Abstract
We present a theoretical analysis of the dynamic stress-strain state of regions in a solid body that are involved in a collective elastic vortexlike motion. It is shown that the initiation of elastic vortexlike motion in the material is accompanied by the appearance of dilatancy and equivalent strain, the magnitudes of which are proportional to the square of the ratio of linear velocity on the periphery of the elastic vortex to the velocity of longitudinal elastic waves (P wave). Under conditions of dynamic loading the described dynamic effects are able to initiate inelastic deformation or destruction of the material at loading speeds of a few percent of the P-wave speed. The obtained analytical estimates suggest that dynamic nonlinear strains can make a significant contribution in a number of widely studied nonlinear dynamic phenomena in solids. Among them are the effect of acoustic (dynamic) dilatancy in solids and granular media, which leads to the generation of longitudinal elastic waves by transverse waves [V. Tournat, Phys. Rev. Lett. 92, 085502 (2004)10.1103/PhysRevLett.92.085502] and the formation of an array of intense "hot spots" (reminiscent of shear-induced hydrodynamic instabilities in fluids) in adiabatic shear bands [P. R. Guduru, Phys. Rev. E 64, 036128 (2001)10.1103/PhysRevE.64.036128].
| Original language | English |
|---|---|
| Article number | 053005 |
| Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |
| Volume | 93 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 18 May 2016 |
Fingerprint
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics
Cite this
Nonlinear effect of elastic vortexlike motion on the dynamic stress state of solids. / Shilko, Evgeny V.; Grinyaev, Yurii V.; Popov, Mikhail V.; Popov, Valentin Leonidovich; Psakhie, Sergey G.
In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 93, No. 5, 053005, 18.05.2016.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Nonlinear effect of elastic vortexlike motion on the dynamic stress state of solids
AU - Shilko, Evgeny V.
AU - Grinyaev, Yurii V.
AU - Popov, Mikhail V.
AU - Popov, Valentin Leonidovich
AU - Psakhie, Sergey G.
PY - 2016/5/18
Y1 - 2016/5/18
N2 - We present a theoretical analysis of the dynamic stress-strain state of regions in a solid body that are involved in a collective elastic vortexlike motion. It is shown that the initiation of elastic vortexlike motion in the material is accompanied by the appearance of dilatancy and equivalent strain, the magnitudes of which are proportional to the square of the ratio of linear velocity on the periphery of the elastic vortex to the velocity of longitudinal elastic waves (P wave). Under conditions of dynamic loading the described dynamic effects are able to initiate inelastic deformation or destruction of the material at loading speeds of a few percent of the P-wave speed. The obtained analytical estimates suggest that dynamic nonlinear strains can make a significant contribution in a number of widely studied nonlinear dynamic phenomena in solids. Among them are the effect of acoustic (dynamic) dilatancy in solids and granular media, which leads to the generation of longitudinal elastic waves by transverse waves [V. Tournat, Phys. Rev. Lett. 92, 085502 (2004)10.1103/PhysRevLett.92.085502] and the formation of an array of intense "hot spots" (reminiscent of shear-induced hydrodynamic instabilities in fluids) in adiabatic shear bands [P. R. Guduru, Phys. Rev. E 64, 036128 (2001)10.1103/PhysRevE.64.036128].
AB - We present a theoretical analysis of the dynamic stress-strain state of regions in a solid body that are involved in a collective elastic vortexlike motion. It is shown that the initiation of elastic vortexlike motion in the material is accompanied by the appearance of dilatancy and equivalent strain, the magnitudes of which are proportional to the square of the ratio of linear velocity on the periphery of the elastic vortex to the velocity of longitudinal elastic waves (P wave). Under conditions of dynamic loading the described dynamic effects are able to initiate inelastic deformation or destruction of the material at loading speeds of a few percent of the P-wave speed. The obtained analytical estimates suggest that dynamic nonlinear strains can make a significant contribution in a number of widely studied nonlinear dynamic phenomena in solids. Among them are the effect of acoustic (dynamic) dilatancy in solids and granular media, which leads to the generation of longitudinal elastic waves by transverse waves [V. Tournat, Phys. Rev. Lett. 92, 085502 (2004)10.1103/PhysRevLett.92.085502] and the formation of an array of intense "hot spots" (reminiscent of shear-induced hydrodynamic instabilities in fluids) in adiabatic shear bands [P. R. Guduru, Phys. Rev. E 64, 036128 (2001)10.1103/PhysRevE.64.036128].
UR - http://www.scopus.com/inward/record.url?scp=84971317640&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84971317640&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.93.053005
DO - 10.1103/PhysRevE.93.053005
M3 - Article
VL - 93
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
SN - 1539-3755
IS - 5
M1 - 053005
ER -