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Gradient enhanced gaussian process regression for constitutive modelling in finite strain hyperelasticity
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Rogelio Ortigosa ,
Jesus Martinez Frutos,
Antonio Gil
Computer Methods in Applied Mechanics and Engineering, Volume: 418, Start page: 116547
Swansea University Authors:
Jesus Martinez Frutos, Antonio Gil
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DOI (Published version): 10.1016/j.cma.2023.116547
Abstract
This paper introduces a metamodelling technique that leverages gradient-enhanced Gaussian process regression (also known as gradient-enhanced Kriging), effectively emulating the response of diverse hyperelastic strain energy densities. The approach adopted incorporates principal invariants as inputs...
| Published in: | Computer Methods in Applied Mechanics and Engineering |
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| ISSN: | 0045-7825 1879-2138 |
| Published: |
Elsevier BV
2024
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa64772 |
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| Abstract: |
This paper introduces a metamodelling technique that leverages gradient-enhanced Gaussian process regression (also known as gradient-enhanced Kriging), effectively emulating the response of diverse hyperelastic strain energy densities. The approach adopted incorporates principal invariants as inputs for the surrogate of the strain energy density. This integration enables the surrogate to inherently enforce fundamental physical constraints, such as material frame indifference and material symmetry, right from the outset. The proposed approach provides accurate interpolation for energy and the first Piola–Kirchhoff stress tensor (e.g. first order derivatives with respect to inputs). The paper presents three notable innovations. Firstly, it introduces the utilisation of Gradient-Enhanced Kriging to approximate a diverse range of phenomenological models, encompassing numerous isotropic hyperelastic strain energies and a transversely isotropic potential. Secondly, this study marks the inaugural application of this technique for approximating the effective response of composite materials. This includes rank-one laminates, for which analytical solutions are feasible. However, it also encompasses more complex composite materials characterised by a Representative Volume Element (RVE) comprising an elastomeric matrix with a centred spherical inclusion. This extension opens the door for future application of this technique to various RVE types, facilitating efficient three-dimensional computational analyses at the macro-scale of such composite materials, significantly reducing computational time compared to FEM. The third innovation, facilitated by the integration of these surrogate models into a 3D Finite Element computational framework, lies in the assessment of these models scenarios encompassing intricate cases of extreme twisting and more importantly, buckling instabilities in thin-walled structures, thereby highlighting both the practical applicability and robustness of the proposed approach. |
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| Keywords: |
Kriging, Machine learning, Constitutive modelling, Hyperelasticity, Anisotropy |
| College: |
Faculty of Science and Engineering |
| Funders: |
R. Ortigosa and J. Martínez-Frutos acknowledge the support of grant PID2022-141957OA-C22 funded by MCIN/AEI/10.13039/501100011033 and by “RDF A way of making Europe”. The authors also acknowledge the support provided by the Autonomous Community of the Region of Murcia, Spain through the programme for the development of scientific and technical research by competitive groups (21996/PI/22), included in the Regional Program for the Promotion of Scientific and Technical Research of Fundacion Seneca - Agencia de Ciencia y Tecnologia de la Region de Murcia. The fourth author also acknowledges the financial support received through the European Training Network Protechtion (Project ID: 764636) and of the UK Defense, Science and Technology Laboratory |
| Start Page: |
116547 |