Skip to main content
SpringerLink
Log in

Dynamic frictional slip along an interface between plastically compressible solids

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

Dynamic frictional slip along an interface between plastically compressible solids is analyzed. The plane strain, small deformation initial/boundary value problem formulation and the numerical method are identical to those in Shi et al. (Int J Fract 162:51, 2010) except that here the material constitutive relation allows for plastic compressibility. The interface is characterized by a rate and state dependent friction law. The specimens have an initial compressive stress and are subject to shear loading by edge impact near the interface. Two loading conditions are analyzed, one giving rise to a crack-like mode of slip propagation and the other to a pulse-like mode of slip propagation. In both cases, the initial compressive stress is taken to vary with plastic compressibility such that the associated initial effective stress is the same for all values of plastic compressibility. The volume change for the crack-like slip mode is mainly plastic while the elastic volume change plays a larger role for the pulse-like mode. For the crack-like slip mode, the proportion of plastic dissipation in the material increases with the increasing plastic compressibility, but the effect of plastic compressibility on the energy partitioning for the pulse-like slip mode is much smaller. The predicted propagation speeds approach a speed about the dilational wave speed for both the crack-like and pulse-like slip modes and this speed is not sensitive to the value of the plastic compressibility parameter. Plastic dissipation is found to be mainly associated with the deformation induced by the loading wave rather than with the deformation arising from slip propagation. The amplitude of the slip rate in the slip pulses is found to be largely governed by the value of the initial compressive stress regardless of the value of plastic compressibility.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  • Adams GG (1995) Self-excited oscillations of two elastic half-spaces sliding with a constant coefficient of friction. J Appl Mech 62:867–872

    Article  Google Scholar 

  • Andrews DJ, Ben-Zion Y (1997) Wrinkle-like slip pulse on a fault between different materials. J Geophys Res 102:553–571

    Article  Google Scholar 

  • Bar-Sinai Y, Aldam M, Spatschek R, Brener EA, Bouchbinder E (2019) Spatiotemporal Dynamics of frictional systems: the interplay of interfacial friction and bulk elasticity. Lubricants 7:91

    Article  Google Scholar 

  • Beeler NM, Tullis TE (1996) Self-healing slip pulses in dynamic rupture models due to velocity dependent strength. Bull Seismol Soc Am 86:1130–1148

    Google Scholar 

  • Belytschko T, Chiapetta RL, Bartel HD (1976) Efficient large scale non-linear transient analysis by finite elements. Int J Numer Meth Eng. 10:579–596

    Article  Google Scholar 

  • Ben-Zion Y, Huang Y (2002) Dynamic rupture on an interface between a compliant fault zone layer and a stiffer surrounding solid. J Geophys Res 107:2042

    Article  Google Scholar 

  • Bouchbinder E, Brener EA, Barel I, Urbakh M (2011) Slow cracklike dynamics at the onset of frictional sliding. Phys Rev Lett 107:235501

    Article  Google Scholar 

  • Cochard A, Rice JR (2000) Fault rupture between dissimilar materials: ill-posedness, regularization, and slip-pulse response. J Geophys Res 105:25891–25907

    Article  Google Scholar 

  • Coker D, Lykotrafitis G, Needleman A, Rosakis AJ (2005) Frictional sliding modes along an interface between identical elastic plates subject to shear impact loading. J Mech Phys Solids 53:884–992

    Article  Google Scholar 

  • Deshpande VS, Fleck NA (2000) Isotropic constitutive models for metallic foams. J Mech Phys Solids 48:1253–1283

    Article  CAS  Google Scholar 

  • Dieterich JH (1979) Modeling of rock friction. 1 Experimental results and constitutive equations. J Geophys Res 84:2161–2168

    Article  Google Scholar 

  • Dunham EM, Bhat HS (2008) Attenuation of radiated ground motion and stresses from three-dimensional supershear ruptures. J Geophys Res 113:B08319

    Article  Google Scholar 

  • Heaton TH (1990) Evidence for and implications of self-healing pulses of slip in earthquake rupture. Phys Earth Planet Int 64:1–20

    Article  Google Scholar 

  • Hutchens SB, Needleman A, Greer JR (2011) Analysis of uniaxial compression of vertically aligned carbon nanotubes. J Mech Phys Solids 59:2227–2237

    Article  CAS  Google Scholar 

  • Krieg RO, Key SW (1973) Transient shell response by numerical time integration. Int J Numer Meth Eng 7:273–286

    Article  Google Scholar 

  • Kurzon I, Lyakhovsky V, Ben-Zion Y (2019) Dynamic rupture and seismic radiation in a damage-breakage rheology model. Pure Appl Geophys 176:1003–1020

