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This study investigates the limitations of small-strain linear elasticity and temperature-independent properties in the topology optimization of thermo-mechanical compliant devices, which often operate at elevated temperatures. By employing a physics-informed framework that incorporates a finite-strain quadratic-Hencky model and temperature-dependent material properties, the authors optimize designs for thermal actuators and grippers across varying temperatures. The findings reveal that neglecting geometric nonlinearity leads to significant design errors, particularly in rotation-rich mechanisms, ultimately demonstrating that full physics-based modeling results in stronger, more reliable devices with only a modest increase in design time.
Ignoring geometric nonlinearity in thermal device design can lead to critical performance errors, particularly as operating temperatures rise.
Thermo-mechanical compliant devices are commonly designed with small-strain linear elasticity and temperature-independent material properties, even though they might operate hundreds of kelvin above ambient where both assumptions are questionable. In this work, we quantify the effect and cost of each assumption in multi-material topology optimization of thermally actuated compliant devices. To this end, we introduce a physics-informed, simultaneous analysis-and-design framework with (i) a finite-strain quadratic-Hencky (logarithmic-strain) constitutive model whose isotropic thermal eigenstrain admits an exact additive split in log-strain space, and (ii) temperature-dependent conductivity, thermal expansion, and elastic moduli for a titanium--copper--steel material system. We optimize a thermal actuator and a thermal gripper at three design temperatures under both a baseline model and the full physics, subject to mass and manufacturability constraints. Every converged design is re-evaluated by verified nonlinear finite element solvers in the full factorial of constitutive law and property model. The comparison between the two factors reveals that the constitutive law is the decisive modeling choice: These devices work as linkages where linear kinematics mistakes rotation for compressive strain; its error therefore grows with the design temperature and concentrates on the very layouts that exploit rotation best. Because a linear optimizer also steers away from the rotation-rich mechanisms that would expose this bias, the model can deceptively appear trustworthy when validated against its own designs. Designing with the full physics yields consistently stronger and more temperature-robust devices at a modest increase in design-time cost.
