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Hyperbolic Heat Conduction and Thermomechanical Response

Scott Miller and Robert B. Haber, Department of Theoretical & Applied Mechanics

Brent Kraczek and Duane Johnson, Department of Materials Science & Engineering

Problem domain of thermomechanical simulation

Problem domain for thermomechanical simulation. An ultrashort laser pulse heats the trapezoidal region at the bottom. Zoom image

Thermomechanical response

Animation of thermomechanical response. Height indicates velocity modulus; color indicates temperature.


The parabolic Fourier heat equation, although useful in many situations, implies infinite propagation speed and is ineffective at the very small length and time scales associated with nanoscale systems. We seek an effective numerical implementation of hyperbolic thermal and thermomechanical models to avoid these problems.


A spacetime discontinuous Galerkin method for conservation laws implements the hyperbolic Maxwell-Cattaneo-Vernotte thermal model and a coupled three-field model for linear elastodynamics. An adaptive spacetime solution procedure resolves multiscale response.


This high-resolution model can be applied to pulsed lasers in corneal surgery, nanotechnology (e.g., CPU overheating, phase-change data storage, micromachining of thin films with pulsed lasers), and thermomechanical dynamic fracture. A similar method can model the dynamics of phase transitions (generalized Cahn-Hilliard equation applied to shape memory alloys), biotransport as well as chemisorption and hydrogen storage.

This material is also available in a Powerpoint slide "nugget".

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