Good day, all!

Currently, I'm interested in the conformability of a membrane with a given surface.

Considering an arbitrarily stretchable but not compressible membrane, whose thickness can be neglected and another two dimensions are enough large, and a given non-developable surface that can't be deformable, namely, stiff, is there any optimal method to let the membrane conformal with the given surface so that the max principle strain of the deformed membrane is minimum? What relation between the strain or stress of the membrane and the geometrical properties of the given surface is? Here we can ignore the adhesive energy between the interface.

Conformability of a Thin Elastic Membrane Laminated on a Soft Substrate With Slightly Wavy Surface

Liu Wang, Nanshu Lu*

When laminating a thin elastic membrane on a substrate with surface roughness, three scenarios can happen: fully conformed (FC), i.e., the membrane completely follows the surface morphology of the substrate without any interfacial gap, nonconformed (NC), i.e., the membrane remains flat if gravity is not concerned, and partially conformed (PC). Good conformability can enhance effective membrane-to-substrate adhesion strength and can facilitate signal/heat/mass transfer across the interface, which are of great importance to soft electronics laminated on rough bio-tissues. To reveal governing parameters in this problem and to predict conformability, energy minimization is implemented after successfully finding the substrate elastic energy under partially conformable contact. Four dimensionless governing parameters involving the substrate roughness, membrane thickness, membrane and substrate elastic moduli, and membrane-to-substrate intrinsic work of adhesion have been identified to analytically predict the conformability status and the area of contact. The analytical prediction has found excellent agreement with experimental observations. In summary, an experimentally validated quantitative guideline for the conformability of elastic membrane on soft corrugated substrate has been established in the four-parameter design space.

http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?arti...

When laminating a thin elastic membrane on a substrate with surface roughness, three scenarios can happen: 1) fully conformed, i.e., the membrane completely follows the surface morphology of the substrate without any interfacial gap; 2) partially conformed; and 3) nonconformed, i.e., the membrane remains flat if gravity is not concerned. Good conformability can enhance effective membrane-to-substrate adhesion and can facilitate heat/signal transfer across the interface, which are of great importance for micromembranes or nanomembranes transferred on target substrates and for flexible electronics laminated on rough biotissues. To reveal the governing parameters in this problem and to predict the conformability, energy minimization method is implemented with two different interfacial models, adhesion energy versus traction-separation relation. Depending on the complexity of the models, one to four dimensionless governing parameters have been identified to analytically predict the conformability status and the point of delamination if partial conformability is expected. In any case, partial conformability is achieved only when membrane energy is considered.