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Updated: Jul 29, 2026
06:07
Studying Large Amplitude Oscillatory Shear Response of Soft Materials
Published on: April 25, 2019
Steady-state cracks in viscoelastic lattice models.
1Department of Mathematics, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA.
Summary
This study reveals that standard continuum mechanics fails to capture unique crack propagation behaviors in viscoelastic lattices. Introducing viscosity reveals velocity selection phenomena missed by traditional models, especially in larger lattice structures.
Area of Science:
- Solid Mechanics
- Materials Science
- Computational Physics
Background:
- Mode III crack propagation is crucial in understanding material fracture.
- Viscoelasticity significantly influences dynamic crack behavior.
- Lattice models offer discrete alternatives to continuum mechanics for material simulation.
Purpose of the Study:
- To investigate steady-state motion of mode III cracks in viscoelastic lattices.
- To compare lattice dynamics with continuum treatments using Kelvin viscosity (eta).
- To analyze the influence of driving displacement (Delta) and lattice size (N) on crack behavior.
Main Methods:
- Employed numerical simulations to model crack propagation on a lattice.
- Utilized analytical Wiener-Hopf techniques for theoretical comparison.
- Varied parameters including Kelvin viscosity (eta), driving displacement (Delta), and lattice size (N).
Main Results:
- Continuum theory fails to predict lattice-trapping phenomena, even at finite N.
- The introduction of Kelvin viscosity (eta) introduces novel behaviors in lattice dynamics.
- For large N and Delta, standard 2D elastodynamics misses eta-dependent velocity selection, which vanishes in the continuum limit.
Conclusions:
- Viscoelastic lattice models exhibit phenomena not present in standard continuum elastodynamics.
- The discrete nature of lattices and viscoelasticity are essential for capturing certain crack dynamics.
- Continuum approximations can oversimplify or miss critical aspects of crack propagation in complex materials.
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