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Updated: May 27, 2025

A Method for Studying the Temperature Dependence of Dynamic Fracture and Fragmentation
Published on: June 28, 2015
Ballistic thermoelasticity of nonlinear chains under thermal shock
Ioanna N Trunova1, Vitaly A Kuzkin1
1HSE University, Peter the Great Saint Petersburg Polytechnic University, Institute for Problems in Mechanical Engineering RAS, Saint Petersburg 199178, Russia; Department of Theoretical Mechanics and Mathematical Physics, Saint Petersburg 195251, Russia; and , Saint Petersburg 190008, Russia.
Ballistic thermoelasticity describes how materials respond to rapid temperature changes. Researchers found that mechanical vibrations can grow infinitely under specific conditions, a phenomenon called ballistic resonance.
Area of Science:
- Physics
- Materials Science
- Nonlinear Dynamics
Background:
- Classical thermoelasticity often assumes slow temperature changes and diffusive heat transfer.
- Understanding material behavior under extreme thermal gradients is crucial for advanced applications.
Purpose of the Study:
- To analytically investigate the thermoelastic behavior of nonlinear chains under ballistic heat transfer conditions.
- To explore the phenomenon of ballistic resonance (BR) and its implications.
Main Methods:
- Analytical solutions of equations for ballistic thermoelasticity in the continuum limit.
- Consideration of various initial temperature profiles (sinusoidal, discontinuous, piecewise linear).
- Analysis of dynamical terms and comparison with experimental conditions.
Main Results:
- Ballistic thermoelasticity is characterized by wave propagation and heat transfer sharing the same timescale.
- The quasistatic approximation is invalid in this regime.
- Ballistic resonance (BR) was observed, leading to infinitely growing vibrations for sinusoidal temperature profiles.
- BR was found in alpha-FPUT, Lennard-Jones, and Toda chains.
- Analytical solutions showed singularities for discontinuous profiles and finite results for piecewise linear profiles.
Conclusions:
- Ballistic thermoelasticity presents unique behaviors distinct from classical thermoelasticity.
- Ballistic resonance is a significant phenomenon in nonlinear chains, observable under specific experimental conditions.
- The analytical models are accurate for piecewise linear profiles when the temperature change length exceeds the lattice constant.
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