PSI - Issue 43

Andrey P. Jivkov et al. / Procedia Structural Integrity 43 (2023) 15–22 Author name / Structural Integrity Procedia 00 (2023) 000–000

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5. Summary

A new approach to modelling materials with complex internal structures was presented. It allows for studying how elements of di ff erent geometric dimensions and physical nature interact to produce macroscopic behaviour. The approach is fundamentally di ff erent from the existing numerical methods mentioned in the introduction. Both the continuum-based and the discrete methods approximate the continuum descriptions of conservation of scalar quanti ties and momenta. In contrast, here the descriptions of these conservation laws are discrete, background-independent and relational, i.e., involve only relations between elements of the internal structures. Referring to a background struc ture, a coordinate system in the case here, is only necessary and inevitable for the communication with the external world via boundary conditions and body forces. The work is a first step in a long path expected to shift the paradigm in modelling materials with complex internal structures. This is becoming increasingly important, considering the rapid progress in additive manufacturing that creates opportunities for producing composites with tailored properties by arranging components of di ff erent nature and size. Due to the page limitation for this paper, only the theoretical basis of the new approach has been presented. This choice has been made to showcase, albeit briefly, the spirit of the method as an exact formulation of the funda mental physical principles respecting existing materials’ structures. The reader is referred to Berbatov et al. (2022) for practical examples for conservation of scalar quantities. Examples with mechanical problems are subject of ongoing work and will be reported in a future publication.

Acknowledgements

Jivkov and Boom acknowledge gratefully the support for this research of the Engineering and Physical Sciences Research Council via grant EP / N026136 / 1.

References

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