Objective optimization and two-way design of double-layer cushion structure enhanced force stability

• A double-layer cushion structure is developed to provide over 30 % better recovery force stability than single-layer designs. • Key factors affecting the recovery force retention of the double-layer cushion structure are identified. • Detailed mechanistic insights based on energy analysis are provided to explain how the stable recovery force is maintained. • An optimized predictive model is proposed to enable two-way design with a relative error below 4.7 %. Programmable metamaterial designs incorporating thermo-induced shape memory polymers (TSMPs) have been widely applied in cushion structure design. Under thermal stimulation, TSMPs exhibit tunable mechanical properties that enable shape memory cushions to meet diverse functional requirements. However, the removal of thermal stimulus leads to instability in these properties, which impedes the maintenance of a stable recovery force. This limitation restricts their practical applications. To address this challenge, a double-layer cushion structure composed of Thermoplastic Polyurethane Elastomers (TPU) and Polylactic Acid (PLA) is proposed as an alternative to the conventional single-layer TSMP cushion structure. By leveraging the recoverable deformation of the TPU layer to store energy, this structure compensates for the substantial reduction in recovery force exhibited by the PLA cushion during cooling. Thermo-mechanical deformation experiments identify the key parameters affecting the recovery force retention rate (RFRR), indicating a more than 30 % improvement compared to the single-layer TSMP cushion. Furthermore, a three-level Box–Behnken design method was employed to integrate polynomial response surface modeling (PRSM) with objective optimization, enabling two-way design between three influencing factors and the recovery force retention rate (RFRR) in the double-layer cushion structure. This study provides novel insights into the design of stable recovery forces for cushion structures under thermal conditions.