A micromechanics-based nonlocal constitutive equation for elastic composites containing randomly oriented spheroidal heterogeneities

Monetto, Ilaria; Drugan, W. J.

doi:10.1016/s0022-5096(03)00103-0

Cited by 37 publications

(21 citation statements)

References 16 publications

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“…There are no theoritical estimations for minimum size of VE having anisotropic inclusions [25]. In such cases the accuracy of the numerical simulations is usually established by comparing the scatter in the effective response for different dispersions of reinforcements; this technique was used by Seguardo et al [26] and Pierard et al [27].…”

Section: Size Of Finite Element Model and Checking For Transverse Isomentioning

confidence: 99%

Pseudo-grain discretization and full Mori Tanaka formulation for random heterogeneous media: Predictive abilities for stresses in individual inclusions and the matrix

Jain

Lomov

Abdin

et al. 2013

Composites Science and Technology

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For modelling damage in short fibre composites, both the predictions of the effective properties and the stresses in the individual inclusions and in the matrix are necessary. Mean field theorems are usually used to calculate the effective properties of composite materials, most common among them is Mori-Tanaka formulation. Owing to occasional mathematical and physical admissibility problems with the Mori-Tanaka formulation; a pseudo-grain discretized Mori-Tanaka formulation (PGMT) was proposed in literature. This paper looks at the predictive capabilities for stresses in individual inclusions and matrix as well as the average stresses in inclusion phase for full Mori-Tanaka formulation and PGMT for 2D-orientation of inclusions.The average stresses inside inclusions and the matrix are compared to solutions of full-scale FE models for a wide range of configurations. It was seen that the Mori-Tanaka formulation gave excellent predictions of average stresses in individual inclusions, even when the basic assumptions of Mori-Tanaka were reported to be too simplistic, while the predictions of PGMT were off significantly in all the cases. However, the predictions of the matrix stresses by the two methods were found to be very similar to each other. The average value of stress averaged over the entire inclusion phase was also very close to each other. Mori-Tanaka must be used as the first choice homogenization scheme.

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Section: Size Of Finite Element Model and Checking For Transverse Isomentioning

confidence: 99%

Pseudo-grain discretization and full Mori Tanaka formulation for random heterogeneous media: Predictive abilities for stresses in individual inclusions and the matrix

Jain

Lomov

Abdin

et al. 2013

Composites Science and Technology

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“…here θ (e) is constant, and the constant vector G (e) j is the equivalent temperature gradient which satisfied the definition (29). It can be decomposed two boundary value problems as follows:…”

Section: Boundary Value Problem Relating To the Linear Distribution Omentioning

confidence: 99%

“…It includes the thermo-mechanical coupling effect, thermal-piezoelectricity effect, electro-magnetic thermo-elastic effect [26][27][28][29][30][31]. In order to establish the framework of micro-polar theory subject to the thermo-mechanical interaction, the key issue is to define the equivalent stress, equivalent couple stress, equivalent displacement gradient, equivalent strain tensor, equivalent torsion tensor, equivalent temperature gradient, equivalent heat flux vector and so on for the cellular or periodic structure materials [7,32,33].…”

Section: Introductionmentioning

confidence: 99%

Generalized form of boundary value problems method for material modeled as micro-polar media subjecting to the thermo-mechanical interaction

Zhang

Chu

et al. 2015

Continuum Mech. Thermodyn.

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In this paper, the periodic structure material is modeled as the continuum homogeneous micro-polar media subjecting to thermo-mechanical interaction. Meanwhile, a series of equivalent quantities such as the equivalent stress, couple stress, displacement gradient and torsion tensor were defined by the integral forms of the boundary values of the external surface force, moment, displacement and the angular displacement, and were proved to satisfy the equivalence conditions of virtual work. Based on above works, the displacement boundary value problem was established to deduce the equivalent constitutive equation. Assume the representative volume element is composed of the spatial cross-framework, and applying the boundary value problem of displacement on frame structures, the equivalent elastic coefficients, temperature coefficients of equivalent stress and the temperature gradient coefficients of equivalent couple stress are deduced. In addition, the method can also be extended to the stress boundary value problem to deduce the equivalent constitutive equation. The calculations indicate that the equivalent result can be obtained from the two kinds of boundary value problems.

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“…The numerical calculation of two-point correlation functions (7)-(10) can be performed by using the algorithm described in [14][15][16]. For example, the calculation of the normalized correlation function (7)…”

Section: ∈ ( )mentioning

confidence: 99%

Correlation Functions and Piezoelectromagnetic Properties of Structures Determined by the Method of Correlation Components

Pan’kov

2015

Mech Compos Mater

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A micromechanics-based nonlocal constitutive equation for elastic composites containing randomly oriented spheroidal heterogeneities

Cited by 37 publications

References 16 publications

Pseudo-grain discretization and full Mori Tanaka formulation for random heterogeneous media: Predictive abilities for stresses in individual inclusions and the matrix

Pseudo-grain discretization and full Mori Tanaka formulation for random heterogeneous media: Predictive abilities for stresses in individual inclusions and the matrix

Generalized form of boundary value problems method for material modeled as micro-polar media subjecting to the thermo-mechanical interaction

Correlation Functions and Piezoelectromagnetic Properties of Structures Determined by the Method of Correlation Components

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