Application de la théorie des déformations finies à la détermination de propriétés élastiques des polycristaux de symétrie hexagonale sous haute pression

Perrin, G.; Delannoy, M.

doi:10.1051/jphys:0197800390100108500

Cited by 11 publications

(10 citation statements)

References 20 publications

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“…Note that (A.7) is consistent with the requirement that when strains are small enough, the difference between E and D becomes negligible (both approach the strain tensor of linear elasticity), and the second-order elastic constants become identical to those used in linear elasticity. Result (A.8) is consistent with the relationship derived elsewhere [Perrin and Delannoy, 1978] by substituting…”

Section: Appendix: Elastic Potentials Elastic Constants and Equatiosupporting

confidence: 90%

“…Second-order elastic constant C 11 and first-order Grüneisen parameter Γ 1 are equal for Eulerian and Lagrangian theories. Third-order elastic constants and secondorder Grüneisen parameters are related by [Weaver, 1976;Perrin and Delannoy, 1978;Clayton, 2013]Ĉ 111 =C 111 + 12C 11 ,Γ 11 =Γ 11 + 4Γ 1 .…”

Section: Analysis Of Planar Shock Compressionmentioning

confidence: 99%

“…This strain, which has historically shown promise for hydrostatic compression [Davies, 1974;Weaver, 1976;Perrin and Delannoy, 1978], is applied in this work to problems involving simultaneous volume change and shear, i.e., shock compression. Herein, the designation "Eulerian" is used to refer to a strain that is a function of the inverse deformation gradient [Davies, 1974;Weaver, 1976;Nielsen, 1986], and not necessarily one referred to spatial coordinates.…”

Section: Introductionmentioning

confidence: 99%

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Shock Compression of Metal Crystals: A Comparison of Eulerian and Lagrangian Elastic-Plastic Theories

Clayton

2014

Int. J. Appl. Mechanics

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An unconventional nonlinear elastic theory is advocated for solids undergoing large compression as may occur in shock loading. This theory incorporates an Eulerian strain measure, in locally unstressed material coordinates. Analytical predictions of this theory and conventional Lagrangian theory for elastic shock stress in anisotropic single crystals of aluminum, copper and magnesium are compared. Eulerian solutions demonstrate greater accuracy compared to atomic simulation (aluminum) and faster convergence with increasing order of elastic constants entering the internal energy. A thermomechanical framework incorporating this Eulerian strain and accounting for elastic and plastic deformations is outlined in parallel with equations for Lagrangian finite strain crystal plasticity. For several symmetric crystal orientations, predicted values of volumetric compression at the Hugoniot elastic limit of the two theories begin to differ substantially when octahedral or prismatic slip system strengths exceed about 1% of the shear modulus. Predicted pressures differ substantially for volumetric compression in excess of 5%. Predictions of Eulerian theory are closer to experimental shock data for aluminum, copper, and magnesium polycrystals.

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Section: Appendix: Elastic Potentials Elastic Constants and Equatiosupporting

confidence: 90%

Section: Analysis Of Planar Shock Compressionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Shock Compression of Metal Crystals: A Comparison of Eulerian and Lagrangian Elastic-Plastic Theories

Clayton

2014

Int. J. Appl. Mechanics

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“…Symmetric tensor D is termed an "Eulerian" strain in material coordinates [28], is invariant under rigid rotations of the spatial coordinate frame, and was introduced by Thomsen [85] and soon thereafter Davies [29] for describing the nonlinear thermoelastic response of pressurized cubic crystals. UnlikeW , potentialŴ can be applied to anisotropic solids [66,90]. This model has demonstrated greater intrinsic stability [43] at large shear and compression than usual Lagrangian elasticity incorporatingW that tends towards instability at large uniaxial compression [16].…”

Section: Introductionmentioning

confidence: 99%

Defects in nonlinear elastic crystals: differential geometry, finite kinematics, and second‐order analytical solutions

Clayton

2013

Z Angew Math Mech

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A differential geometric description of crystals with continuous distributions of lattice defects and undergoing potentially large deformations is presented. This description is specialized to describe discrete defects, i.e., singular defect distributions. Three isolated defects are considered in detail: the screw dislocation, the wedge disclination, and the point defect. New analytical solutions are obtained for elastic fields of these defects in isotropic solids of finite extent, whereby terms up to second order in strain, involving elastic constants up to third order, are retained in the stress components. The strain measure used in the nonlinear elastic potential – a symmetric function, expressed in material coordinates, of the inverse deformation gradient – differs from that used in previous solutions for crystal defects, and is thought to provide a more realistic depiction of mechanics of large deformation than previous theory involving third‐order Lagrangian elastic constants and the Green strain tensor. For the screw dislocation and wedge disclination, effects of core pressure and/or possible contraction along the defect line are considered, and radial displacement contributions arise that are absent in the linear elastic solution, affecting dilatation. Stress components are shown to differ from those of linear elastic solutions near defect cores. Volume change from point defects is strongly affected by elastic nonlinearity.

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“…Thermal effects for cubic crystals were considered later in an Eulerian formulation (15), and a mechanical theory for noncubic crystals was initiated in (16) and exercised soon thereafter (17). With the exception of (13,14), these papers remain obscure, and theoretical derivations/predictions and comparisons with data are limited to hydrostatic pressure loading.…”

Section: Objectivementioning

confidence: 99%

A Reformulation of Nonlinear Anisotropic Elasticity for Impact Physics

Clayton¹

2014

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Approved for public release; distribution unlimited. ii REPORT DOCUMENTATION PAGEForm Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY) February 20142. REPORT TYPE ARL-TR-6837 SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution unlimited. SUPPLEMENTARY NOTES ABSTRACTA new anisotropic Eulerian theory of nonlinear thermoelasticity developed in the present work has been shown to provide superior accuracy and/or stability over existing Lagrangian thermoelasticity theory for large static compression and shear deformation of ideal cubic crystals and diamond, and for the shock response of three different metallic crystals. For the shock response of single crystals of quartz and sapphire, Eulerian and Lagrangian theories are of comparable accuracy, with fourthorder elastic constants (quartz) and third-order elastic constants (diamond) necessary for a best fit to published experimental shock-compression data. Superior accuracy of this Eulerian theory, which degenerates to a Birch-Murnaghan equation-of-state when deviatoric stresses are negligible, has been demonstrated for representing the shock-compression response of aluminum, copper, and magnesium.

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Application de la théorie des déformations finies à la détermination de propriétés élastiques des polycristaux de symétrie hexagonale sous haute pression

Cited by 11 publications

References 20 publications

Shock Compression of Metal Crystals: A Comparison of Eulerian and Lagrangian Elastic-Plastic Theories

Shock Compression of Metal Crystals: A Comparison of Eulerian and Lagrangian Elastic-Plastic Theories

Defects in nonlinear elastic crystals: differential geometry, finite kinematics, and second‐order analytical solutions

A Reformulation of Nonlinear Anisotropic Elasticity for Impact Physics

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