Effective thermoelastic constants of discretely-fibrous composites with anisotropic components

Khoroshun, L. P.; Leshchenko, P. V.; Nazarenko, L. V.

doi:10.1007/bf00901920

Cited by 2 publications

(3 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Both approaches are well developed for periodic granular composites with isotropic phases; for a review on the subject see [2,4,5]. The statistical theory of deformation and damage of composites with anisotropic phases is developed in [6][7][8]. All well-known applications of the regularization method are restricted to fibrous materials alone [1,4].…”

Section: Introductionmentioning

confidence: 99%

“…Introduction. The best known approaches to predicting the macroscopic properties of structurally inhomogeneous materials are, probably, the stochastic approach based on methods of statistical mechanics [5][6][7][8] and the regularization method [1,2,4,9,12]. The latter consists in modeling a real composite by a periodic structure and solving boundary-value problems, followed by averaging of local fields.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Effective elastic moduli of periodic granular composite with transversely isotropic phases

Кущ

2004

Int Appl Mech

View full text Add to dashboard Cite

We find a rigorous solution describing the macroscopically uniform stress state of a periodic granular composite with transversely isotropic phases. The structure of the composite is modeled by a cube containing a finite number of arbitrarily arranged and oriented, transversely isotropic spherical inclusions. This provides the model with a flexible means of describing the microstructure. Applying periodic vector solutions and local expansion formulas reduces the initial boundary-value problem to a system of linear algebraic equations. By averaging the solution over the unit cell, we derived exact finite expressions for the components of the effective stiffness tensor. The numerical data presented help to evaluate the efficiency of the method and the limits of applicability of available approximate theories.Keywords: periodic granular composite, transversely isotropic elastic phases, periodic structural model, spherical inclusion, effective stiffness tensor 1. Introduction. The best known approaches to predicting the macroscopic properties of structurally inhomogeneous materials are, probably, the stochastic approach based on methods of statistical mechanics [5][6][7][8] and the regularization method [1,2,4,9,12]. The latter consists in modeling a real composite by a periodic structure and solving boundary-value problems, followed by averaging of local fields. Both approaches are well developed for periodic granular composites with isotropic phases; for a review on the subject see [2,4,5]. The statistical theory of deformation and damage of composites with anisotropic phases is developed in [6-8]. All well-known applications of the regularization method are restricted to fibrous materials alone [1,4].In the present paper, we will find a rigorous, asymptotically exact solution describing the elastic equilibrium of a periodic composite with spherical inclusions, assuming transverse isotropy of the phases. The unit cell is a cube containing a finite number of arbitrarily arranged and oriented, transversely isotropic spherical inclusions. This provides the model with a general and flexible means of describing the microstructure [2]. To derive the solution, we will employ the earlier results for a transversely isotropic body with one [10, 11] and several [3] inclusions and a fast-summation method for triple series [12].2. Composite Model. The generalized periodic structural model of a granular composite [2] is an infinite matrix containing periodically arranged spherical inclusions. This model has a unit cell in the form of a cube with side length a containing N spherical inclusions of radius R q centered at points Q q N q , , ,... , = 12 . This cell, when repeated in three mutually perpendicular directions, produces the entire structure of the composite. Both the matrix and inclusions are assumed elastic and

show abstract

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Effective elastic moduli of periodic granular composite with transversely isotropic phases

Кущ

2004

Int Appl Mech

View full text Add to dashboard Cite

show abstract

“…ijkl * is the effective stiffness tensor, which is a function of the elastic moduli of the damaged components, fraction of inclusions, c 1 , and the shape parameter of inclusions, s[6], i.e., 1 and s 2 are the transverse and longitudinal semiaxes of spheroidal inclusions, respectively. The tensors l ijkl defined[24] in terms of the stiffness tensors of the skeletons of the components, l ijkl 1 and l ijkl 2 , and their porosities, p 1 and p 2 , characterizing damage:…”

mentioning

confidence: 99%

Elastic properties and long-term damage of transversely isotropic composites with stress-rupture microstrength described by a fractional-power function

Khoroshun

Nazarenko

2009

Int Appl Mech

Self Cite

View full text Add to dashboard Cite

The damage process is modeled by randomly dispersed micropores occurring in places of destroyed microvolumes according to the stress-rupture microstrength, which is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, according to the Huber-Mises criterion, and is a random function of coordinates. Given microstresses or microstrains, the equations of porosity balance at an arbitrary time are derived. Together with the macrostressmacrostrain relationships for a discrete fibrous composite with porous components, they describe the coupled processes of deformation and long-term damage. A specific problem with a bounded stress-rupture microstrength function is solved Keywords: discrete-fiber-reinforced composite, stochastic structure, long-term damage, porosity balance equationIntroduction. The damage of homogeneous and composite materials, manifested as dispersed microdamages occurred under loading, can be either short-term/instantaneous (at the instant the load is applied) and long-term (accumulation of microdamages after the load is applied). The theory of short-term damage based on the mechanics of stochastically inhomogeneous media is formulated and developed in [7][8][9][10][11][12][13][14][15]. The theory of long-term damage proposed in [21, 23] is a generalization of the theory of short-term damage. It is based on the concept of stress-rupture microstrength, which is a random function of coordinates, and modeling destroyed microvolumes by randomly dispersed micropores.The present paper generalizes the theory of long-term damage to discrete-fiber-reinforced composites of stochastic structure. It is assumed that the matrix is isotropic, while the inclusions are transversely isotropic. Let damage occur in the matrix of the composite. The damage of the matrix is modeled by dispersed microvolumes destroyed to become randomly arranged micropores [7,21]. The failure criterion for a single microvolume is determined by its stress-rupture strength described by a fractional-power function, which is, in turn, determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which characterizes the tensile strength according to the Huber-Mises criterion [1]. The tensile strength is assumed to be a random function of coordinates whose one-point distribution is described by a power function on some interval or by the Weibull function. The effective elastic properties and the stress-strain state of a composite with randomly arranged microdamages are determined from the stochastic equations of elasticity. We will derive the balance equation for destroyed microvolumes from the general properties of the distribution function of tensile microstrength. This will make it possible to set up a closed-form system of equations describing the coupled processes of deformation and long-term damage. We will develop algorithms for calculating the time dependence of microdamage, macrostress, and macrostrain and to pl...

show abstract

Effective thermoelastic constants of discretely-fibrous composites with anisotropic components

Cited by 2 publications

References 1 publication

Effective elastic moduli of periodic granular composite with transversely isotropic phases

Effective elastic moduli of periodic granular composite with transversely isotropic phases

Elastic properties and long-term damage of transversely isotropic composites with stress-rupture microstrength described by a fractional-power function

Contact Info

Product

Resources

About