Thermo-Structural Topology Optimization Considering Nonlinear Creep

2026-07-24

AI Summary

This work addresses the challenge of modeling irreversible deformation in high-temperature metallic components subjected to thermomechanical coupling and sustained loading, where nonlinear creep induces history-dependent behavior that conventional topology optimization struggles to capture accurately. The study proposes a differentiable thermo-structural topology optimization framework that, for the first time, integrates Norton’s creep constitutive law, thermomechanical coupling, and multi-material gradient design within a three-dimensional setting, overcoming limitations of prior linear viscoelastic models. Transient creep responses are simulated using the backward Euler method, and sensitivities are efficiently computed via JAX-based automatic differentiation combined with the adjoint method. The framework performs gradient-based optimization to minimize creep-induced deformation under a volume constraint. Numerical examples demonstrate significant reduction in permanent deformation in 2D cases, while a 3D turbine blade design validates its effectiveness under complex high-temperature operating conditions.

Abstract

Creep is a primary life-limiting mechanism for metallic components operating at high temperature, producing permanent deformation under sustained loads even when stresses remain below yield. The design of structures to minimize this deformation is critical to extending the service life of components. Incorporating creep into topology optimization (TO) remains open because the response is nonlinear, history-dependent, and thermomechanically coupled, and prior work often relies on linear viscoelastic models, which do not capture the behavior of metals at high temperatures. To bridge this gap, we introduce a differentiable thermo-structural TO framework. The approach considers creep deformation using the Norton model and leverages JAX's automatic differentiation to perform adjoint sensitivity analysis, enabling efficient gradient-based optimization. The transient material response is solved via a backward Euler scheme over a prescribed service life. Our objective is to minimize creep deformation subject to a volume constraint. We first demonstrate the framework on canonical two-dimensional benchmarks, showing that the proposed formulation significantly reduces permanent deformation compared to designs optimized solely for elastic stiffness. We then pose, as a challenge problem, the compositional design of a three-dimensional graded material turbine blade in which the local mixture of two candidate alloys is optimized. This challenge problem exercises the full capability of the framework, including transient nonlinear creep, coupled thermal loading, three-dimensional geometry, and gradient-based multi-material design, highlighting the need for creep-aware design in high-temperature applications.

Problem

• creep
• topology optimization
• thermo-structural
• nonlinear
• high-temperature

Innovation

• topology optimization
• nonlinear creep
• thermo-structural coupling
• automatic differentiation
• graded material design