Transparent anisotropy for the relaxed micromorphic model: macroscopic consistency conditions and long wave length asymptotics
暂无分享,去创建一个
Patrizio Neff | Ionel-Dumitrel Ghiba | Angela Madeo | Marco Valerio d'Agostino | P. Neff | A. Madeo | Gabriele Barbagallo | Rafael Abreu | I. Ghiba | Gabriele Barbagallo | Rafael Abreu | M. d’Agostino
[1] Roman Teisseyre,et al. Earthquake processes in a micromorphic continuum , 1973 .
[3] Patrizio Neff,et al. Curl bounds Grad on SO(3) , 2006 .
[4] W. D. Claus,et al. Dislocation dispersion of elastic waves , 1971 .
[5] N. Auffray. On the algebraic structure of isotropic generalized elasticity theories , 2013, 1309.3939.
[6] P. Neff,et al. Existence Theorem for Geometrically Nonlinear Cosserat Micropolar Model Under Uniform Convexity Requirements , 2014, 1410.4225.
[7] Giuseppe Rosi,et al. Reflection and transmission of elastic waves at interfaces embedded in non-local band-gap metamaterials : a comprehensive study via the relaxed micromorphic model , 2016, 1602.05218.
[8] Samuel Forest,et al. Generalized continua and non‐homogeneous boundary conditions in homogenisation methods , 2011 .
[9] Youping Chen,et al. Determining material constants in micromorphic theory through phonon dispersion relations , 2003 .
[10] G. Rosi,et al. Band gaps in the relaxed linear micromorphic continuum , 2014, 1405.3493.
[11] P. Neff,et al. A canonical extension of Kornʼs first inequality to H(Curl) motivated by gradient plasticity with plastic spin , 2011, 1106.4731.
[12] S. Koh,et al. Wave propagation in a micro-isotropic, micro-elastic solid , 1973 .
[13] S. Vidoli,et al. Generalized Hooke's law for isotropic second gradient materials , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[14] P. Neff,et al. Complete band gaps including non-local effects occur only in the relaxed micromorphic model , 2016, 1602.04315.
[15] Patrizio Neff,et al. Existence, Uniqueness and Stability in Linear Cosserat Elasticity for Weakest Curvature Conditions , 2010 .
[16] M. Lazar. On Conservation and Balance Laws in Micromorphic Elastodynamics , 2007 .
[17] P. Neff,et al. Stable identification of linear isotropic Cosserat parameters: bounded stiffness in bending and torsion implies conformal invariance of curvature , 2010 .
[18] R. Teisseyre. Symmetric Micromorphic Continuum: Wave Propagation, Point Source Solutions and some Applications to Earthquake Processes , 1974 .
[19] E. Cosserat,et al. Théorie des Corps déformables , 1909, Nature.
[20] C. Sansour. A unified concept of elastic-viscoplastic Cosserat and micromorphic continua , 1998 .
[21] Paul Steinmann,et al. A unifying treatise on variational principles for gradient and micromorphic continua , 2005 .
[22] Samuel Forest,et al. Micromorphic Approach for Gradient Elasticity, Viscoplasticity, and Damage , 2009 .
[23] Carlo Sansour,et al. A formulation for the micromorphic continuum at finite inelastic strains , 2010 .
[24] A. Misra,et al. Granular micromechanics based micromorphic model predicts frequency band gaps , 2015, Continuum Mechanics and Thermodynamics.
[25] R. Bhatia. Positive Definite Matrices , 2007 .
[26] M. Lazar,et al. The relaxed linear micromorphic continuum: well-posedness of the static problem and relations to the gauge theory of dislocations , 2014, 1403.3442.
[27] E. Kröner. Der fundamentale Zusammenhang zwischen Versetzungsdichte und Spannungsfunktionen , 1955 .
[28] Luca Placidi,et al. The relaxed linear micromorphic continuum: Existence, uniqueness and continuous dependence in dynamics , 2013, 1308.3762.
[29] Samuel Forest,et al. Nonlinear microstrain theories , 2006 .
