A Multiscale Approach to Modeling the Passive Mechanical Contribution of Cells in Tissues

In addition to their obvious biological roles in tissue function, cells often play a significant mechanical role through a combination of passive and active behaviors. This study focused on the passive mechanical contribution of cells in tissues by improving our multiscale model via the addition of cells, which were treated as dilute spherical inclusions. The first set of simulations considered a rigid cell, with the surrounding ECM modeled as (1) linear elastic, (2) Neo-Hookean, and (3) a fiber network. Comparison with the classical composite theory for rigid inclusions showed close agreement at low cell volume fraction. The fiber network case exhibited nonlinear stress–strain behavior and Poisson's ratios larger than the elastic limit of 0.5, characteristics similar to those of biological tissues. The second set of simulations used a fiber network for both the cell (simulating cytoskeletal filaments) and matrix, and investigated the effect of varying relative stiffness between the cell and matrix, as well as the effect of a cytoplasmic pressure to enforce incompressibility of the cell. Results showed that the ECM network exerted negligible compression on the cell, even when the stiffness of fibers in the network was increased relative to the cell. Introduction of a cytoplasmic pressure significantly increased the stresses in the cell filament network, and altered how the cell changed its shape under tension. Findings from this study have implications on understanding how cells interact with their surrounding ECM, as well as in the context of mechanosensation.

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Mechanical properties and mechanical behavior of (SiO2)f/SiO2 composites with 3D six-directional braided quartz fiber preform

Science and Engineering of Composite Materials ◽

10.1515/secm-2011-0134 ◽

2012 ◽

Vol 19 (2) ◽

pp. 113-117 ◽

Cited By ~ 3

Author(s):

Yong Liu ◽

Zhaofeng Chen ◽

Jianxun Zhu ◽

Yun Jiang ◽

Binbin Li

Keyword(s):

Mechanical Properties ◽

Volume Fraction ◽

Thermal Structure ◽

Three Dimensional ◽

Shear Loading ◽

Failure Behavior ◽

Fiber Volume ◽

Strain Behavior ◽

Highly Nonlinear ◽

Nonlinear Stress

Abstract(SiO2)f/SiO2 composites reinforced with three-dimensional (3D) six-directional preform were fabricated by the silicasol-infiltration-sintering method. The nominal fiber volume fraction was 47%. To characterize the mechanical properties of the composites, mechanical testing was carried out under various loading conditions, including tensile, flexural, and shear loading. The composite exhibited highly nonlinear stress-strain behavior under all the three types of loading. The results indicated that the 3D six-directional braided (SiO2)f/SiO2 composites exhibited superior flexural properties and good shear resistant as compared with other types of preform (2.5D and 3D four-directional)-reinforced (SiO2)f/SiO2 composites. 3D six-directional braided (SiO2)f/SiO2 composite exhibited graceful failure behavior under loading. The addition of 5th and 6th yarns resulted in controlled fracture and hence these 3D six-directional braided composites could possibly be suitable for thermal structure components.

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Deformation in Multilayer Stacked Assemblies

Journal of Electronic Packaging ◽

10.1115/1.2904337 ◽

1990 ◽

Vol 112 (1) ◽

pp. 30-34 ◽

Cited By ~ 29

Author(s):

Tsung-Yu Pan ◽

Yi-Hsin Pao

Keyword(s):

Thermal Loading ◽

Bending Moment ◽

Radius Of Curvature ◽

Element Analysis ◽

First Order ◽

Strain Behavior ◽

Linear Elastic ◽

Nonlinear Stress ◽

Order Polynomial ◽

Vertical Displacements

A linear-elastic analytical model has been developed to describe the deformed geometry of a multi-layered stack assembly subject to thermal loading. The model is based on Timoshenko’s bimetal thermostat analysis [1] and consists of a series of first-order polynomial equations. The radius of curvature, bending moment, force, horizontal and vertical displacements can be determined numerically. These quantities match well with finite element analysis. Calculations for silicon power transistor stacks are presented in order to demonstrate the model capability. The results from this analyitcal model have been found to correlate well with experimental measurements when an appropriate secant modulus is used to represent the nonlinear stress-strain behavior of solder.

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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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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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Observation of dislocations in dynamically loaded Cu-SiO2

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100143705 ◽

1986 ◽

Vol 44 ◽

pp. 424-425

Author(s):

D. S. Pritchard

Keyword(s):

Electron Microscope ◽

Strain Rate ◽

Single Crystal ◽

Transmission Electron Microscope ◽

Volume Fraction ◽

Screw Dislocations ◽

Spherical Inclusions ◽

Transmission Electron ◽

Crystal Dispersion ◽

Strain Rate Loading

The effect of varying the strain rate loading conditions in compression on a copper single crystal dispersion-hardened with SiO2 particles has been examined. These particles appear as small spherical inclusions in the copper lattice and have a volume fraction of 0.6%. The structure of representative crystals was examined prior to any testing on a transmission electron microscope (TEM) to determine the nature of the dislocations initially present in the tested crystals. Only a few scattered edge and screw dislocations were viewed in those specimens.

