Probabilistic homogenization of hyper-elastic particulate composites with random interface

2020 ◽  
Vol 241 ◽  
pp. 112118 ◽  
Author(s):  
Damian Sokołowski ◽  
Marcin Kamiński
Keyword(s):  
Particulate Composites ◽  
Random Interface ◽  
Hyper Elastic

scholarly journals Energy Fluctuations in the Homogenized Hyper-Elastic Particulate Composites with Stochastic Interface Defects

Energies ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 2011
Author(s):  
Damian Sokołowski ◽  
Marcin Kamiński ◽  
Artur Wirowski
Keyword(s):  
Perturbation Method ◽  
Volume Fraction ◽  
Stochastic Perturbation ◽  
Fem Analysis ◽  
Spherical Shape ◽  
Deformation Energy ◽  
Particulate Composites ◽  
Interface Defects ◽  
Hyper Elastic ◽  
Stochastic Perturbation Method

The principle aim of this study is to analyze deformation energy of hyper-elastic particulate composites, which is the basis for their further probabilistic homogenization. These composites have some uncertain interface defects, which are modelled as small semi-spheres with random radius and with bases positioned on the particle-matrix interface. These defects are smeared into thin layer of the interphase surrounding the reinforcing particle introduced as the third component of this composite. Matrix properties are determined from the experimental tests of Laripur LPR 5020 High Density Polyurethane (HDPU). It is strengthened with the Carbon Black particles of spherical shape. The Arruda–Boyce potential has been selected for numerical experiments as fitting the best stress-strain curves for the matrix behavior. A homogenization procedure is numerically implemented using the cubic Representative Volume Element (RVE). Spherical particle is located centrally, and computations of deformation energy probabilistic characteristics are carried out using the Iterative Stochastic Finite Element Method (ISFEM). This ISFEM is implemented in the algebra system MAPLE 2019 as dual approach based upon the stochastic perturbation method and, independently, upon a classical Monte-Carlo simulation, and uniform uniaxial deformations of this RVE are determined in the system ABAQUS and its 20-noded solid hexahedral finite elements. Computational experiments include initial deterministic numerical error analysis and the basic probabilistic characteristics, i.e., expectations, deviations, skewness and kurtosis of the deformation energy. They are performed for various expected values of the defects volume fraction. We analyze numerically (1) if randomness of homogenized deformation energy can correspond to the normal distribution, (2) how variability of the interface defects volume fraction affects the deterministic and stochastic characteristics of composite deformation energy and (3) whether the stochastic perturbation method is efficient in deformation energy computations (and in FEM analysis) of hyper-elastic media.

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

Materials ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 6676
Author(s):  
Damian Sokołowski ◽  
Marcin Kamiński
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Method ◽  
Volume Fraction ◽  
Effective Stiffness ◽  
Particulate Composites ◽  
Stiffness Tensor ◽  
The Matrix ◽  
Hyper Elastic

The main aim of this study is determination of the basic probabilistic characteristics of the effective stiffness for inelastic particulate composites with spherical reinforcement and an uncertain Gaussian volume fraction of the interphase defects. This is determined using a homogenization method with a cubic single-particle representative volume element (RVE) of such a composite and the finite element method solution. A reinforcing particle is spherical, located centrally in the RVE, surrounded by the thin interphase of constant thickness, and remains in an elastic reversible regime opposite to the matrix, which is hyper-elastic. The interphase defects are represented as semi-spherical voids, which are placed on the outer surface of this particle. The interphase is modeled as hyper-elastic and isotropic, whose effective stiffness is calculated by the spatial averaging of hyper-elastic parameters of the matrix and of the defects. A constitutive relation of the matrix is recovered experimentally by its uniaxial stretch. The 3D homogenization problem solution is based upon a numerical determination of strain energy density in the given RVE under specific uniaxial and biaxial stretches as well as under shear deformations. The analytical relation of the effective composite stiffness to the input uncertain parameter is recovered via the response function method, using a polynomial basis and an optimized order. Probabilistic calculations are completed using three concurrent approaches, namely the iterative stochastic finite element method (SFEM), Monte Carlo simulation and by the semi-analytical method. Previous papers consider the composite fully elastic, which limits the applicability of the resulting effective stiffness tensor computed therein. The current study voids this assumption and defines the composite as fully hyper-elastic, thus extending applicability of this tensor to strains up to 0.25. The most important research finding is that (1) the effective stiffness tensor is sensitive to random interface defects in its hyper-elastic range, (2) its resulting randomness is not close to Gaussian, (3) the semi-analytical method is not perfectly suited to stochastic calculations in this region of strains, as opposed to the linear elastic region, and (4) that the increase in random dispersion of defects volume fraction has a much higher effect on the stochastic characteristics of this stiffness tensor than fluctuation of the strain.

Multiscale damage plasticity modeling and inverse characterization for particulate composites

2020 ◽  
Vol 149 ◽  
pp. 103564 ◽  
Author(s):  
Hyoung Jun Lim ◽  
Hoil Choi ◽  
Fei-Yan Zhu ◽  
Tomas Webbe Kerekes ◽  
Gun Jin Yun
Keyword(s):  
Particulate Composites
Sign in / Sign up

Export Citation Format

Share Document