[30] I. Kunin,et al. Elastic Media with Microstructure II , 1982 .
[31] Patrizio Neff,et al. The modified indeterminate couple stress model: Why Yang et al.'s arguments motivating a symmetric couple stress tensor contain a gap and why the couple stress tensor may be chosen symmetric nevertheless , 2015, 1512.02053.
[32] Youping Chen,et al. Connecting molecular dynamics to micromorphic theory. (I). Instantaneous and averaged mechanical variables , 2003 .
[33] G. Starke,et al. New Poincaré-type inequalities , 2014 .
[34] P. Neff,et al. First evidence of non-locality in real band-gap metamaterials: determining parameters in the relaxed micromorphic model , 2016, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[35] W. Voigt,et al. Lehrbuch der Kristallphysik , 1966 .
[36] Patrizio Neff,et al. Existence and Uniqueness for Rate-Independent Infinitesimal Gradient Plasticity with Isotropic Hardening and Plastic Spin , 2010 .
[37] Patrizio Neff,et al. Existence of minimizers for a finite-strain micromorphic elastic solid , 2006, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.
[38] D. Ieşan,et al. Extremum principles and existence results in micromorphic elasticity , 2001 .
[39] T. Böhlke,et al. A Minimum Problem Defining Effective Isotropic Elastic Properties , 2000 .
[40] Youping Chen,et al. Connecting molecular dynamics to micromorphic theory. (II). Balance laws , 2003 .
[41] Luca Placidi,et al. Wave propagation in relaxed micromorphic continua: modeling metamaterials with frequency band-gaps , 2013, 1309.1722.
[42] Franck J. Vernerey,et al. A micromorphic model for the multiple scale failure of heterogeneous materials , 2008 .
[43] A. Cemal Eringen,et al. A MICROMORPHIC APPROACH TO DISLOCATION THEORY AND ITS RELATION TO SEVERAL EXISTING THEORIES. , 1969 .
[44] P. Neff,et al. A variant of the linear isotropic indeterminate couple-stress model with symmetric local force-stress, symmetric nonlocal force-stress, symmetric couple-stresses and orthogonal boundary conditions , 2015, 1504.00868.
[45] Maher Moakher,et al. The Closest Elastic Tensor of Arbitrary Symmetry to an Elasticity Tensor of Lower Symmetry , 2006, cond-mat/0608311.
[46] A.J.M. Spencer,et al. Theory of invariants , 1971 .
[47] P. Neff,et al. A numerical study for linear isotropic Cosserat elasticity with conformally invariant curvature , 2009 .
[48] A. Cemal Eringen,et al. NONLINEAR THEORY OF SIMPLE MICRO-ELASTIC SOLIDS-I , 1964 .
[49] Masaru Shimbo. A Geometrical Formulation of Asymmetric Features in Plasticity , 1975 .
[50] Micromorphic Continuum and Fractal Fracturing in the Lithosphere , 2000 .
[51] P. Neff,et al. Maxwell meets Korn: A new coercive inequality for tensor fields in RN×N with square‐integrable exterior derivative , 2011, 1105.5013.
[52] H. Altenbach,et al. A Variationally Consistent Derivation of Microcontinuum Theories , 2011 .
[53] P. M. Mariano,et al. Computational aspects of the mechanics of complex materials , 2005 .
[54] T. Pence,et al. Finite Stretching and Shearing of an Internally Balanced Elastic Solid , 2015 .
[55] Alexander Düster,et al. Two-scale modelling of micromorphic continua , 2009 .
[56] P. Neff,et al. Modeling Phononic Crystals via the Weighted Relaxed Micromorphic Model with Free and Gradient Micro-Inertia , 2016, 1610.03878.
[57] Raffaele Barretta,et al. Micromorphic continua: non-redundant formulations , 2016 .
[58] Patrizio Neff,et al. Real wave propagation in the isotropic-relaxed micromorphic model , 2016, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[59] P. Neff,et al. A new paradigm: the linear isotropic Cosserat model with conformally invariant curvature energy , 2009 .
