Tissue regeneration requires structural holding and movement support using tissue-type-specific aids such as bone casts, skin bandages, and joint protectors. Currently, an unmet need exists in aiding breast fat regeneration as the breast moves following continuous body motion by exposing the breast fat to dynamic stresses. Here, the concept of elastic structural holding is applied to develop a shape-fitting moldable membrane for breast fat regeneration ("adipoconductive") after surgical defects are made. The membrane has the following key characteristics: (a) It contains a panel of honeycomb structures, thereby efficiently handling motion stress through the entire membrane; (b) a strut is added into each honeycomb in a direction perpendicular to gravity, thereby suppressing the deformation and stress concentration upon lying and standing; and (c) thermo-responsive moldable elastomers are used to support structural holding by suppressing large deviations of movement that occur sporadically. The elastomer became moldable upon a temperature shift above . The structure can then be fixed as the temperature decreases. As a result, the membrane promotes adipogenesis by activating mechanotransduction in a fat miniature model with pre-adipocyte spheroids under continuous shaking in vitro and in a subcutaneous implant placed on the motion-prone back areas of rodents in vivo.