Comparison of Levels of Physical Informativeness in Neural Networks
for Constitutive Modeling of a Soft Elastomer
DOI: http://dx.doi.org/10.30970/vam.2026.36.14036
Анотація
Over the past decade, machine learning (ML) methods have demonstrated significant progress in regression,
classification, and modeling of complex dependencies. However, the application of ML in the physical
sciences, particularly in solid mechanics, faces a fundamental limitation: classical neural networks do not
explicitly incorporate physical laws and may produce predictions that contradict conservation principles,
symmetry, or material behavior.
In response, a number of approaches have emerged that integrate physics into the learning process, most
notably Physics-Informed Neural Networks (PINNs). Such models have become especially popular in
materials science, biomechanics, aerodynamics, and heat transfer. Depending on how strongly physical
knowledge is integrated, four main approaches can be distinguished: from purely empirical models (without
physics) to models with hard-coded physical relations.
In this paper, we consider the problem of approximating the stress-strain relationship for the soft material
Ecoflex~00-10 using experimental data obtained according to ISO~37:2017 (uniaxial tension) and ASTM~D575-91
(uniaxial compression). The averaged monotonic curve is used as a reference for comparing the approaches.
The aim of the study is to compare four levels of physical informativeness in neural networks and to evaluate
their impact on accuracy, generalization, and physical reliability in the small-strain regime and during
extrapolation.
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