A thermomechanical anisotropic model for shock loading of elastic-plastic and elastic-viscoplastic materials with application to jointed rock

Rubin, M. B.; Vorobiev, O.; Vitali, E.

doi:10.1007/s00466-016-1284-0

A thermomechanical anisotropic model for shock loading of elastic-plastic and elastic-viscoplastic materials with application to jointed rock

Journal Article · Thu Apr 21 00:00:00 EDT 2016 · Computational Mechanics

DOI:https://doi.org/10.1007/s00466-016-1284-0· OSTI ID:1375299

Rubin, M. B. ^[1]; Vorobiev, O. ^[2]; Vitali, E. ^[2]

Technion - Israel Institute of Technology, Haifa (Israel)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Here, a large deformation thermomechanical model is developed for shock loading of a material that can exhibit elastic and inelastic anisotropy. Use is made of evolution equations for a triad of microstructural vectors m_i(i=1,2,3) which model elastic deformations and directions of anisotropy. Specific constitutive equations are presented for a material with orthotropic elastic response. The rate of inelasticity depends on an orthotropic yield function that can be used to model weak fault planes with failure in shear and which exhibits a smooth transition to isotropic response at high compression. Moreover, a robust, strongly objective numerical algorithm is proposed for both rate-independent and rate-dependent response. The predictions of the continuum model are examined by comparison with exact steady-state solutions. Also, the constitutive equations are used to obtain a simplified continuum model of jointed rock which is compared with high fidelity numerical solutions that model a persistent system of joints explicitly in the rock medium.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1375299

Report Number(s):: LLNL-JRNL--678007

Journal Information:: Computational Mechanics, Journal Name: Computational Mechanics Journal Issue: 1 Vol. 58; ISSN 0178-7675

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

References (21)

The Thermodynamics of Irreversible Processes. IV. The Theory of Elasticity and Anelasticity Eckart, Carl Physical Review, Vol. 73, Issue 4 https://doi.org/10.1103/physrev.73.373	journal	February 1948
Calculation of Hyperelastic Response of Finitely Deformed Elastic-Viscoplastic Materials Rubin, M. B.; Attia, A. International Journal for Numerical Methods in Engineering, Vol. 39, Issue 2 https://doi.org/10.1002/(SICI)1097-0207(19960130)39:2<309::AID-NME858>3.0.CO;2-B	journal	January 1996
Review of a Unified Elastic—Viscoplastic Theory Bodner, S. R. Unified Constitutive Equations for Creep and Plasticity https://doi.org/10.1007/978-94-009-3439-9_6	book	January 1987
A critical review of the state of finite plasticity Naghdi, P. M. ZAMP Zeitschrift f�r angewandte Mathematik und Physik, Vol. 41, Issue 3 https://doi.org/10.1007/BF00959986	journal	May 1990
Nonequilibrium thermodynamics and rheology of viscoelastic polymer media Leonov, A. I. Rheologica Acta, Vol. 15, Issue 2 https://doi.org/10.1007/BF01517499	journal	February 1976
Modeling a smooth elastic–inelastic transition with a strongly objective numerical integrator needing no iteration Hollenstein, M.; Jabareen, M.; Rubin, M. B. Computational Mechanics, Vol. 52, Issue 3 https://doi.org/10.1007/s00466-013-0838-7	journal	February 2013
The significance of formulating plasticity theory with reference to loading surfaces in strain space Naghdi, P. M.; Trapp, J. A. International Journal of Engineering Science, Vol. 13, Issue 9-10 https://doi.org/10.1016/0020-7225(75)90080-4	journal	September 1975
Hyperbolic heat conduction and the second law Rubin, M. B. International Journal of Engineering Science, Vol. 30, Issue 11 https://doi.org/10.1016/0020-7225(92)90134-3	journal	November 1992
Plasticity theory formulated in terms of physically based microstructural variables—Part I. Theory Rubin, M. B. International Journal of Solids and Structures, Vol. 31, Issue 19 https://doi.org/10.1016/0020-7683(94)90222-4	journal	October 1994
Plasticity theory formulated in terms of physically based microstructural variables—Part II. Examples Rubin, M. B. International Journal of Solids and Structures, Vol. 31, Issue 19 https://doi.org/10.1016/0020-7683(94)90223-2	journal	October 1994
Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory Simo, J. C. Computer Methods in Applied Mechanics and Engineering, Vol. 99, Issue 1 https://doi.org/10.1016/0045-7825(92)90123-2	journal	August 1992
Thermomechanical constitutive equations for the dynamic response of ceramics Bar-on, E.; Rubin, M. B.; Yankelevsky, D. Z. International Journal of Solids and Structures, Vol. 40, Issue 17 https://doi.org/10.1016/S0020-7683(03)00211-7	journal	August 2003
Practical estimates of rock mass strength Hoek, E.; Brown, E. T. International Journal of Rock Mechanics and Mining Sciences, Vol. 34, Issue 8 https://doi.org/10.1016/S1365-1609(97)80069-X	journal	December 1997
Removal of unphysical arbitrariness in constitutive equations for elastically anisotropic nonlinear elastic–viscoplastic solids Rubin, M. B. International Journal of Engineering Science, Vol. 53 https://doi.org/10.1016/j.ijengsci.2011.12.008	journal	April 2012
Thermodynamic relations for high elastic materials Flory, P. J. Transactions of the Faraday Society, Vol. 57 https://doi.org/10.1039/tf9615700829	journal	January 1961
Finite‐Strain Elastic—Plastic Theory with Application to Plane‐Wave Analysis Lee, E. H.; Liu, D. T. Journal of Applied Physics, Vol. 38, Issue 1 https://doi.org/10.1063/1.1708953	journal	January 1967
On the generation of tangential ground motion by underground explosions in jointed rocks Vorobiev, Oleg; Ezzedine, Souheil; Antoun, Tarabay Geophysical Journal International, Vol. 200, Issue 3 https://doi.org/10.1093/gji/ggu478	journal	February 2015
An Elastic-Viscoplastic Model for Metals Subjected to High Compression Rubin, M. B. Journal of Applied Mechanics, Vol. 54, Issue 3 https://doi.org/10.1115/1.3173065	journal	September 1987
The Second Law of Thermodynamics and Cyclic Processes Green, A. E.; Naghdi, P. M. Journal of Applied Mechanics, Vol. 45, Issue 3 https://doi.org/10.1115/1.3424350	journal	September 1978
Elastic-Plastic Deformation at Finite Strains Lee, E. H. Journal of Applied Mechanics, Vol. 36, Issue 1 https://doi.org/10.1115/1.3564580	journal	March 1969
Advantages of formulating evolution equations for elastic-viscoplastic materials in terms of the velocity gradient instead of the spin tensor Rubin, Miles; Papes, Ondrej Journal of Mechanics of Materials and Structures, Vol. 6, Issue 1-4 https://doi.org/10.2140/jomms.2011.6.529	journal	January 2011

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A new approach to modeling the thermomechanical, orthotropic, elastic-inelastic response of soft materials Rubin, M. B. Mechanics of Soft Materials, Vol. 1, Issue 1 https://doi.org/10.1007/s42558-018-0003-8	journal	December 2018

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58 GEOSCIENCES
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A thermomechanical anisotropic model for shock loading of elastic-plastic and elastic-viscoplastic materials with application to jointed rock

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References (21)

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