### Homogenous Numerical Models for Porous Hyperelastic Materials

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#### Abstract

In this work, a general micromechanics framework for the development of constitutive models of the large-strain deformation of porous elastomeric materials is developped. The framework is applicable to any type of isotropic hyperelastic matrix material which obeys pointwise incompressibility: such as the Neo–Hookean, Mooney–Rivlin and Ogden model. The strain energy density function depends on the properties of the incompressible hyperelastic matrix material, the initial level of porosity, and the macroscopic deformation. The constitutive model is used to predict the stress–strain behavior of the pore-containing matrix as a function of initial porosity and macroscopic loading conditions. As an example, a constitutive model is analytically developed for a porous Neo–Hookean material. The stress is observed to depend on the material properties of the elastomers matrix, the initial void volume fraction (porosity) and the applied state of strain. Constitutive model predictions compared well with those obtained from a numerical three-dimensional micromechanical cell model for a range of initial void volume fractions and tensile load cases. The applicability of the model to compressive loading situations is discussed, such as uniaxial compression. *Copyright © 2015 Praise Worthy Prize - All rights reserved.*

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C.O. Horgan and D.A. Polignone. Cavitation in nonlinear elastic solids, A review, Appl. Mech. 48, pp. 471–85, 1995.

http://dx.doi.org/10.1115/1.3005108

M.C. Boyce and E.M. Arruda. Constitutive models of rubber elasticity, A review, Rubber Chem. Tech. 191, pp 4971–5005, 2002.

http://dx.doi.org/10.5254/1.3547602

Z. Hashin. Analysis of composite materials a survey, Journal of Applied Mechanics. 50, pp 481–505, 1983,.

http://dx.doi.org/10.1115/1.3167081

R. Hill. On constitutive macro-variables for heterogeneous solids at finite strain, Proceedings of the Royal Society London. Series A 326, pp 131–147, 1972.

http://dx.doi.org/10.1098/rspa.1972.0001

S. Nemat-Nasser, M. Hori. Micromechanics: Overall Properties of Heterogeneous Materials. North-Holland Series in: Applied Mathematics and Mechanics, vol. 37,1993.

http://dx.doi.org/10.1016/b978-0-444-89881-4.50004-9

P. Ponte Castaneda, P. Suquet, Nonlinear composites. Advances in Applied Mechanics, 34, pp 171–303, 1998.

http://dx.doi.org/10.1016/s0065-2156(08)70321-1

P.M. Suquet. Elements of Homogenization for Inelastic Solid Mechanics. Homogenization Techniques for Composite Materials. 272, pp. 193–278, 1987.

http://dx.doi.org/10.1007/3-540-17616-0_15

A. Anthoine. Derivation of in-plane characteristics of masonry through homogenization theory. International Journal of Solids and Structures. 32, pp 137–163, 1995.

http://dx.doi.org/10.1016/0020-7683(94)00140-r

J.C. Michel, H. Moulinec, P. Suquet. Effective properties of composite materials with periodic microstructure: a omputational approach. Computer Methods in Applied Mechanics and Engineering. 172, pp 109–143, 1999.

http://dx.doi.org/10.1016/s0045-7825(98)00227-8

K. Terada, N. Kikuchi. A class of general algorithms for multi-scale analyses of heterogeneous media. Computer Methods in Applied Mechanics and Engineering. 190, pp 5427–5464, 2001.

http://dx.doi.org/10.1016/s0045-7825(01)00179-7

R.J.M. Smit, W.A.M. Brekelmans, H.E.H. Meijer. Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modelling. Computer Methods in Applied Mechanics and Engineering. 155, pp 181–192, 1998.

http://dx.doi.org/10.1016/s0045-7825(97)00139-4

C. Miehe, J. Schroder, J. Schotte. Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials. Computer Methods in Applied Mechanics and Engineering. 171, pp 387–418, 1999.

http://dx.doi.org/10.1016/s0045-7825(98)00218-7

V. Kouznetsova, W.A.M. Brekelmans, F.T.P. Baaijens. An approach to micro–macro modelling of heterogeneous materials. Computational Mechanics. 27, pp 37–48, 2001.

http://dx.doi.org/10.1007/s004660000212

M. Danielsson, D.M. Parks, M.C. Boyce. Constitutive modeling of porous hyperelastic materials. Mechanics of Materials. 36, pp 347–358, 2004.

http://dx.doi.org/10.1016/s0167-6636(03)00064-4

P.A. Kakavas. Influence of the cavitation on the post stress-strain fields of compressible Blatz-Ko materials at finite deformation. International journal of solids and structures. 39, pp 783-795, 2002.

http://dx.doi.org/10.1016/s0020-7683(01)00211-6

A.C. Steenbrink, E. Van der Giessen. On cavitation post cavitation and yield in amorphous polymer rubber blends. Journal of the Mechanics and Physics of Solids. 47, pp 843-876, 1999.

http://dx.doi.org/10.1016/s0022-5096(98)00075-1

A.L.Gurson. Continuum theory of ductile rupture by void nucleation and growth: Part I––Yield criteria and flow rules for porous ductile media. ASME Trans., J. Eng. Mater. Technol. 99, Ser. H 1, pp 2–15, 1977.

http://dx.doi.org/10.1115/1.3443401

M. Danielson, M.C. Boyce, D.M. Parks. Micromechanical modelling of porous glassy polymers: The effects of a random microstructure. J. Mech. Phys. Solids. 2003.

M. Haghi, L. Anand. Analysis of strain-hardening viscoplastic thick-walled sphere and cylinder under external pressure. Int. J. Plasticity 7. pp123–140, 1991.

http://dx.doi.org/10.1016/0749-6419(91)90027-v

Hang-sheng hou. Cavitation instability in solids. Massachusetts institute of technologie. 1990.

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