A thickness of material may be detached from a substrate along a cleave plane, utilizing a cleaving process controlled by a releasable constraint plate. In some embodiments this constraint plate may comprise a plate that can couple side forces (the “P-plate”) and a thin, softer compliant layer (the “S-layer”) situated between the P-plate and the substrate. In certain embodiments a porous surface within the releasable constraint plate and in contact to the substrate, allows the constraint plate to be secured to the substrate via a first pressure differential. Application of a combination of a second pressure differential within a pre-existing cleaved portion, and a linear force to a side of the releasable constraint plate bound to the substrate, generates loading that results in controlled cleaving along the cleave plane.