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Improved Voigt and Reuss Formulas with the Poisson Effect
1Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB R3T 2N2, Canada.
Materials (Basel, Switzerland)
|August 26, 2022
Summary
The Poisson effect significantly impacts composite material stiffness, contrary to conventional formulas. New models incorporating this effect reveal increased stiffness due to secondary stresses and strains.
Area of Science:
- Materials Science
- Solid Mechanics
- Composite Materials
Background:
- Conventional formulas (Voigt, Reuss) for composite elastic properties neglect the Poisson effect.
- This omission leads to inaccuracies in predicting material behavior, even under ideal conditions.
Purpose of the Study:
- To derive new formulas for composite elastic properties that incorporate the Poisson effect.
- To investigate the influence of the Poisson effect on composite stiffness using finite element models.
Main Methods:
- Derivation of novel elasticity-based formulas accounting for the Poisson effect.
- Development and simulation using two types of finite element models (FEM) to compare scenarios with and without Poisson effect influence.
Main Results:
- The derived formulas generalize the conventional Voigt and Reuss models.
- The Poisson effect introduces secondary strains and stresses, increasing composite stiffness.
- The magnitude of stiffness increase is proportional to the contrast in phase properties.
Conclusions:
- The Poisson effect is crucial for accurate prediction of composite material elastic properties.
- New formulas and FEM simulations provide a more comprehensive understanding, applicable to advanced materials like nanocomposites and functionally graded materials.
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