Constitutive relations and their time integration for anisotropic elasto-plastic porous materials

A micromechanics-based elastoplastic constitutive model for porous materials is proposed. With an assumption of modified three-dimensional Ramberg–Osgood equation for the compressible matrix material, the variational principle based on a linear comparison composite is applied to study the effective mechanical properties of the porous materials. Analytical expressions of elastoplastic constitutive relations are derived by means of micromechanics principles and homogenization procedures. It is demonstrated that the derived expressions do not involve any additional material constants to be fitted with experimental data. The model can be useful in the prediction of mechanical properties of elastoplastic porous solids.

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Second‐order constitutive relations for transversely isotropic piezoelectric porous materials

The Journal of the Acoustical Society of America ◽

10.1121/1.411915 ◽

1995 ◽

Vol 97 (4) ◽

pp. 2595-2598 ◽

Cited By ~ 3

Author(s):

R. C. Batra ◽

J. S. Yang

Keyword(s):

Porous Materials ◽

Constitutive Relations ◽

Transversely Isotropic ◽

Second Order

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Cellular Materials With Extremely High Negative and Positive Poisson’s Ratios: A Mechanism Based Material Design

Volume 9: Mechanics of Solids, Structures and Fluids ◽

10.1115/imece2013-63598 ◽

2013 ◽

Author(s):

Kwangwon Kim ◽

Jaehyung Ju ◽

Doo-Man Kim

Keyword(s):

Porous Materials ◽

Analytical Model ◽

Compliant Mechanisms ◽

Constitutive Relations ◽

Functional Materials ◽

Material Design ◽

The Other ◽

Yield Strain ◽

Poisson's Ratios ◽

Poisson’S Ratios

In an effort to tailor functional materials with customized anisotropic properties — stiffness and yield strain, we propose porous materials consisting of flexible mesostructures designed from the deformation of a re-entrant auxetic honeycomb and compliant mechanisms. Using an analogy between compliant mechanisms and a cellular material’s deformation, we can tailor in-plane properties of mesostructures; low stiffness and high strain in one direction and high stiffness and low strain in the other direction. Two mesostructures based on hexagonal honeycombs with positive and negative cell angles are generated. An analytical model is developed to obtain effective moduli and yield strains of the porous materials by combining the kinematics of a rigid link mechanism and deformation of flexure hinges. A numerical technique is implemented to the analytical model for nonlinear constitutive relations of the mesostructures and their strain dependent Poisson’s ratios. A Finite Element Analysis (FEA) is used to validate the analytical and numerical model. The moduli and yield strain of a porous aluminum alloy are about 6.3GPa and 0.26% in one direction and about 2.8MPa and 12% in the other direction. The mesostructures have extremely high positive and negative Poisson’s ratios, νxy* (∼ ±40) due to the large rotation of the link member in the transverse direction caused by the input displacement in the longitudinal direction. The mesostructures also show higher moduli for compressive loading due to the contact of slit edges at the center region. This paper demonstrates that compliant mesostructures can be used for a next generation material design in terms of tailoring mechanical properties; moduli, strength, strain, and Poisson’s ratios. The proposed mesostructures can also be easily manufactured using a conventional cutting method.

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