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Constitutive model for fiber-reinforced materials with deformable matrices
J Planas1, G V Guinea, M Elices
1Departamento Ciencia de Materiales, Universidad Politécnica de Madrid, ETSI Caminos, c/ Prof. Aranguren s/n, ES28040-Madrid, Spain.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2007
Summary
This study introduces a simple macroscopic model for fiber-reinforced biological tissues. The model effectively captures microstructural alignment under large deformations, aiding mechanical analysis of complex biological materials.
Area of Science:
- Biomechanics
- Materials Science
- Continuum Mechanics
Background:
- Biological tissues often comprise fibers (e.g., elastin, collagen) within an aqueous matrix, presenting complex microstructures.
- Detailed mechanical analysis based on individual microconstituents is often impractical for these heterogeneous materials.
Purpose of the Study:
- To develop a simplified macroscopic model for fiber-reinforced materials with deformable matrices.
- To create a constitutive equation that homogenizes behavior while retaining key microstructural features of biological tissues.
Main Methods:
- Derived a constitutive equation using virtual work equivalence between fiber-reinforced and equivalent continuum media.
- Model was particularized for incompressible materials and extended to orthotropic biological fibers.
- Employed numerical simulations of uniaxial tests on silk fibers.
Main Results:
- The derived constitutive equation is independent of the control volume used for equivalence.
- The model successfully captures the progressive alignment of microconstituents during large deformations.
- Demonstrated the model's applicability to biological structural tissues.
Conclusions:
- The proposed macroscopic model offers a practical approach to understanding the mechanical behavior of fiber-reinforced biological materials.
- The model's ability to simulate microconstituent alignment under strain is validated by silk fiber tests.
- This work provides a valuable tool for analyzing complex biological structures.
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