A double cantilever beam specimen, with thickness $b($very large$),$ is loaded by two horizontal forces P $,$ as shown in the figure. The moment $M=P.h$ is necessary to balance the binary $P$ acting in the crack flanges. Considering the stress field is characterized by plane strain condition, determine the energy release rate and the stress intensity factor for this component. Discuss the validity of the linear elastic solution. What is the loading mode in this problem?

We know that:

Deformation energy due to the force $P$:$W_{ep}=\frac{1}{2}P.$;

Deformation energy due to the balancing moment $M$:$W_{em}=\frac{1}{2}M*$;

Work done by the force $P$:$W_p=P.$;

Work done by the moment $M$:$W_M=M.$;

$=M.\frac{w-\text{I}}{E^{\text{'}}.\text{I}}$;

$=P.\frac{\text{I}}{E^{\text{'}}A},$ with ${}_1={}_{2\text{;}}$

$A=h.b$;

$E^{\text{'}}=\frac{E}{I-V^2}$;

$I=\frac{1}{12}b(2h{)}^3=\frac{2}{3}b.h^3$