Thermo-mechanically coupled Nonuniform Transformation Field Analysis

Felix Fritzen

The Nonuniform Transformation Field Analysis (NTFA) of Michel & Suquet (International Journal of Solids and Structures, 2003) is a micro-mechanical reduced order model. It introduces a reduced basis for the description of the kinetics of the internal state variables in dissipative microstructured materials. Then the remaining fields are derived from micromechanical considerations and related simulations. The reduced basis emerges from a data-driven approach on explicative training data building on the established snapshot proper orthogonal decomposition (POD). Unfortunately, a major short-coming of the NTFA is its restriction to constant elastic properties within the material. However, in reality, state changes such as elevated temperatures do introduce eigenstresses and they modify the stiffness of the materials within the microstructure.

Building on a recent model order reduction approach of the authors (Sharba, Herb, Fritzen, Archives of Applied Mechanics (2023)), we present a methodology that enables the use of the NTFA for metal matrix composites at high volume fraction ceramic reinforcements for temperatures ranging from room temperature to melting temperature. The affine model order reduction of Sharba et al. (2023) will be recaped and its application to the NTFA problem will be presented. Then we present a variety of recent simulation results including thermo-mechanical two-scale simulations, that employ the thermomechanically coupled NTFA. The results are validated against reference finite element simulations which attest superb accuracy across the full temperature range with a handful of additional state variables and at computational speedups on the order of 100000 and more.


J. C. Michel and P. Suquet, “Nonuniform transformation field analysis,” International Journal of Solids and Structures, vol. 40, pp. 6937–6955, 2003, doi:

S. Sharba, J. Herb, and F. Fritzen, “Reduced order homogenization of thermoelastic materials with strong temperature-dependence and comparison to a machine-learned model,” Archives Of Applied Mechanics, vol. 93, pp. 2855–2876, 2023. doi:

To the top of the page