A Mechanical Model for Mammalian Tendon

1975 ◽  
Vol 42 (4) ◽  
pp. 755-758 ◽  
Author(s):  
D. E. Beskos ◽  
J. T. Jenkins
Keyword(s):  
Mechanical Model ◽  
Elastic Solid ◽  
Material Behavior ◽  
Circular Cylinders ◽  
Elastic Solids ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite ◽  
Constant Pitch ◽  
Inextensible Fibers ◽  
Nonlinear Elastic

A theoretical model is proposed to describe the mechanical behavior of mammalian tendon. The tendon is modeled as an incompressible fiber-reinforced composite with continuously distributed inextensible fibers. The fibers describe helices with constant pitch on concentric right circular cylinders. The analysis is, essentially, independent of the material behavior and, for example, applies to nonlinear elastic solids and viscoelastic materials. A boundary-value problem for tendon extension is discussed in detail and, for a particular nonlinear elastic solid, the deformation and stress are determined to be in qualitative agreement with existing experimental results.

Universal deformations in inhomogeneous isotropic nonlinear elastic solids

2021 ◽  
Vol 477 (2253) ◽  
Author(s):  
Arash Yavari
Keyword(s):  
Strain Energy ◽  
Elastic Solid ◽  
Necessary Condition ◽  
Density Functions ◽  
Elastic Solids ◽  
Universal Deformations ◽  
Green Strain ◽  
The Right ◽  
Nonlinear Elastic ◽  
Isotropic Solids

Universal (controllable) deformations of an elastic solid are those deformations that can be maintained for all possible strain-energy density functions and suitable boundary tractions. Universal deformations have played a central role in nonlinear elasticity and anelasticity. However, their classification has been mostly established for homogeneous isotropic solids following the seminal works of Ericksen. In this article, we extend Ericksen’s analysis of universal deformations to inhomogeneous compressible and incompressible isotropic solids. We show that a necessary condition for the known universal deformations of homogeneous isotropic solids to be universal for inhomogeneous solids is that inhomogeneities respect the symmetries of the deformations. Symmetries of a deformation are encoded in the symmetries of its pulled-back metric (the right Cauchy–Green strain). We show that this necessary condition is sufficient as well for all the known families of universal deformations except for Family 5.

The Elastic Moduli of a Fiber-Reinforced Composite

1977 ◽  
Vol 44 (1) ◽  
pp. 61-67 ◽  
Author(s):  
A. K. Mal ◽  
A. K. Chatterjee
Keyword(s):  
Spatial Distribution ◽  
Physical Properties ◽  
Elastic Moduli ◽  
Composite Model ◽  
Elastic Matrix ◽  
Circular Cylinders ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite ◽  
The Matrix ◽  
Approximate Formulas

A composite consisting of a homogeneous isotropic elastic matrix containing infinitely long parallel circular cylinders is considered. The cylindrical fibers have identical physical properties and are firmly bonded to the matrix with uniform spatial distribution. Only plane problems are considered. Approximate formulas for the three average elastic moduli of the composite are derived by retaining the interaction between the fibers. The interaction effects are explicitly calculated as functions of the spacing between the fibers. Numerical results for a specific composite model are given.

Failure Prevention in Fiber Reinforced Composite Materials

2001 ◽  
Author(s):  
J. Merodio ◽  
R. Sancibrian ◽  
F. Viadero
Keyword(s):  
Composite Materials ◽  
Fiber Direction ◽  
Fiber Reinforced ◽  
Elastic Solids ◽  
Material Models ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite ◽  
Fiber Reinforced Materials ◽  
Anisotropic Character ◽  
Nonlinear Performance

Abstract The study focuses on instabilities for fiber-reinforced nonlinearly elastic solids under plane deformations. The plane of deformation contains the fiber reinforcement. In particular, fiber kinking and fiber debonding instabilities in fiber-reinforced composite materials are examined in terms of the anisotropic character of the material models. The material models consider simultaneously the material anisotropy and the nonlinear performance of the fiber reinforced materials. Fiber kinking is captured under fiber compresion. Fiber debonding is captured under shearing deformations in the fiber direction.

A New Micromechanical Elasto-Plastic Constitutive Model for Fiber-Reinforced Composite Laminates

2010 ◽  
Vol 654-656 ◽  
pp. 2459-2462 ◽  
Author(s):  
Hua Shan Zhang ◽  
Yi Xia Zhang
Keyword(s):  
Constitutive Model ◽  
Composite Laminates ◽  
Plastic Material ◽  
Material Behavior ◽  
Elastic Behavior ◽  
Matrix Elements ◽  
Fiber Reinforced ◽  
Fiber Reinforced Composite ◽  
Elastic Plastic ◽  
Reinforced Composite

A micromechanical elastic-plastic bridging constitutive model is developed in this paper for accurate representation of material behavior of fiber-reinforced composite laminates. In the bridging constitutive model, elastic behavior is represented by bridging matrix elements and interaction between the average stresses in matrix with those in fibers are included. A transient plastic bridging matrix is developed to describe accurately the elastic-plastic material properties of the fiber reinforced composites, and the effects of the material parameters of matrix and fiber on the bridging matrix elements have been accounted for. The proposed constitutive model is validated against experiment investigation.

Mathematical Model of the Effective Properties of a Fiber Reinforced Composite with a Linearly Graded Transition Zone

2010 ◽  
Vol 38 (4) ◽  
pp. 286-307
Author(s):  
Carey F. Childers
Keyword(s):  
Mathematical Model ◽  
Transition Zone ◽  
Effective Properties ◽  
Local Stress ◽  
Stress And Strain ◽  
Fiber Reinforced ◽  
Strain Fields ◽  
Shear Moduli ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite

Abstract Tires are fabricated using single ply fiber reinforced composite materials, which consist of a set of aligned stiff fibers of steel material embedded in a softer matrix of rubber material. The main goal is to develop a mathematical model to determine the local stress and strain fields for this isotropic fiber and matrix separated by a linearly graded transition zone. This model will then yield expressions for the internal stress and strain fields surrounding a single fiber. The fields will be obtained when radial, axial, and shear loads are applied. The composite is then homogenized to determine its effective mechanical properties—elastic moduli, Poisson ratios, and shear moduli. The model allows for analysis of how composites interact in order to design composites which gain full advantage of their properties.

Connected-Tube MPP Model for Unsupervised 3D Fiber Detection

2020 ◽  
Vol 2020 (14) ◽  
pp. 305-1-305-6
Author(s):  
Tianyu Li ◽  
Camilo G. Aguilar ◽  
Ronald F. Agyei ◽  
Imad A. Hanhan ◽  
Michael D. Sangid ◽  
...  
Keyword(s):  
Composite Material ◽  
Point Process ◽  
Marked Point ◽  
Experimental Results ◽  
Marked Point Process ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite ◽  
Proposed Model ◽  
Cylinder Model ◽  
Reinforced Composite Material

In this paper, we extend our previous 2D connected-tube marked point process (MPP) model to a 3D connected-tube MPP model for fiber detection. In the 3D case, a tube is represented by a cylinder model with two spherical areas at its ends. The spherical area is used to define connection priors that encourage connection of tubes that belong to the same fiber. Since each long fiber can be fitted by a series of connected short tubes, the proposed model is capable of detecting curved long tubes. We present experimental results on fiber-reinforced composite material images to show the performance of our method.

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