On the Importance of Geometric Nonlinearity and Temperature-Dependent Properties in Multi-Material Thermo-Mechanical Topology Optimization

Research Question and Approach

This paper investigates the accuracy of common modeling assumptions in the topology optimization of thermally actuated compliant devices. Standard design practices typically rely on small-strain linear elasticity and temperature-independent material properties. The authors introduce a physics-informed, simultaneous analysis-and-design framework (m-PIGP) to quantify the impact of these assumptions. They compare a baseline model—using linear kinematics and properties anchored at the design temperature—against a high-fidelity model that incorporates finite-strain quadratic-Hencky kinematics and fully temperature-dependent conductivity, thermal expansion, and elastic moduli for a titanium-copper-steel system.

Key Findings

The study reveals that the choice of constitutive law is the most critical factor in design reliability. Because compliant mechanisms function as linkages, they undergo significant rotations. Linear kinematic models incorrectly interpret these rotations as compressive strain, causing the optimizer to avoid rotation-rich mechanisms that would otherwise be highly effective. Consequently, linear models can appear deceptively accurate when validated against their own biased designs. The authors demonstrate that incorporating finite-strain physics and temperature-dependent properties yields devices that are significantly more robust and stronger across varying operating temperatures, with only a modest increase in computational design cost.

Thermally actuated devices, such as MEMS grippers and actuators, often operate hundreds of degrees above ambient temperature. Relying on room-temperature-anchored linear models leads to designs that fail to meet performance targets in real-world conditions. By identifying that the constitutive law—rather than just material property variation—is the primary source of error, this work provides a clear path for engineers to improve the reliability of thermo-mechanical designs without prohibitive increases in design-time complexity.