Computationally Efficient Concept of Representative Directions for Anisotropic Fibrous Materials

Area of Science:

• Materials Science
• Computational Mechanics
• Polymer Physics

Background:

• Representative directions enable multi-axial constitutive equation generation from uni-axial models.
• Fibrous polymeric materials exhibit inherent anisotropy, requiring specialized analysis methods.

Purpose of the Study:

• To adapt the representative directions concept for anisotropic fibrous polymers using an orientation probability density function (OPDF).
• To develop and compare novel algorithms for generating representative directions aligned with a given OPDF, enhancing computational efficiency.

Main Methods:

• Incorporation of an OPDF to explicitly model material anisotropy.
• Development of three algorithms for generating representative directions: potential energy minimization, equilibration method, and Voronoi cells.
• Comparison of algorithm performance across various OPDFs.

Main Results:

• The second version of the concept, encapsulating anisotropy in direction distribution, proves computationally more efficient.
• The presented algorithms successfully generate representative directions matching specified OPDFs.
• Demonstrated applicability to modeling the mechanical behavior of anisotropic polymers.

Conclusions:

• The modified concept with OPDF is effective for analyzing anisotropic fibrous polymers.
• The developed algorithms offer computationally efficient methods for generating necessary representative directions.
• A calibration procedure is proposed for cases where OPDF is unknown, facilitating practical application.