To develop material models for concrete one naturally arrives to the  conclusion that the effects of tensile deformation has to be separated from those of the compressive one. One way to do that is to decompose the strain in two (E+ and E-), thus introducing an interface (defined by trace(E)=0) into the strain space. I know that Alain Curnier has found relationships about elastic energy continuity and its derivatives across this interface. The following paper recall those relations: http://www.iop.org/EJ/article/0965-0393/15/4/S07/msmse7_4_S07.pdf (section 3.2, page 5)
 

I have two questions

1) Could someone provide me the complete demonstration of those relations ?

2) Is there some experimental results that  such decomposition is releavant or is it only a trick to introduce distinction between traction and compression behaviors ?

Thank you very much for your answers !