Onset of macroscopic instabilities in fiber-reinforced elastomers at finite strain

Agoras, M.; Lopez-Pamies, Oscar; Castañeda, Pedro Ponte

doi:10.1016/j.jmps.2009.08.001

Cited by 36 publications

(45 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, the out-of-phase buckling of the fibers could result in a stabilizing effect, this is in contrast to the postcritical behavior of the in-phase buckling of the fibers. For a detailed analysis of possible bifurcation modes on the micro-scale as well as associated possible macroscopic material instabilities, we refer to Triantafyllidis and Maker (1985), Müller (1987), Abeyaratne and Triantafyllidis (1984), Triantafyllidis and Maker (1985), Geymonat et al (1993), Miehe et al (2002), Aubert et al (2008), and Agoras et al (2009) and the references therein.…”

Section: ψ(F ) := Infmentioning

confidence: 99%

“…Applying a Bloch-wave ansatz to a fiber-reinforced composite, the authors showed that the onset of a bifurcation on the micro-scale corresponding to the long-wavelength limit (infinite wavelength) leads to a macroscopic material instability. A detailed computational homogenization analysis of structural instabilities on the micro-scale and possible material instabilities on the macro-scale as well as their interactions is performed in Miehe et al (2002), in this context see also Agoras et al (2009) and Aubert et al (2008). A microscopic bifurcation condition of cellular solids, like elastic cellular honeycombs, have been presented in Ohno et al (2002).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A numerical two-scale homogenization scheme: the FE2-method

Schröder

2014

CISM International Centre for Mechanical Sciences

110

123

View full text Add to dashboard Cite

A wide class of micro-heterogeneous materials is designed to satisfy the advanced challenges of modern materials occurring in a variety of technical applications. The effective macroscopic properties of such materials are governed by the complex interaction of the individual constituents of the associated microstructure. A sufficient macroscopic phenomenological description of these materials up to a certain order of accuracy can be very complicated or even impossible. On the contrary, a whole resolution of the fine scale for the macroscopic boundary value problem by means of a classical discretization technique seems to be too elaborate. Instead of developing a macroscopic phenomenological constitutive law, it is possible to attach a representative volume element (RVE ) of the microstructure at each point of the macrostructure; this results in a two-scale modeling scheme. A discrete version of this scheme performing finite element (FE) discretizations of the boundary value problems on both scales, the macro-and the micro-scale, is denoted as the FE 2 -method or as the multilevel finite element method. The main advantage of this procedure is based on the fact that we do not have to define a macroscopic phenomenological constitutive law; this is replaced by suitable averages of stress measures and deformation tensors over the microstructure. Details concerning the definition of the macroscopic quantities in terms of their microscopic counterparts, the definition/construction of boundary conditions on the RVE as well as the consistent linearization of the macroscopic constitutive equations are discussed in this contribution. Furthermore, remarks concerning stability problems on both scales as well as their interactions are given and representative numerical examples for elasto-plastic microstructures are discussed.

show abstract

Section: ψ(F ) := Infmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A numerical two-scale homogenization scheme: the FE2-method

Schröder

2014

CISM International Centre for Mechanical Sciences

110

123

View full text Add to dashboard Cite

show abstract

“…, it is not difficult to show that: along an arbitrary loading path with starting point F = I, the macroscopic stability condition (18) first ceases to hold true at critical deformations cr F with (19) As discussed in Section 6.1 of [5] (see also [25]), the critical condition (19) has a direct physical interpretation. Indeed, the fourth invariant 4 I is a measure of the applied stretch along the fiber direction.…”

Section: Overall Constitutive Behavior and Stabilitymentioning

confidence: 99%

“…We begin by solving equation (10) (20) where (21)  1 is a scalar function of the principal invariants 1 I , 4 I , 5 I given by (22) and (23) Here, it is fitting to remark that (20) We are now in a position to utilize the solution (20) in the general equations (5)- On the other hand, the second-order tensor Z introduced in (7) can be shown to specialize to (24) Given (24), it is not difficult to deduce that the eigenvalues of the symmetric secondorder tensor Z T Z defining the Eulerian ellipsoid (6) are given by (25) where (26) are principal transversely isotropic invariants of …”

