavior, the stress-stretch behavior of the membrane under uniaxial tension is simulated at large stretches and the behavior of the constituent chains is monitored. Domain unfolding occurs within constituent chains during network deformation and the effects of this domain unfolding on the overall macroscopic stress-strain behavior of the network subject to deformation at different strain rates is revealed.

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