A Physics-guided Machine Learning Model Based on PeridynamicsCong Tien Nguyen, Selda Oterkus and Erkan OterkusUniversity of Strathclyde, 100 Montrose Street Glasgow G4 0LZ United KingdomPeridynamics [1,2] is a non-local continuum mechanics formulation introduced mainly for making failure predictions in materials and structures. Peridynamics equations of motion are in integro-differential equation form and do not contain any spatial derivatives as opposed to partial differential equations of classical continuum mechanics. Therefore, these equations are always valid regardless of discontinuities. In peridynamics, each material point can interact with other material points inside its domain of influence, named as horizon. Peridynamic equations motion cannot usually be solved analytically and numerical techniques, such as meshless method, are usually utilised. If meshless method is used for the numerical solution, the solution domain is divided into finite number volumes represented by material points located at the center of the corresponding volumes. Depending on the number of interactions between material points inside the horizon of each material point, peridynamic computations can take considerable time for certain problems. It is then important to find approaches which can help to reduce the computational time of peridynamic simulations. In this study, a physics-guided machine learning model based on multiple linear regression is developed for peridynamic calculations [3,4]. The training data was obtained by using modal analysis in ANSYS. While the developed model is used for parts of the material points with complete horizon, regular peridynamics is used for material points with lack of interactions due to bond breakage or surfaces. The regions which belong to the machine learning model and regular peridynamics model are updated in an adaptive manner depending on the number of interactions inside each horizon. The developed approach is adapted to both bond-based peridynamics and ordinary-state based peridynamics formulations. By using this coupled formulation, 30% decrease in computational time is observed for two-dimensional problems. To demonstrate the capability of the developed approach, various numerical examples will be presented.&nbsp;REFERENCES[1] Silling, S.A., 2000. Reformulation of elasticity theory for discontinuities and long-range forces.&nbsp;Journal of the Mechanics and Physics of Solids,&nbsp;48(1), pp.175-209.[2] E. Madenci and E. Oterkus,&nbsp;Peridynamic theory and its applications, New York: Springer, 2014.[3]&nbsp;Nguyen, C.T., Oterkus, S. and Oterkus, E., 2020. A peridynamic-based machine learning model for one-dimensional and two-dimensional structures.&nbsp;Continuum Mechanics and Thermodynamics, pp.1-33.[4]&nbsp;Nguyen, C.T., Oterkus, S. and Oterkus, E., 2021. A physics-guided machine learning model for two-dimensional structures based on ordinary state-based peridynamics.&nbsp;Theoretical and Applied Fracture Mechanics,&nbsp;112, p.102872.

A Physics-Guided Machine Learning Model Based on Peridynamics

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

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