Details

Autor(en) / Beteiligte

• Ellmer, Nathan
• Ortigosa, Rogelio
• Martínez-Frutos, Jesús
• Gil, Antonio J.

Titel

Gradient enhanced gaussian process regression for constitutive modelling in finite strain hyperelasticity

Ist Teil von

• Computer methods in applied mechanics and engineering, 2024-01, Vol.418, p.116547, Article 116547

Ort / Verlag

Elsevier B.V

Erscheinungsjahr

2024

Quelle

Elsevier ScienceDirect Journals

Beschreibungen/Notizen

• 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 utilization 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 characterized by a Representative Volume Element (RVE) comprising an elastomeric matrix with a centered 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 FEM2. 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. •Gradient-enhanced Gaussian process regression approach effectively emulating the response of diverse hyperelastic strain energy densities.•Incorporation of principal invariants as inputs for the surrogate of the strain energy density.•Accurate interpolation for energy and first order derivatives with respect to inputs, ensuring stress-free conditions for vanishing deformations.•Implementation of surrogate models within in-house 3D Finite Element computational platform.•Comparison between gradient Kriging metamodel and the ground truth models in bending and torsion scenarios and under wrinkling instabilities.•Similar behaviour in terms of positive definiteness (e.g. convexity/concativity) and ellipticity properties for Gradient Kriging trainined models and ground truth counterparts.