Continuum Theory of the Mechanics of Fibre-Reinforced Composites

Spencer, A. J. M.; Hashin, Zvi

doi:10.1115/1.3171730

Cited by 133 publications

(170 citation statements)

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“…It is assumed that = is an isotropic scalar function of the tensors (C, a �a , b �b ), and that the two "ber families are mechanically equivalent such that = is symmetric with respect to interchanging the "ber directions a and b � (the dyadic product � is de"ned by (a�b)c"a(bzc) for all vectors a, b, and c and where z denotes the dot product of two vectors). With these assumptions, Spencer (1984) showed that = can be expressed as…”

Section: ) �Cmentioning

confidence: 99%

“…In the theory for a "ber-reinforced continuum, it is assumed that the anisotropic properties of the material are solely attributed to the presence of the families of "bers (Spencer, 1984). For two families of "bers, the directions of the "ber elements are represented by mater ial line elements in the reference con"guration, denoted by the vectors a and b .…”

Section: ) �Cmentioning

confidence: 99%

“…(11) for = were: (1) it contains the necessary terms involving the invariants so that it reduces to the most general quad ratic expression suggested by Spencer (1984) for use in a linear theory, resulting in 9 independent material con stants for a linear orthotropic material; and (2) the de pendence on the various invariants were expressed in separate exponentials which we believe allows for more #exibility in simultaneously matching data from several experimental protocols. We chose an exponential form instead of a polynomial for both strain energy functions as Fung et al (1997) have shown that the exponential form results in smaller coe$cients of variation in mater ial constants determined from experimental data of bio logical tissues.…”

Section: Specixcation Of the Strain Energy Functionmentioning

confidence: 99%

“…The motiva � � � � � � � � � �� tions for choosing the form (9) for = were: (1) by setting b � "0 to recover a one-"ber family theory (i.e., trans verse isotropy), it reduces to that used by Almeida et al (1995); (2) extra terms involving the invariants were ad ded so that it reduces to the most general quadratic expression suggested by Spencer (1984) for use in a linear theory; and (3) these extra terms were included in the single exponential as proposed by Almeida et al (1995).…”

Section: Specixcation Of the Strain Energy Functionmentioning

confidence: 99%

“…Alternatively, we sought to simultaneously consider data from multiple experimental deformations to prescribe the requisite ma terial constants. In developing our constitutive model, we utilized a theory for an isotropic continuum reinforced with two families of "bers (Spencer, 1984).…”

Section: Introductionmentioning

confidence: 99%

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Application of a fiber-reinforced continuum theory to multiple deformations of the annulus fibrosus

Klisch

Lotz

1999

Journal of Biomechanics

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Accurate tissue stress predictions for the annulus fibrosus are essential for understanding the factors that cause or contribute to disc degeneration and mechanical failure. Current computational models used to predict in vivo disc stresses utilize material laws for annular tissue that are not rigorously validated against experimental data. Consequently, predictions of disc stress resulting from physical activities may be inaccurate and therefore unreliable as a basis for defining mechanical-biologic injury criteria. To address this need we present a model for the annulus as an isotropic ground substance reinforced with two families of collagen fibers, and an approach for determining the material constants by simultaneous consideration of multiple experimental data sets. Two strain energy functions for the annulus are proposed and used in the theory to derive the constitutive equations relating the stress to pure stretch deformations. These equations are applied to four distinct experimental protocols and the material constants are determined from a simultaneous, nonlinear regression analysis. Good agreement between theory and experiment is achieved when the invariants are included within multiple, separate exponentials in the strain energy function.

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Section: ) �Cmentioning

confidence: 99%

Section: ) �Cmentioning

confidence: 99%

Section: Specixcation Of the Strain Energy Functionmentioning

confidence: 99%

Section: Specixcation Of the Strain Energy Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Application of a fiber-reinforced continuum theory to multiple deformations of the annulus fibrosus

Klisch

Lotz

1999

Journal of Biomechanics

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The Modeling of Magnetorheological Elastomers: A State‐of‐the‐Art Review

Saber

2023

Adv Eng Mater

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The magnetorheological elastomers (MREs) are novel multifunctional materials wherein their viscoelastic properties can be varied instantly under an application of applied magnetic field. Due to their field‐dependent stiffness and damping properties, MREs are widely used in the development and design of MRE‐based adaptive vibration isolators and absorbers and also biomedical engineering. Moreover, MREs due to their inherent magnetostriction effect have enormous potential for the development of soft actuators. The dynamic behavior of MREs is affected by various material parameters (e.g., matrix and particle types, particle concentration, additives) as well as mechanical and magnetic loading parameters (e.g., frequency, amplitude, temperature, magnetic flux density). Understanding and predicting the effect of materials and loading parameters on the response behavior of MREs are of paramount importance for the design of MRE‐based adaptive structures and systems. This review paper mainly aims to provide a comprehensive study of material constitutive models to predict the nonlinear magnetomechanical behavior of MREs. Particular emphasis is paid to physics‐based models including continuum‐ and microstructure‐based models. Moreover, phenomenological models describing the dynamic magnetoviscoelastic behavior of MREs as well as the effect of temperature on the magnetomechanical behavior of such materials are properly addressed.

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Numerical modelling of the fibre–matrix interaction in biaxial loading for hyperelastic soft tissue models

Lyu

Zhu

Richmond

et al. 2011

Numer Methods Biomed Eng

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This paper assumes that a neo-Hookean matrix with neo-Hookean fibres is representative of soft tissue. Under this assumption, a unit cell model is proposed to investigate the fibre-matrix interfacial stress field for biological soft tissue under biaxial loadings. In this unit cell model, the soft tissue is treated as a composite where the matrix is unidirectionally reinforced with a single family of aligned fibres. The results are compared with the model of Guo et al., which accounts for the fibre-matrix interfacial stress field, and Qiu and Pence's model, which does not proceed from the assumption that the fibres are themselves neo-Hookean. It is found that the stress representative of the fibre-matrix interface plays an important role in the deformation of the composite, and the model of Guo et al. underestimates this stress under large biaxial deformation.

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Continuum Theory of the Mechanics of Fibre-Reinforced Composites

Cited by 133 publications

References 0 publications

Application of a fiber-reinforced continuum theory to multiple deformations of the annulus fibrosus

Application of a fiber-reinforced continuum theory to multiple deformations of the annulus fibrosus

The Modeling of Magnetorheological Elastomers: A State‐of‐the‐Art Review

Numerical modelling of the fibre–matrix interaction in biaxial loading for hyperelastic soft tissue models

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