High-Fidelity Micromechanical Modeling of Continuously Reinforced Elastic Multiphase Materials Undergoing Finite Deformations

Abstract

The purpose of this communication is twofold. First, we demonstrate the predictive capability of a recently extended micromechanics model known as the high-fidelity generalized method of cells, originally developed for unidirectionally reinforced periodic multiphase materials characterized by elastic or elasto-plastic phases undergoing infinitesimal deformation. The recent extension incorporates finite-deformation capabilities to enable modeling of heterogeneous materials such as fiber-reinforced rubbers or certain types of biological tissues characterized by potential-based, nonlinear elastic phases. The model's capability to accurately estimate both the homogenized nonlinear elastic response and the local stress fields in the individual phases is demonstrated by comparison with an exact elasticity solution for a porous composite with four different types of the matrix material under axisyrmnetric loading, and a finite-element analysis of a repeating unit cell representative of a unidirectionally reinforced periodic composite subjected to transverse loading. Second, we demonstrate the micromechanics model's utility as a subroutine in a structural analysis setting by implementing it into a specialized lamination theory framework in the absence of bending. Examples of the nonlinear response of families of [±θ]_s lay-ups under biaxial inplane loading are provided, demonstrating how the developed model can be used either to validate or to construct macroscopic constitutive laws for materials, such as certain biological tissues, characterized by multi-directional reinforcement.

Keywords

micromechanics finite deformations multiphase materials homogenization

Get full access to this article

View all access options for this article.

References

[1] Paley, M. and Aboudi, J. Micromechanical analysis of composites by the generalized method of cells . Mechanics of Materials, 14, 127-139 (1992).

[2] Aboudi, J. , Pindera, M-J. and Armold, S. M. Higher-order theory for functionally graded materials . Composites: Part B (Engineering),>rJ 30, 777-832 (1999).

[3] Aboudi, J. , Pindera, M-J. and Arnold, S. M. Linear thermoelastic higher-order theory for periodic multiphase materials . Journal oqfApplied Mechanics, 68, 697-707 (2001).

[4] Aboudi, J. , Pindera, M-J. and Arnold, S. M. Higher-order theory for periodic multiphase materials with inelastic phases . International Journal of Plasticity 19, 805-847 (2003).

[5] Aboudi, J. High-fidelity micromechanical modeling of elastic multiphase materials undergoing finite deformation: theory. EMC Report No. 2002-1, EMC, Charlottesville, VA , 2002

[6] Aboudi, J. Micromechanical analysis of the fully coupled finite thermoelastic response of rubberlike matrix composites . International Journal ojfSolids & Structures, 39, 2587-2612 (2002).

[7] Holzapfel, G. A. , Gassei; T C. and Ogden, R. W A new constitutive framework for arterial wall mechanics and a comparative study of material models . Journal of Elasticity, 61, 1-48 (2000).

[8] Holzapfel, G. A. and Gassei; T. C. A viscoelastic model for fiber-reinforced composites at finite strains: continuum basis, computational aspects and applications . Computer Methods in Applied Mechanics and Engineering, 190, 4379-4403 (2001).

[9] Holzapfel, G. A. Nonlinear Solid Mechanics, Wiley, New York , 2000h

10.

[10] Aboudi, J. Overall finite deformation of elastic and elastoplastic composites . Mechanics nf/Materials, 5, 73-86 (1986).

11.

[11] Parton, V Z. and Kudiyavtsev, B. A. Engineering Mechanics of Composite Structures, CRC Press, Boca Raton, FL , 1993.

12.

[12] Kalamkarov, A. L. and Kolpakov, A. G. Analysis, Design and Optimization of Composite Structures, Wiley, New York , 1997.

13.

[13] Hill, R. Elastic properties of reinforced solids: some theoretical principles . Journal qf the Mechanics and Physics of Solids, 11, 357-372 (1963).

14.

[14] Ogden, R. W (1984). Non-Linear Elastic Deformnations, Ellis Horwood, Chichester, UK .

15.

[15] Jafari, A. H. , Abeyaratne, R. and Horgan, C. O. The finite deformation of a pressurized circular tube for a class of compressible materials . Zeitschrift fur Angewandte Mathemnatik und Physik, 35, 227-246 (1984).

16.

[16] Haughton, D. M. Inflation and bifurcation of thick-walled compressible elastic spherical shells . IMA Journal of Applied Mathematics, 39, 259-272 (1987).

17.

[17] Blatz, P J. and Ko, W L. Application of finite elastic theory to the deformation of rubbeiy materials . Transactions of the Society for Rheology, 6 223-251 (1962).

18.

[18] Hashin, Z. and Rosen, B. W The elastic moduli of fiber-reinforced materials . Journal of Applied Mechanics, 31, 223-232 (1964).

19.

[19] Sussman, T. and Bathe, K. J. (1987). A finite element formulation of nonlinear incompressible elastic and inelastic analysis . Computers & Structures, 26, 357-409 .

20.

[20] Aboudi, J. and Pindera, M-J. High-fidelity micromechanical modeling of elastic multiphase materials undergoing finite deformation: model validation and user's guide. EMC Report No. 2002-2, EMC, Charlottesville, VA , 2002.

21.

[21] Horgan, C. O. On axisymmetric solutions for compressible nonlinearly elastic solids . Zeitschriftfir Angewvandte Mathematik und Physik, 46, S107-S125 (1995).

22.

[22] Chung, D. T. , Horgan, C. O. and Abeyaratne, R. The finite deformation of internally pressurized hollow cylinders and spheres for a class of compressible elastic materials . hiternational Journal of Solids & Structures, 22, 1557-1570 (1986).