The Mori–Tanaka method for composite materials with nonlinear interface debonding

Tan, Henry; Huang, Y.; Liu, C.; Geubelle, Philippe H.

doi:10.1016/j.ijplas.2004.10.001

Cited by 191 publications

(107 citation statements)

References 83 publications

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“…Other approaches rely on micromechanics [5,24,25]. Most theories, however, are based on phenomenological continuum models of various features of the constitutive response of filled elastomers.…”

Section: Introductionmentioning

confidence: 99%

Multiscale modelling of particle debonding in reinforced elastomers subjected to finite deformations

Matouš

Geubelle

2005

Numerical Meth Engineering

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SUMMARYInterfacial damage nucleation and evolution in reinforced elastomers subjected to finite strains is modelled using the mathematical theory of homogenization based on the asymptotic expansion of unknown variables. The microscale is characterized by a periodic unit cell, which contains particles dispersed in a blend and the particle matrix interface is characterized by a cohesive law. A novel numerical framework based on the perturbed Petrov-Galerkin method for the treatment of nearly incompressible behaviour is employed to solve the resulting boundary value problem on the microscale and the deformation path of a macroscale particle is predefined as in the micro-history recovery procedure. A fully implicit and efficient finite element formulation, including consistent linearization, is presented. The proposed multiscale framework is capable of predicting the non-homogeneous microfields and damage nucleation and propagation along the particle matrix interface, as well as the macroscopic response and mechanical properties of the damaged continuum. Examples are considered involving simple unit cells in order to illustrate the multiscale algorithm and demonstrate the complexity of the underlying physical processes.

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Section: Introductionmentioning

confidence: 99%

Multiscale modelling of particle debonding in reinforced elastomers subjected to finite deformations

Matouš

Geubelle

2005

Numerical Meth Engineering

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“…[29][30][31][32]) and high volume fraction [33]. However, additional structural factors, such as non-random and non-periodic distribution [7] and de-bonding between particles and matrix, are not well modelled by any of these traditional analytical methods [34,35], necessitating the application of multiscale numerical models [36].…”

Section: Multiscale Modellingmentioning

confidence: 99%

Tunability of collagen matrix mechanical properties via multiple modes of mineralization

et al. 2016

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Functionally graded, mineralized collagen tissues exist at soft-to-hard material attachments throughout the body. However, the details of how collagen and hydroxyapatite mineral (HA) interact are not fully understood, hampering efforts to develop tissue-engineered constructs that can assist with repair of injuries at the attachments of soft tissues to bone. In this study, spatial control of mineralization was achieved in collagen matrices using simulated body fluids (SBFs). Based upon previous observations of poor bonding between reconstituted collagen and HA deposited using SBF, we hypothesized that mineralizing collagen in the presence of fetuin (which inhibits surface mineralization) would lead to more mineral deposition within the scaffold and therefore a greater increase in stiffness and toughness compared with collagen mineralized without fetuin. We tested this hypothesis through integrated synthesis, mechanical testing and modelling of graded, mineralized reconstituted collagen constructs. Results supported the hypothesis, and further suggested that mineralization on the interior of reconstituted collagen constructs, as promoted by fetuin, led to superior bonding between HA and collagen. The results provide us guidance for the development of mineralized collagen scaffolds, with implications for bone and tendon-to-bone tissue engineering.

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“…When implemented in the finite element method, the cohesive zone model is capable of simulating interface debonding and sliding. [58][59][60][61][62][63][64][65][66][67][68] The existing cohesive models, however, are all phenomenological because it is difficult to measure directly the cohesive laws for interfaces in experiments. There are some recent experimental studies of microscale cohesive laws, 67,[69][70][71][72][73][74] but none on nanoscale cohesive laws such as for the CNT/polymer interfaces.…”

Section: (Iii)mentioning

confidence: 99%

Continuum Modeling of Interfaces in Polymer Matrix Composites Reinforced by Carbon Nanotubes

Jiang

Tan²,

et al. 2007

NANO

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The interface behavior may significantly influence the mechanical properties of carbon nanotube (CNT)-reinforced composites due to the large interface area per unit volume at the composite. The modeling of CNT/polymer interfaces has been a challenge in the continuum modeling of CNTreinforced composites. This paper presents a review of recent progress to model the CNT/matrix interfaces via a cohesive law established from the van der Waals force. A simple, analytical cohesive law is obtained from the interatomic potential, and is used to study the effect of CNT/matrix interfaces on the macroscopic properties of CNT-reinforced composites.

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The Mori–Tanaka method for composite materials with nonlinear interface debonding

Cited by 191 publications

References 83 publications

Multiscale modelling of particle debonding in reinforced elastomers subjected to finite deformations

Multiscale modelling of particle debonding in reinforced elastomers subjected to finite deformations

Tunability of collagen matrix mechanical properties via multiple modes of mineralization

Continuum Modeling of Interfaces in Polymer Matrix Composites Reinforced by Carbon Nanotubes

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