Review article
https://doi.org/10.21857/mnlqgcpq4y
On physics informed neural networks - imposing constraints in infinitesimal strain continuum mechanics
Marko Čanađija
orcid.org/0000-0001-6550-0258
; Faculty of Engineering University of Rijeka
Martin Zlatić
; Faculty of Engineering University of Rijeka
Abstract
The paper presents methods for implementing physical constraints from continuum mechanics in neural networks that serve as constitutive models. The focus is on infinitesimal strains in nonlinear elasticity. Basic constraints are presented with a brief overview of continuum mechanics, and then implemented in feed-forward neural networks. Among others, the topics of convexity, objectivity, thermodynamic consistency and normalization are addressed. Where appropriate, several possible techniques have been presented. Performance is demonstrated by developing a constitutive model for a single-walled carbon nanotube using physics informed neural networks
Keywords
physics informed neural networks; physical constraints; continuum mechanics; convexity
Hrčak ID:
343849
URI
Publication date:
27.1.2026.
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