Random Stiffness Tensor of Particulate Composites with Hyper-Elastic Matrix and Imperfect Interface

Area of Science:

• Materials Science
• Computational Mechanics
• Solid Mechanics

Background:

• Previous studies on particulate composites often assumed linear elasticity, limiting their applicability to real-world scenarios with large deformations.
• Understanding the probabilistic characteristics of effective stiffness in inelastic composites is crucial for accurate performance prediction.
• Interphase defects in composites can significantly alter mechanical properties, especially under hyper-elastic conditions.

Purpose of the Study:

• To determine the probabilistic characteristics of effective stiffness for hyper-elastic particulate composites with uncertain interphase defects.
• To analyze the influence of random interphase defects on the stiffness tensor of inelastic composites.
• To extend the applicability of effective stiffness tensor calculations to higher strain levels (up to 0.25).

Main Methods:

• Employed a homogenization method using a single-particle representative volume element (RVE) and finite element analysis.
• Modeled the composite matrix as hyper-elastic and the interphase with semi-spherical voids representing defects.
• Utilized the response function method for analytical relation recovery and compared three probabilistic calculation approaches: stochastic finite element method (SFEM), Monte Carlo simulation, and semi-analytical method.

Main Results:

• The effective stiffness tensor is sensitive to random interface defects within the hyper-elastic range.
• The distribution of the resulting stiffness randomness is non-Gaussian.
• Increased random dispersion of defects has a greater effect on stiffness stochastic characteristics than strain fluctuations.

Conclusions:

• The hyper-elastic modeling approach extends the applicability of effective stiffness tensors for particulate composites.
• The semi-analytical method is less suited for stochastic calculations in the hyper-elastic region compared to the linear elastic region.
• Accurate characterization of interphase defects is critical for predicting the probabilistic behavior of inelastic composites.