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.

References

References
1.
Stefanou
,
G.
,
Savvas
,
D.
, and
Papadrakakis
,
M.
,
2017
, “
Stochastic Finite Element Analysis of Composite Structures Based on Mesoscale Random Fields of Material Properties
,”
Comput. Methods Appl. Eng.
,
326
, pp.
319
337
.
2.
Sokolowski
,
D.
, and
Kaminski
,
M.
,
2018
, “
Computational Homogenization of Carbon/Polymer Composites With Stochastic Interface Defects
,”
Compos. Struct.
,
183
, pp.
434
449
.
3.
Sakata
,
S.
,
Okuda
,
K.
, and
Ikeda
,
K.
,
2015
, “
Stochastic Analysis of Laminated Composite Plate Considering Stochastic Homogenization Problem
,”
Front. Struct. Civ. Eng.
,
9
(
2
), pp.
141
153
.
4.
Sakata
,
S.
,
Ashida
,
F.
, and
Enya
,
K.
,
2012
, “
A Microscopic Failure Probability Analysis of a Unidirectional Fiber Reinforced Composite Material Via a Multiscale Stochastic Stress Analysis for a Microscopic Random Variation of an Elastic Property
,”
Comput. Mater. Sci.
,
62
, pp.
35
46
.
5.
Kaminski
,
M.
, and
Kleiber
,
M.
,
1996
, “
Stochastic Structural Interface Defects in Fiber Composites
,”
Int. J. Solids Struct.
,
33
(
20–22
), pp.
3035
3056
.
6.
Sakata
,
S.
,
Ashida
,
F.
,
Kojima
,
T.
, and
Zako
,
M.
,
2008
, “
Influence of Uncertainty in Microscopic Material Property on Homogenized Elastic Property of Unidirectional Fiber Reinforced Composites
,”
Theor. Appl. Mech.
,
56
, pp.
67
76
.
7.
Ostoja-Starzewski
,
M.
,
1998
, “
Random Field Models of Heterogeneous Materials
,”
Int. J. Solids Struct.
,
35
(
19
), pp.
2429
2455
.
8.
Kaminski
,
M.
, and
Kleiber
,
M.
,
2000
, “
Perturbation Based Stochastic Finite Element Method for Homogenization of Two-Phase Elastic Composites
,”
Comput. Struct.
,
78
, pp.
811
826
.
9.
Sakata
,
S.
,
Ashida
,
F.
,
Kojima
,
T.
, and
Zako
,
M.
,
2008
, “
Three-Dimensional Stochastic Analysis Using a Perturbation-Based Homogenization Method for Homogenized Elastic Property of Inhomogeneous Material Considering Microscopic Uncertainty
,”
Int. J. Solids Struct.
,
45
(
3–4
), pp.
894
907
.
10.
Sakata
,
S.
,
Ashida
,
F.
, and
Zako
,
M.
,
2008
, “
Stochastic Response Analysis of FRP Using the Second-Order Perturbation-Based Homogenization Method
,”
J. Solid Mech. Mater. Eng.
,
2
(
1
), pp.
70
81
.
11.
Kaminski
,
M.
,
2007
, “
Generalized Perturbation-Based Stochastic Finite Element Method in Elastostatics
,”
Comput. Struct.
,
85
(
10
), pp.
586
594
.
12.
Kaminski
,
M.
,
2013
,
The Stochastic Perturbation Method for Computational Mechanics
,
Wiley
, Chichester, UK.
13.
Tootkaboni
,
M.
, and
Brady
,
L. G.
,
2010
, “
A Multi-Scale Spectral Stochastic Method for Homogenization of Multi-Phase Periodic Composites With Random Material Properties
,”
Int. J. Numer. Methods Eng.
,
83
(1), pp.
59
90
.
14.
Kaminski
,
M.
,
2009
, “
Sensitivity and Randomness in Homogenization of Periodic Fiber-Reinforced Composites Via the Response Function Method
,”
Int. J. Solids Struct.
,
46
(
3–4
), pp.
923
937
.
15.
Sakata
,
S.
,
Ashida
,
F.
, and
Zako
,
M.
,
2008
, “
Kriging-Based Approximate Stochastic Homogenization Analysis for Composite Material
,”
Comput. Methods Appl. Mech. Eng.
,
197
(
21–24
), pp.
1953
1964
.
16.
Kaminski
,
M.
,
2011
, “
Homogenization of Fiber-Reinforced Composites With Random Properties Using the Weighted Least Squares Response Function Approach
,”
Arch. Mech.
,
63
, pp.
479
505
.
17.
Sakata
,
S.
,
Ashida
,
F.
, and
Iwahashi
,
D.
,
2013
, “
Stochastic Homogenization Analysis of a Particle Reinforced Composite Material Using and Approximate Monte Carlo Simulation With the Weighted Least Square Method
,”
J. Comput. Sci. Technol.
,
7
(
1
), pp.
1
11
.
18.
Kaminski
,
M.
, and
Lauke
,
B.
,
2013
, “
Parameter Sensitivity and Probabilistic Analysis of the Elastic Homogenized Properties for Rubber Filled Polymers
,”
Comput. Model. Eng. Sci.
,
93
(6), pp.
411
440
.
19.
Sakata
,
S.
, and
Torigoe
,
I.
,
2015
, “
A Successive Perturbation-Based Multiscale Stochastic Analysis Method for Composite Materials
,”
Finite Elem. Anal. Des.
,
102
, pp.
74
84
.
20.
Sakata
,
S.
,
Ashida
,
F.
, and
Enya
,
K.
,
2011
, “
Perturbation-Based Stochastic Stress Analysis of a Particle Reinforced Composite Material Via the Stochastic Homogenization Analysis Considering Uncertainty in Material Properties
,”
Int. J. Multiscale Comput. Eng.
,
9
(
4
), pp.
395
408
.
21.
Sakata
,
S.
,
Ashida
,
F.
, and
Ohsumimoto
,
K.
,
2013
, “
Multiscale Stochastic Stress Analysis of a Porous Material With the Perturbation-Based Stochastic Homogenization Method for a Microscopic Geometrical Random Variation
,”
J. Comput. Sci. Technol.
,
7
(
1
), pp.
99
112
.
22.
Guedes
,
M.
, and
Kikuchi
,
N.
,
1990
, “
Preprocessing and Postprocessing for Materials Based on the Homogenization Method With Adaptive Finite Element Methods
,”
Comput. Methods Appl. Mech. Eng.
,
83
(
2
), pp.
143
198
.
23.
Press
,
W. H.
,
Teukolski
,
S. A.
,
Vetterling
,
W. T.
, and
Flannery
,
B. P.
,
1993
,
Numerical Recipes in C (Japanese Edition)
,
Gijutsu-Hyoron Sha
, Tokyo, Japan.
You do not currently have access to this content.