Abstract
Machine learning methods have been extensively explored for constitutive relation that is essential in material and structural analyses. However, most existing approaches rely on neural networks, which lack interpretability and treat stress–strain data as discrete values, disregarding their inherent continuous nature. Therefore, this paper proposes novel functional order-reduced Gaussian Processes emulators, which are more interpretable by leveraging Bayesian theory and account for the uncertainty arising from microstructural homogenisation, providing the non-parametric probabilistic and continuous constitutive modelling of composite microstructure undergoing fracture/failure. Its most salient point is the capability of predicting the continuous and probabilistic stress–strain function only using limited (i.e., 400) samples, where the uncertain data is high-dimensional in large-scale composite (up to 250,000). An illustrative example demonstrates that the emulator accurately captures the probabilistic constitutive relation, providing insights into the maximum stress and strain values. Notably, the results highlight the significant variation in maximum stress due to fibre uncertainty. Moreover, the example showcases that as the fibre volume fraction increases from 0.4 to 0.6, the maximum stress tends to increase, while the maximum strain decreases, namely, more fibre results in higher strength and stiffness.
Original language | English |
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Article number | 107695 |
Number of pages | 10 |
Journal | Composites Part A: Applied Science and Manufacturing |
Volume | 173 |
Early online date | 16 Jul 2023 |
DOIs | |
Publication status | Published - 31 Oct 2023 |
Bibliographical note
Funding Information:The study presented was funded by the National Key R&D Program of China ( 2022YFB3303400 ), the Fundamental Research Funds for the Central Universities, China , Peking University, China , and the EPSRC, United Kingdom Programme Grant ‘Certification for Design – Reshaping the Testing Pyramid’ (CerTest, EP/S017038/1 ). The funder played no role in study design, data collection, analysis and interpretation of data, or the writing of this manuscript.
Data availability:
Data will be made available on request
Funding
The study presented was funded by the National Key R&D Program of China ( 2022YFB3303400 ), the Fundamental Research Funds for the Central Universities, China , Peking University, China , and the EPSRC, United Kingdom Programme Grant ‘Certification for Design – Reshaping the Testing Pyramid’ (CerTest, EP/S017038/1 ). The funder played no role in study design, data collection, analysis and interpretation of data, or the writing of this manuscript.
Keywords
- Carbon fibre composite
- Functional Gaussian Process regression
- Machine learning for probabilistic constitutive modelling
- Statistical properties/methods
ASJC Scopus subject areas
- Ceramics and Composites
- Mechanics of Materials