Transversely isotropic sequentially laminated composites in finite elasticity

deBotton, Gal

doi:10.1016/j.jmps.2005.01.006

Cited by 87 publications

(65 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Roughly speaking, the idea is to construct a special, but yet sufficiently general, family of random microstructures that permit the exact computation of the resulting homogenization problem. The strategy comprises two main steps: i) the first step [16] consists of an iterated homogenization procedure (or differential scheme) that provides an exact solution for W in terms of an auxiliary dilute problem; ii) the second step [17] (see also [18]) deals with the auxiliary dilute problem which consists in the construction of suitable classes of sequential laminates. The combination of these two steps (see Section 3.3 in [5]) leads to an explicit framework for generating solutions for the total elastic energy W and the local fields, including…”

Section: The Iterative Homogenization Methodsmentioning

confidence: 99%

“…Similarly, the corresponding incremental modulus tensor can be easily computed to take the form (in indicial notation) (17) Upon direct use of (17) and some algebraic manipulation, the macroscopic stability condition (4) can be shown to simplify to (18) where the unit vectors a and b are required to satisfy the (incremental) incompressibility…”

Section: Overall Constitutive Behavior and Stabilitymentioning

confidence: 99%

See 1 more Smart Citation

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

Section: The Iterative Homogenization Methodsmentioning

confidence: 99%

Section: Overall Constitutive Behavior and Stabilitymentioning

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

show abstract

“…[141] and [142]. Later, deBotton and Hariton [143] and deBotton [144] obtained a general expression for the behavior of incompressible sequentially laminated composites in small deformation and finite elasticity and compared their results with Hashin-Shtrikman bounds and proposed estimates of Ponte Castañeda [136]. In passing, we mention that an important application of homogenization is to predict the behavior of fiber-reinforced materials reported in Refs.…”

Section: Introductionmentioning

confidence: 91%

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

185

138

View full text Add to dashboard Cite

The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill-Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE 2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two-and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

show abstract

“…Accordingly, very few exact results for W have been generated thus far [2][3][4][5]. Approximate results have also remained elusive until very recently (see, e.g., [6][7][8] and references therein).…”

Section: Introductionmentioning

confidence: 99%

An Exact Result for the Macroscopic Response of Porous Neo-Hookean Solids

Lopez-Pamies

Idiart

2009

J Elasticity

View full text Add to dashboard Cite

Making use of the particulate microgeometries of Idiart (J. Mech. Phys. Solids 56:2599-2617, 2008), we derive an exact and closed-form result for the macroscopic response of porous Neo-Hookean solids with random microstructures. The stored-energy function is a solution to a Hamilton-Jacobi equation with initial porosity and macroscopic deformation gradient playing the roles of time and space. The main theoretical and practical aspects of the result are discussed.

show abstract

Transversely isotropic sequentially laminated composites in finite elasticity

Cited by 87 publications

References 31 publications

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

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

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

An Exact Result for the Macroscopic Response of Porous Neo-Hookean Solids

Contact Info

Product

Resources

About