Section: Microstructure Evolutionmentioning

confidence: 99%

On Microstructure Evolution in Fiber-Reinforced Elastomers and Implications for Their Mechanical Response and Stability

Lopez-Pamies

Idiart

2010

Journal of Engineering Materials and Technology

View full text Add to dashboard Cite

S S S t t t o o o n n n y y y B B B r r r o o o o o o k k k U U U n n n i i i v v v e e e r r r s s s i i i t t t y y yThe official electronic file of this thesis or dissertation is maintained by the University Libraries on behalf of The Graduate School at Stony Brook University. Master of Science in Mechanical EngineeringStony Brook University May 2010Copyright by Zhiyun Li 2010ii Stony Brook UniversityThe Graduate School Zhiyun LiWe, the thesis committee for the above candidate for the homogenization theory with the capability to generate exact results not only for the macroscopic response and stability, but also for the evolution of the microstructure in fiber-reinforced hyperelastic solids subjected to finite deformations. In this thesis, we make use of this new theory to construct exact, closed-form solutions for the change in size, shape, and orientation undergone by the underlying fibers in a model class of fiberreinforced hyperelastic solids along arbitrary 3D loading conditions. Making use of these results we then establish connections between the evolution of the microstructure and the overall stress-strain relation and macroscopic stability in fiber-reinforced elastomers. In particular, we show that the rotation of the fibers may lead to the softening of the overall stiffness of fiber-reinforced elastomers under certain loading conditions. Furthermore, weshow that this geometric mechanism is intimately related to the development of longiv wavelength instabilities. These findings are discussed in light of comparisons with recent results for related material systems.

show abstract

“…Email addresses: bertoldi@seas.harvard.edu (Katia Bertoldi), pamies@illinois.edu (Oscar Lopez-Pamies) Since 2D idealizations of fiber-reinforced materials -utilized by Rosen [10] and later formalized by Triantafyllidis and Maker [11] in their classical works -are known to lead to results that are qualitatively similar to their 3D counterparts [12,13], here we consider a 2D periodic distribution of long aligned fibers that are bonded to a matrix phase through interphases. Thus we focus on fiber-reinforced elastomers made up of layers of three different materials (r = 1, 2, 3), with volume fractions c…”

Section: Introductionmentioning

confidence: 99%

Some Remarks on the Effect of Interphases on the Mechanical Response and Stability of Fiber-Reinforced Elastomers

Bertoldi

Lopez-Pamies

2012

Journal of Applied Mechanics

View full text Add to dashboard Cite

In filled elastomers, the mechanical behavior of the material surrounding the fillers -termed interphasial material-can be significantly different (softer or stiffer) from the bulk behavior of the elastomeric matrix. In this paper, motivated by recent experiments, we study the effect that such interphases can have on the mechanical response and stability of fiber-reinforced elastomers at large deformations. We work out in particular analytical solutions for the overall response and onset of microscopic and macroscopic instabilities in axially stretched 2D fiber-reinforced nonlinear elastic solids. These solutions generalize the classical results of Rosen (1965, “Mechanics of Composite Strengthening,” Fiber Composite Materials, American Society for Metals, Materials Park, OH, pp. 37–75), and Triantafyllidis and Maker (1985, “On the Comparison between Microscopic and Macroscopic Instability Mechanisms in a Class of Fiber-Reinforced Composites,” J. Appl. Mech., 52, pp. 794–800), for materials without interphases. It is found that while the presence of interphases does not significantly affect the overall axial response of fiber-reinforced materials, it can have a drastic effect on their stability.

show abstract

Onset of macroscopic instabilities in fiber-reinforced elastomers at finite strain

Cited by 36 publications

References 46 publications

A numerical two-scale homogenization scheme: the FE2-method

A numerical two-scale homogenization scheme: the FE2-method

On Microstructure Evolution in Fiber-Reinforced Elastomers and Implications for Their Mechanical Response and Stability

Some Remarks on the Effect of Interphases on the Mechanical Response and Stability of Fiber-Reinforced Elastomers

Contact Info

Product

Resources

About