    Article  Google Scholar 

  • Linker MF, Dieterich JH (1992) Effects of variable normal stress on rock friction: observations and constitutive equations. J Geophys Res 97:4923–4940

    Article  Google Scholar 

  • Lu X, Lapusta N, Rosakis AJ (2007) Pulse-like and crack-like ruptures in experiments mimicking crustal earthquakes. Proc Natl Acad Sci USA 104:18931–18936

    Article  Google Scholar 

  • Lu X, Lapusta N, Rosakis AJ (2010) Pulse-like and crack-like dynamic shear ruptures on frictional interfaces: experimental evidence, numerical modeling, and implications. Int J Fract 163:27–39

    Article  Google Scholar 

  • Lykotrafitis G, Rosakis AJ (2006) Dynamic sliding of frictionally held bimaterial interfaces subjected to impact shear loading. Proc R Soc A 462:2997–3026

    Article  Google Scholar 

  • Needleman A (2018) Dynamic mode II crack growth along an interface between an elastic solid and a plastic solid. J Mech Phys Solids 120:22–35

    Article  Google Scholar 

  • Passelègue FX, Schubnel A, Nielsen S, Bhat HS, Madariaga R (2013) From sub-Rayleigh to supershear ruptures during stick-slip experiments on crustal rocks. Science 340:1208–1211

    Article  Google Scholar 

  • Peirce D, Shih CF, Needleman A (1984) A tangent modulus method for rate dependent solids. Comput Struct 18:875–887

    Article  Google Scholar 

  • Povirk GL, Needleman A (1993) Finite element simulations of fiber pull-out. J Eng Mater Tech 115:286–291

    Article  Google Scholar 

  • Prakash V (1998) Frictional response of sliding interfaces subjected to time varying normal pressures. J Tribol 120:97–102

    Article  CAS  Google Scholar 

  • Prakash V, Clifton RJ (1993) Pressure-shear plate impact measurement of dynamic friction for high speed machining applications. In: Proceedings of the 7th International Congress on Exp. Mech., Society of Experimental Mechanics, Bethel, pp. 556–564

  • Ranjith K, Rice JR (2001) Slip dynamics at an interface between dissimilar materials. J Mech Phys Solids 49:341–361

    Article  Google Scholar 

  • Renardy M (1992) Ill-posedness at the boundary for elastic solids sliding under Coulomb friction. J. Elasticity 27:281–287

    Article  Google Scholar 

  • Rice JR, Ruina AL (1983) Stability of frictional sliding. J Appl Mech 50:343–349

    Article  Google Scholar 

  • Rosakis AJ, Xia K, Lykotrafitis G, Kanamori H (2007) Dynamic shear rupture in frictional interfaces: speeds, directionality, and modes. In: Schubert G (ed) Treatise on Geophysics, Elsevier, 153–192

  • Ruina AL (1983) Slip instability and state variable friction laws. J Geophys Res 88:10359–10370

    Article  Google Scholar 

  • Shi Z, Ben-Zion Y, Needleman A (2008) Properties of dynamic rupture and energy partition in a solid with a frictional interface. J Mech Phys Solids 56:5–24

    Article  Google Scholar 

  • Shi Z, Needleman A, Ben-Zion Y (2010) Frictional slip modes and partition of energy during dynamical frictional sliding between identical elastic-viscoplastic solids. Int J Fract 162:51–67

    Article  Google Scholar 

  • Shlomai H, Fineberg J (2016) The structure of slip-pulses and supershear ruptures driving slip in bimaterial friction. Nat Commun 7:11787

    Article  CAS  Google Scholar 

  • Taj W, Coker D (2018) Dynamic frictional sliding modes between two homogenous interfaces. IOP Conf Ser 295, 012001

  • Templeton EI, Baudet A, Bhat HS, Dmowska R, Rice JR, Rosakis AJ, Rousseau C-E (2009) Finite element simulations of dynamic shear rupture experiments and dynamic path selection along kinked and branched faults. J Geophys Res 114:B08304

    Article  Google Scholar 

  • Xu S, Ben-Zion Y (2013) Numerical and theoretical analyses of in-plane dynamic rupture on a frictional interface and off-fault yielding patterns at different scales. Geophys J Int 193:304–320

    Article  Google Scholar 

  • Zheng G, Rice JR (1998) Conditions under which velocity-weakening friction allows a self-healing versus a crack-like mode of rupture. Bull Seismol Soc Am 88:1466–1483

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Materials Science and Engineering, Texas A&M University, College Station, TX, 77843, USA

    Alan Needleman

Authors
  1. Alan Needleman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alan Needleman.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Needleman, A. Dynamic frictional slip along an interface between plastically compressible solids. Int J Fract 230, 179–191 (2021). https://doi.org/10.1007/s10704-021-00551-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-021-00551-w

Keywords

Search

Navigation