Formulation and Analysis of a Dynamic Fiber Composite Continuum Model of the Tympanic Membrane

A fibrous dynamic continuum model of the tympanic membrane

The Journal of the Acoustical Society of America ◽

10.1121/1.394284 ◽

1986 ◽

Vol 80 (6) ◽

pp. 1716-1728 ◽

Cited By ~ 33

Author(s):

Richard D. Rabbitt ◽

Mark H. Holmes

Keyword(s):

Tympanic Membrane ◽

Continuum Model

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A Simple Continuum Model of Creep in a Fiber Composite Beam

Journal of Applied Mechanics ◽

10.1115/1.2900744 ◽

1993 ◽

Vol 60 (1) ◽

pp. 190-194 ◽

Cited By ~ 4

Author(s):

J. T. Evans

Keyword(s):

Tensile Stress ◽

Linear Model ◽

Composite Beam ◽

Continuum Model ◽

Fiber Composite ◽

Life Time ◽

Square Root ◽

Simple Linear Model ◽

Time Prediction ◽

Fiber Reinforced Materials

A simple linear model of creep of a fiber composite beam treated as a continuum is presented. The model predicts that the displacement of a tip-loaded cantilever is linear with time but that the surface tensile stress increases approximately with the square root of time. The increase in tensile stress is in line with the prediction of stress channelling in the theory of ideal fiber-reinforced materials. The results are discussed in relation to some previous experimental observations and a generalization of the model which might be of value in life-time prediction is suggested.

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Compressive Failure of Fiber Composites: A Homogenized, Mesh-Independent Model

Journal of Applied Mechanics ◽

10.1115/1.4039754 ◽

2018 ◽

Vol 85 (9) ◽

Cited By ~ 4

Author(s):

Armanj D. Hasanyan ◽

Anthony M. Waas

Keyword(s):

Continuum Model ◽

Degrees Of Freedom ◽

Fiber Composite ◽

Matrix Material ◽

Fiber Composites ◽

Length Scale ◽

Compressive Failure ◽

Localized Deformation ◽

Micropolar Continuum ◽

The Continuum

Micromechanics models of fiber kinking provide insight into the compressive failure mechanism of fiber reinforced composites, but are computationally inefficient in capturing the progressive damage and failure of the material. A homogenized model is desirable for this purpose. Yet, if a proper length scale is not incorporated into the continuum, the resulting implementation becomes mesh dependent when a numerical approach is used for computation. In this paper, a micropolar continuum is discussed to characterize the compressive failure of fiber composites dominated by kinking. Kink banding is an instability associated with a snap-back behavior in the load–displacement response, leading to the formation of a finite region of localized deformation. The challenge in modeling this mode of failure is the inherent geometric and matrix material nonlinearity that must be considered. To overcome the mesh dependency of numerical results, a length scale is naturally introduced when modeling the composite as a micropolar continuum. A new approach is presented to approximate the effective transversely isotropic micropolar constitutive relation of a fiber composite. Using an updated Lagrangian, nonlinear finite element code, previously developed for incorporating the additional rotational degrees-of-freedom (DOFs) of micropolar theory, the simulation of localized deformation in a continuum model, corresponding to fiber kinking, is demonstrated and is found to be comparable with the micromechanics simulation results. Most importantly, the elusive kink band width is a natural outcome of the continuum model.

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