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\begin{document}

\title{An interpretation and modification of the SWT function}



\author[1]{Daniel Kujawski}%
\affil[1]{Affiliation not available}%


\vspace{-1em}



  
  \date{June 13, 2024}


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\begin{abstract}
In this paper a new interpretation and modification of the SWT function
in terms of the total damaging energy density is proposed and discussed.
The total damaging energy density is the sum of the damaging part of the
strain energy density and complementary energy density corresponding to
the first quadrant in damaging ?\selectlanguage{greek}σ\selectlanguage{english}\textsubscript{D}-\selectlanguage{greek}ε\selectlanguage{english}\textsubscript{D}
axes. For cyclic loading with positive mean stress
(\selectlanguage{greek}σ\selectlanguage{english}\textsubscript{m}[?]0) the proposed function reduces to the original SWT
formulation. For cyclic loading with negative mean stress
(\selectlanguage{greek}σ\selectlanguage{english}\textsubscript{m}\textless{}0) the maximum stress is augmented by 1/3
of absolute value of the mean stress. The proposed approach shows a
consistent correlation of the mean stress effects for both positive and
negative mean stresses.%
\end{abstract}%



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