[60] Ch. Tsakmakis,et al. Micromorphic continuum Part I: Strain and stress tensors and their associated rates , 2009 .
[61] P. Germain,et al. The Method of Virtual Power in Continuum Mechanics. Part 2: Microstructure , 1973 .
[62] P. Neff. On Korn's first inequality with non-constant coefficients , 2002, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.
[63] Patrizio Neff,et al. Existence results in dislocation based rate-independent isotropic gradient plasticity with kinematical hardening and plastic spin: The case with symmetric local backstress , 2015, 1504.01973.
[64] Franck J. Vernerey,et al. Multi-scale micromorphic theory for hierarchical materials , 2007 .
[65] Samuel Forest,et al. Homogenization methods and mechanics of generalized continua - part 2 , 2002 .
[66] P. Neff,et al. Poincare meets Korn via Maxwell: Extending Korn's First Inequality to Incompatible Tensor Fields , 2012, 1203.2744.
[67] G. Maugin,et al. Modelling of complex elastic crystals by means of multi-spin micromorphic media , 2005 .
[68] Stephen C. Cowin,et al. A new proof that the number of linear elastic symmetries is eight , 2001 .
[69] G. Starke,et al. Dev-Div- and DevSym-DevCurl-inequalities for incompatible square tensor fields with mixed boundary conditions , 2013, 1307.1434.
[70] Azim Eskandarian,et al. Atomistic viewpoint of the applicability of microcontinuum theories , 2004 .
[71] A. Eringen. Mechanics of micromorphic materials , 1966 .
[72] P. Neff,et al. Rotational invariance conditions in elasticity, gradient elasticity and its connection to isotropy , 2016, 1603.06153.
[73] A. C. Smith. Inequalities between the constants of a linear micro-elastic solid , 1968 .
[74] Paul Steinmann,et al. On deformational and configurational mechanics of micromorphic hyperelasticity – Theory and computation , 2007 .
[75] Patrizio Neff,et al. On material constants for micromorphic continua , 2004 .
[76] Luca Placidi,et al. A unifying perspective: the relaxed linear micromorphic continuum , 2013, Continuum Mechanics and Thermodynamics.
[77] R. D. Mindlin. Micro-structure in linear elasticity , 1964 .
[78] W. Voigt. Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper , 1889 .
[79] P. Neff,et al. Integrability conditions between the first and second Cosserat deformation tensor in geometrically nonlinear micropolar models and existence of minimizers , 2015, 1504.08003.
[80] P. Neff,et al. A variant of the linear isotropic indeterminate couple stress model with symmetric local force-stress, symmetric nonlocal force-stress, symmetric couple-stresses and complete traction boundary conditions , 2015 .
[81] S. Forest. Mechanics of generalized continua: construction by homogenizaton , 1998 .
[82] D. Lovett,et al. Tensor Properties of Crystals , 1989 .
[83] G. Modica,et al. Ground states in complex bodies , 2008, 0802.1435.
[84] S. Koh. A special theory of microelasticity , 1970 .
[85] P. Neff,et al. The Cosserat couple modulus for continuous solids is zero viz the linearized Cauchy‐stress tensor is symmetric , 2006 .
[86] A. Eringen. Microcontinuum Field Theories , 2020, Advanced Continuum Theories and Finite Element Analyses.
[87] Non-Classical Continuum Mechanics , 2017 .
[88] G. Bonnet,et al. On the inversion of non symmetric sixth-order isotropic tensors and conditions of positiveness of third-order tensor valued quadratic functions , 2011 .
[89] Patrizio Neff,et al. A Geometrically Exact Micromorphic Model for Elastic Metallic Foams Accounting for Affine Microstructure. Modelling, Existence of Minimizers, Identification of Moduli and Computational Results , 2007 .
[90] C. Boehmer,et al. Soliton-like solutions based on geometrically nonlinear Cosserat micropolar elasticity , 2015, 1503.08860.