The Bresler–Pister yield criterion[1] is a function that was originally devised to predict the strength of concrete under multiaxial stress states. This yield criterion is an extension of the Drucker–Prager yield criterion and can be expressed on terms of the stress invariants as
\sqrt{J2}=A+B~I1+
2 | |
C~I | |
1 |
I1
J2
A,B,C
Yield criteria of this form have also been used for polypropylene[2] and polymeric foams.[3]
The parameters
A,B,C
\sigmac
\sigmat
\sigmab
\begin{align} B=&\left(\cfrac{\sigmat-\sigmac}{\sqrt{3}(\sigmat+\sigmac)}\right)
2 | |
\left(\cfrac{4\sigma | |
b |
-\sigmab(\sigmac+\sigmat)+\sigmac\sigmat}{4\sigma
2 | |
b |
+2\sigmab(\sigmat-\sigmac)-\sigmac\sigmat}\right)\\ C=&\left(\cfrac{1}{\sqrt{3}(\sigmat+\sigmac)}\right) \left(\cfrac{\sigmab(3\sigmat-\sigmac)-2\sigmac\sigmat}{4\sigma
2 | |
b |
+2\sigmab(\sigmat-\sigmac)-\sigmac\sigmat}\right)\\ A=&\cfrac{\sigmac}{\sqrt{3}}+B\sigmac
2 | |
-C\sigma | |
c |
\end{align}
In terms of the equivalent stress (
\sigmae
\sigmam
\sigmae=a+b~\sigmam+
2 | |
c~\sigma | |
m |
~;~~\sigmae=\sqrt{3J2}~,~~\sigmam=I1/3~.
The Etse-Willam[4] form of the Bresler–Pister yield criterion for concrete can be expressed as
\sqrt{J2}=\cfrac{1}{\sqrt{3}}~I1-\cfrac{1}{2\sqrt{3}}~\left(\cfrac{\sigmat}{\sigma
2 | |
1 |
\sigmac
\sigmat
The GAZT yield criterion[5] for plastic collapse of foams also has a form similar to the Bresler–Pister yield criterion and can be expressed as
\sqrt{J2}=\begin{cases} \cfrac{1}{\sqrt{3}}~\sigmat-0.03\sqrt{3}\cfrac{\rho}{\rhom~\sigmat}~I
2 | |
1 |
\\ -\cfrac{1}{\sqrt{3}}~\sigmac+0.03\sqrt{3}\cfrac{\rho}{\rhom~\sigmac}~I
2 | |
1 |
\end{cases}
\rho
\rhom