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Cord/Rubber Material Properties

Rubber Chemistry and Technology ◽

10.5254/1.3536096 ◽

1985 ◽

Vol 58 (4) ◽

pp. 830-856 ◽

Cited By ~ 20

Author(s):

R. J. Cembrola ◽

T. J. Dudek

Keyword(s):

Finite Element ◽

Material Model ◽

Rubber Composites ◽

Stress Strain ◽

Element Analysis ◽

Rubber Layer ◽

Strain Behavior ◽

Nonlinear Stress ◽

Interlaminar Shear ◽

Mechanics Of Composite Materials

Abstract Recent developments in nonlinear finite element methods (FEM) and mechanics of composite materials have made it possible to handle complex tire mechanics problems involving large deformations and moderate strains. The development of an accurate material model for cord/rubber composites is a necessary requirement for the application of these powerful finite element programs to practical problems but involves numerous complexities. Difficulties associated with the application of classical lamination theory to cord/rubber composites were reviewed. The complexity of the material characterization of cord/rubber composites by experimental means was also discussed. This complexity arises from the highly anisotropic properties of twisted cords and the nonlinear stress—strain behavior of the laminates. Micromechanics theories, which have been successfully applied to hard composites (i.e., graphite—epoxy) have been shown to be inadequate in predicting some of the properties of the calendered fabric ply material from the properties of the cord and rubber. Finite element models which include an interply rubber layer to account for the interlaminar shear have been shown to give a better representation of cord/rubber laminate behavior in tension and bending. The application of finite element analysis to more refined models of complex structures like tires, however, requires the development of a more realistic material model which would account for the nonlinear stress—strain properties of cord/rubber composites.

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Continuum Description of the Time- and Strain-Dependent Poisson’s Ratio of Ligament Under Finite Deformation

Volume 1B: Extremity; Fluid Mechanics; Gait; Growth, Remodeling, and Repair; Heart Valves; Injury Biomechanics; Mechanotransduction and Sub-Cellular Biophysics; MultiScale Biotransport; Muscle, Tendon and Ligament; Musculoskeletal Devices; Multiscale Mechanics; Thermal Medicine; Ocular Biomechanics; Pediatric Hemodynamics; Pericellular Phenomena; Tissue Mechanics; Biotransport Design and Devices; Spine; Stent Device Hemodynamics; Vascular Solid Mechanics; Student Paper and Design Competitions ◽

10.1115/sbc2013-14323 ◽

2013 ◽

Author(s):

Aaron M. Swedberg ◽

Shawn P. Reese ◽

Steve A. Maas ◽

Benjamin J. Ellis ◽

Jeffrey A. Weiss

Keyword(s):

Large Scale ◽

Mechanical Response ◽

Tensile Deformation ◽

Large Strain ◽

Fiber Direction ◽

Strain Behavior ◽

Nonlinear Stress ◽

Poisson's Ratios ◽

Poisson’S Ratios ◽

Strain Dependent

Ligament volumetric behavior controls fluid and thus nutrient movement as well as the mechanical response of the tissue to applied loads. The reported Poisson’s ratios for tendon and ligament subjected to tensile deformation loading along the fiber direction are large, ranging from 0.8 ± 0.3 in rat tail tendon fascicles [1] to 2.98 ± 2.59 in bovine flexor tendon [2]. These Poisson’s ratios are indicative of volume loss and thus fluid exudation [3,4]. We have developed micromechanical finite element models that can reproduce both the characteristic nonlinear stress-strain behavior and large, strain-dependent Poisson’s ratios seen in tendons and ligaments [5], but these models are computationally expensive and unfeasible for large scale, whole joint models. The objectives of this research were to develop an anisotropic, continuum based constitutive model for ligaments and tendons that can describe strain-dependent Poisson’s ratios much larger than the isotropic limit of 0.5. Further, we sought to demonstrate the ability of the model to describe experimental data, and to show that the model can be combined with biphasic theory to describe the rate- and time-dependent behavior of ligament and tendon.

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A Multiscale Approach to Modeling the Passive Mechanical Contribution of Cells in Tissues

10.1115/sbc2013-14533 ◽

2013 ◽

Author(s):

Victor K. Lai ◽

Mohammad F. Hadi ◽

Robert T. Tranquillo ◽

Victor H. Barocas

Keyword(s):

Extracellular Matrix ◽

Soft Tissues ◽

Multiscale Model ◽

Tissue Mechanics ◽

Multiscale Approach ◽

Cellular Solids ◽

Comprehensive Model ◽

Modeling Framework ◽

Tissue Biomechanics ◽

Tensegrity Model

In addition to their obvious biological roles in tissue function, cells often play a significant mechanical role through a combination of passive and active behaviors. Phenomenological and continuum modeling approaches to understand tissue biomechanics have included improved constitutive laws that incorporate anisotropy in the extracellular matrix (ECM) and/or cellular phenomenon, e.g, [1]. The lack of microstructural detail in these models, however, limits their ability to explore the respective contributions and interactions between different components within a tissue. In contrast, structural approaches attempt to understand tissue biomechanics by incorporating microstructural details directly into the model, e.g., the tensegrity model [2], cellular solids models [3], or biopolymer models [4]. Research in our group focuses on developing a comprehensive model to predict the mechanical behavior of soft tissues via a multiscale approach, a technique that allows integration of the microstructural details of different components into the modeling framework. A significant gap in our previous models, however, is the absence of cells. The current work represents an improvement of the multiscale model via the addition of cells, and investigates the passive mechanical contribution of cells to overall tissue mechanics.

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