Anisotropic separable free energy functions for elastic and non-elastic solids

Shariff, M. H. B. M.

doi:10.1007/s00707-015-1534-9

Cited by 27 publications

(21 citation statements)

References 40 publications

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“…In this communication, our objective is to develop a novel strain energy function using spectral invariants that contains only single-variable functions. These strain energy types are experimentally attractive [19] and have been fortunate in modelling non-elastic and elastic solids [8][9][10][11][12][13][14][15][16]20,21]. It is important to note that knowing the number of independent invariants facilitates a stringent development of a strain energy via an experiment [22], and in our spectral analysis, we derive that only 11 independent spectral invariants are required in the constitutive equation.…”

Section: Introductionmentioning

confidence: 84%

“…According to Shariff [ 13 ], the strain energy function must satisfy the P -property [ 13 ]. To facilitate the construction of the P -property, the following six independent spectral invariants

are used rather than the invariants

.…”

Section: Spectral Representationmentioning

confidence: 99%

“…The general single-variable functions that depend on a principal stretch

, appearing in

, facilitate the construction of a specific form of strain energy function from experimental data. We note that, recently, separable single-variable strain energy functions have been used to model both elastic and non-elastic solids [ 8 , 9 , 10 , 11 , 12 , 13 , 14 ]. We note in passing that, it is shown in Shariff [ 14 ], the constitutive Equation ( 19 ) has successfully predicted the mechanical behaviour of soft tissues.…”

Section: Transversely Isotropic Elastic Solid Without Residual Strmentioning

confidence: 99%

“…A review on the presence of residual stress, for example, in fiber reinforced composite materials can be found in [7]. In this paper, we focus on the modelling of the mechanical anisotropic response of a residually stressed fiber material with a preferred direction (RSPD) based on the spectral method (method that used the eigenvalues and eigenvectors of tensors) developed recently in the literature [8][9][10][11][12][13][14][15][16]. Applications can be found, for example, in the mathematical modelling of the mechanical behaviour of carbon fibre reinforced solids and other types of RSPD, like soft biological tissue.…”

Section: Introductionmentioning

confidence: 99%

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Residually Stressed Fiber Reinforced Solids: A Spectral Approach

Shariff

Merodio

2020

Materials

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We use a spectral approach to model residually stressed elastic solids that can be applied to carbon fiber reinforced solids with a preferred direction; since the spectral formulation is more general than the classical-invariant formulation, it facilitates the search for an adequate constitutive equation for these solids. The constitutive equation is governed by spectral invariants, where each of them has a direct meaning, and are functions of the preferred direction, the residual stress tensor and the right stretch tensor. Invariants that have a transparent interpretation are useful in assisting the construction of a stringent experiment to seek a specific form of strain energy function. A separable nonlinear (finite strain) strain energy function containing single-variable functions is postulated and the associated infinitesimal strain energy function is straightforwardly obtained from its finite strain counterpart. We prove that only 11 invariants are independent. Some illustrative boundary value calculations are given. The proposed strain energy function can be simply transformed to admit the mechanical influence of compressed fibers to be partially or fully excluded.

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Section: Introductionmentioning

confidence: 84%

“…According to Shariff [ 13 ], the strain energy function must satisfy the P -property [ 13 ]. To facilitate the construction of the P -property, the following six independent spectral invariants

are used rather than the invariants

.…”

Section: Spectral Representationmentioning

confidence: 99%

“…The general single-variable functions that depend on a principal stretch

, appearing in

Section: Transversely Isotropic Elastic Solid Without Residual Strmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Residually Stressed Fiber Reinforced Solids: A Spectral Approach

Shariff

Merodio

2020

Materials

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“…and hence only 13 of the 15 spectral invariants in equation ( 23) are independent. It is important to note that the total energy O in must satisfy the P-property, as described in Shariff [17]. To facilitate the satisfaction of the P-property and to consider that O depends on a a and f f, we express…”

Section: Spectral Representation: a Preferred Direction Electro-elastic Body With Residual Stressesmentioning

confidence: 99%

A nonlinear electro-elastic model with residual stresses and a preferred direction

Shariff

Bustamante

Merodio

2019

Mathematics and Mechanics of Solids

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In this communication, a spectral model is developed for a residually stressed electro-elastic body with a preferred direction. The model uses a total energy function that depends on the right stretch tensor, the residual stress tensor, a preferred direction structural tensor and one of the electric variables. The proposed spectral invariants have a clear physical meaning; using these invariants, we prove that only [Formula: see text] of the [Formula: see text] classical invariants in the corresponding minimal integrity basis are independent. A method for exclusion or partial exclusion of compressed fibres is proposed. Some boundary value problems with cylindrical symmetry are studied. Results for the inflation of a hollow sphere, where the residual stress is assumed to depend only on the radial position, are also given. The spectral constitutive formulation is useful in a rigorous construction of a specific form of the total energy function via appropriate experiments.

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