Inverse Identification of Elastic Properties of Constituents of Discontinuously Reinforced Composites
Abstract
:1. Introduction
2. Identification Procedure
2.1. Optimization Problem
2.2. Micromechanical Modeling
3. Results and Discussion
3.1. Composite Reinforced with Short Fibers
3.2. Composite Reinforced with Cubic Particles
4. Concluding Remarks
Funding
Conflicts of Interest
References
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Phase | Young Modulus (MPa) | Poisson Ratio |
---|---|---|
Matrix | 70,000 | 0.33 |
Fiber | 300,000 | 0.20 |
Volume Fraction of Fibers | Young Modulus (MPa) | Poisson Ratio |
---|---|---|
0.05 | Ec5% = 74,955.83 | νc5% = 0.32446 |
0.10 | Ec10% = 80,486.48 | νc10% = 0.31897 |
0.15 | Ec15% = 85,820.04 | νc15% = 0.31383 |
Input Data | Analysis Number | Identified Elastic Constants | |||
---|---|---|---|---|---|
Em | Er | vm | vr | ||
Ec5%, νc5% | 1 | 68,383.3, 2.3% | 512,943.6, 71.0% | 0.33013, 0.0% | 0.16642, 16.8% |
2 | 69,287.1, 1.0% | 393,597.7, 31.2% | 0.32500, 1.5% | 0.38210, 91.1% | |
3 | 72,330.0, 3.3% | 152,002.5, 49.3% | 0.32536, 1.4% | 0.31336, 56.7% | |
Ec10%, νc10% | 1 | 65,642.5, 6.2% | 663,675.3,121.2% | 0.32863, 0.4% | 0.21423, 7.1% |
2 | 79,190.7, 13.1% | 92,946.0, 69.0% | 0.32298, 2.1% | 0.27911, 39.6% | |
3 | 71,523.3, 2.2% | 250,707.2, 16.4% | 0.32895, 0.3% | 0.19039, 4.8% | |
Ec15%, νc15% | 1 | 77,654.0, 10.9% | 155,795.0, 48.1% | 0.31281, 5.2% | 0.32879, 64.4% |
2 | 62,787.5, 10.3% | 709,421.2, 136.5% | 0.32567, 1.3% | 0.25722, 28.6% | |
3 | 60,758.4, 13.2% | 929,659.3, 209.9% | 0.32381, 1.9% | 0.32073, 60.4% | |
Ec5%, νc5%, Ec10%, νc10% | 1 | 69,708.4, 0.4% | 331,100.2, 10.4% | 0.33001, 0.0% | 0.16767, 16.2% |
2 | 69,708.4, 0.4% | 331,097.8, 10.4% | 0.33001, 0.0% | 0.16766, 16.2% | |
3 | 69,708.4, 0.4% | 331,098.0, 10.4% | 0.33001, 0.0% | 0.16766, 16.2% | |
Ec10%, νc10%, Ec15%, νc15% | 1 | 70,608.3, 0.9% | 288,238.8, 3.9% | 0.32927, 0.2% | 0.18351, 8.2% |
2 | 70,608.3, 0.9% | 288,237.8, 3.9% | 0.32927, 0.2% | 0.18351, 8.2% | |
3 | 70,608.4, 0.9% | 288,237.4, 3.9% | 0.32927, 0.2% | 0.18353, 8.2% | |
Ec5%, νc5%, Ec15%, νc15% | 1 | 69,934.1, 0.1% | 308,332.5, 2.8% | 0.32982, 0.1% | 0.17573, 12.1% |
2 | 69,934.1, 0.1% | 308,332.6, 2.8% | 0.32982, 0.1% | 0.17573, 12.1% | |
3 | 69,934.04, 0.1% | 308,333.81, 2.8% | 0.32982, 0.1% | 0.17573, 12.1% | |
Ec5%, νc5%, Ec15%, νc15%, Ec15%, νc15% | 1 | 70,001.2, 0.0% | 308,842.0, 2.9% | 0.32976, 0.1% | 0.17571, 12.1% |
2 | 70,001.2, 0.0% | 308,841.9, 2.9% | 0.32976, 0.1% | 0.17571, 12.1% | |
3 | 70,001.2, 0.0% | 308,841.8, 2.9% | 0.32976, 0.1% | 0.17571, 12.1% |
Volume Fraction of Fibers | Young Modulus (Mpa) | Poisson Ratio |
---|---|---|
0.05 | Μ = 74,955.83 | μ = 0.32446 |
s1 = 500.00 | s1 = 0.0015 | |
s2 = 1000.00 | s2 = 0.0030 | |
0.10 | μ = 80,486.48 | μ = 0.31897 |
s1 = 500.00 | s1 = 0.0015 | |
s2 = 1000.00 | s2 = 0.0030 | |
0.15 | μ = 85,820.04 | μ = 0.31383 |
s1 = 500.00 | s1 = 0.0015 | |
s2 = 1000.00 | s2 = 0.0030 |
Phase | Young Modulus (MPa) | Poisson Ratio |
---|---|---|
Matrix | 70,000 | 0.30 |
Particle | 415,000 | 0.16 |
Volume Fraction of Fibers | Young Modulus(MPa) | Poisson Ratio |
---|---|---|
0.10 | 82,012.65 | 0.28828 |
0.15 | 88,707.98 | 0.28269 |
Micromechanical Model | Identified Elastic Constants | |||
---|---|---|---|---|
Em | Ei | vm | vi | |
Mori–Tanaka (M-T) | 70,180.5, 0.3% | 518,546.8, 22.2% | 0.29849, 0.5% | 0.12000, 18.2% |
Hybrid M-T/FE | 70,042.9, 0.1% | 432,482.4, 4.1% | 0.29924, 0.3% | 0.15423, 3.7% |
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Ogierman, W. Inverse Identification of Elastic Properties of Constituents of Discontinuously Reinforced Composites. Materials 2018, 11, 2332. https://doi.org/10.3390/ma11112332
Ogierman W. Inverse Identification of Elastic Properties of Constituents of Discontinuously Reinforced Composites. Materials. 2018; 11(11):2332. https://doi.org/10.3390/ma11112332
Chicago/Turabian StyleOgierman, Witold. 2018. "Inverse Identification of Elastic Properties of Constituents of Discontinuously Reinforced Composites" Materials 11, no. 11: 2332. https://doi.org/10.3390/ma11112332