A Local Sensitivity-Based Multiscale Stochastic Stress Analysis of a Unidirectional Fiber-Reinforced Composite Material Considering Random Location Variation of Multifibers

Abstract

This paper describes an efficient computational method for estimating the probabilistic properties of the maximum microscopic stresses in a unidirectional fiber-reinforced composite material against microscopic random variations of fibers locations. Some microscopic geometrical random variations will cause a large variation of the microscopic stresses, even if the influence on the homogenized elastic properties is small. The random variation of the microscopic stresses will have a significant influence on the apparent strength of composites, and therefore, estimation of the random variation will be important for reliability-based design of a composite structure. Further, for more precise analysis, a unit cell containing many inclusions should be employed. When the number of random variables becomes large, a multipoint approximation-based approach will not be appropriate. Therefore, a computational approach with a local surrogate constructed by a successive sensitivity analysis is proposed in this paper. The realizations of the microscopic stresses are estimated with the successive sensitivity-based local surrogate, and the probabilistic properties of the stresses are estimated with using the approximated realizations in the Monte Carlo simulation. As an example, the multiscale stochastic stress analysis of a unidirectional fiber-reinforced composite plate under unidirectional tensile load along the transverse direction is performed with considering randomness in fibers locations. For this problem, probabilistic properties as the expectation and coefficient of variation of the maximum microscopic stresses in resin are estimated. From comparisons between the direct Monte Carlo simulation and the proposed method, validity and effectiveness of the proposed approach are discussed.

Mesh superposition‐based multiscale stress analysis of composites using homogenization theory and re‐localization technique considering fiber location variation

“…The homogenization method 17,34,35 is a method of finding the equivalent elastic constant by macroscopically considering heterogeneous materials as materials having periodic structures in a very small region. It is possible to analyze the microscopic behavior from the macroscopic external force and deformation.…”

“…From this viewpoint, several related repots on the analysis considering stochastic homogenization or macroscopic stochastic analysis reflecting the stochastic homogenization problem have been reported, [11][12][13][14] while the reports on the stochastic multiscale stress analysis estimating probabilistic properties of the maximum stresses in microscale are limited. [15][16][17][18] From this reason, a statistical approach considering random parameters for estimating the probabilistic properties of maximum stresses should be established for the reliable design of composite structures.…”

Multiscale Stochastic Stress Analysis of Unidirectional FRP Considering Random Fiber Location Variation by an Improved Successive Local Approximation

“…multiscale stochastic stress analysis of unidirectional fiber reinforced composite material considering many embedded fibers and their random location [16] can be found.…”

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

“…Such studies, where randomness serves for a specific intermediate step, are only able to return some mean material properties or, at least, upper and lower bounds of these properties. When more information is required, the only possibility is a stochastic or probabilistic approach, which allows for the determination of further characteristics, such as the expected values, statistical dispersion or even the full probability densities of these macroscopic properties; some examples are demonstrated in [24,25]. A major problem in such considerations is a proper determination of the nature and properties of the input probability densities.…”