Interfacial discontinuity relations for coupled multifield phenomena and their application to the modeling of thin interphases as imperfect interfaces

Interfacial continuity and discontinuity relations are needed in dealing with a variety of mechanical and physical phenomena in heterogeneous media. The present work consists of two parts. In the first part concerned with perfect interfaces, two orthogonal projection operators reflecting the interfacial continuity and discontinuity of the field variables of coupled mechanical and physical phenomena are introduced and some coordinate-free interfacial relations involving the surface decomposition of a generic linear constitutive law are deduced. In the second part dedicated to the derivation of a general imperfect interface model for coupled multifield phenomena by applying Taylor's expansion to a 3D curved thin interphase perfectly bonded to its two neighboring phases, the interfacial operators and relations given in the first part are used directly so as to render the derivation more direct and to write the final interfacial jump relations characterizing the model in a unified and compact way. The general imperfect interface model obtained in the present work includes as special cases all the relevant ones reported in the literature. (C) 2011 Elsevier Ltd. All rights reserved.

[1]  Zvi Hashin,et al.  Thermoelastic properties and conductivity of carbon/carbon fiber composites , 1990 .

[2]  E. Sanchez-Palencia,et al.  Phénomènes de transmission à travers des couches minces de conductivitéélevée , 1974 .

[3]  L. Walpole,et al.  A coated inclusion in an elastic medium , 1978, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  J. Lothe,et al.  On the existence of surface waves in half-infinite anisotropic elastic media with piezoelectric and piezomagnetic properties , 1992 .

[5]  Qi-Chang He,et al.  A more fundamental approach to damaged elastic stress-strain relations , 1995 .

[6]  Vijay B. Shenoy.  Size-dependent rigidities of nanosized torsional elements , 2001 .

[7]  J. Hadamard,et al.  Leçons sur la propagation des ondes et les equations de l'hydrodynamique , 2015 .

[8]  Julien Yvonnet,et al.  An XFEM/level set approach to modelling surface/interface effects and to computing the size-dependent effective properties of nanocomposites , 2008 .

[9]  G. Milton.  The Theory of Composites , 2002 .

[10]  Bhushan Lal Karihaloo,et al.  Theory of Elasticity at the Nanoscale , 2009 .

[11]  G. Dvorak,et al.  Size-dependent elastic properties of unidirectional nano-composites with interface stresses , 2007 .

[12]  Zvi Hashin,et al.  The Spherical Inclusion With Imperfect Interface , 1991 .

[13]  Rodney Hill,et al.  Progress in solid mechanics , 1963 .

[14]  Manfredo P. do Carmo,et al.  Differential geometry of curves and surfaces , 1976 .

[15]  Rodney Hill,et al.  Interfacial operators in the mechanics of composite media , 1983 .

[16]  Bhushan Lal Karihaloo,et al.  Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress , 2005 .

[17]  J. Yvonnet,et al.  Finite element model of ionic nanowires with size-dependent mechanical properties determined by ab initio calculations , 2011 .

[18]  G. Dvorak,et al.  Fibrous nanocomposites with interface stress: Hill’s and Levin’s connections for effective moduli , 2006 .

[19]  Jianmin Qu,et al.  The effect of slightly weakened interfaces on the overall elastic properties of composite materials , 1993 .

[20]  Bhushan Lal Karihaloo,et al.  Eshelby formalism for nano-inhomogeneities , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[21]  N. Laws.  On interfacial discontinuities in elastic composites , 1975 .

[22]  Y. Benveniste.  An Interface Model for a Three-Dimensional Curved Thin Piezoelectric Interphase between Two Piezoelectric Media , 2009 .

[23]  Touvia Miloh,et al.  The effective conductivity of composites with imperfect thermal contact at constituent interfaces , 1986 .

[24]  Y. Benveniste,et al.  Effective thermal conductivity of composites with a thermal contact resistance between the constituents: Nondilute case , 1987 .

[25]  C. Toulemonde,et al.  Numerical modelling of the effective conductivities of composites with arbitrarily shaped inclusions and highly conducting interface , 2008 .

[26]  Zhu-ping Huang,et al.  Stress concentration tensors of inhomogeneities with interface effects , 2005 .

[27]  Jianmin Qu,et al.  Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films , 2005 .

[28]  Peter Bövik.  On the Modelling of Thin Interface Layers in Elastic and Acoustic Scattering Problems , 1994 .

[29]  E. S. Yang,et al.  Current suppression induced by conduction‐band discontinuity in Al0.35Ga0.65As‐GaAs N‐p heterojunction diodes , 1980 .

[30]  Pradeep Sharma,et al.  Size-Dependent Eshelby’s Tensor for Embedded Nano-Inclusions Incorporating Surface/Interface Energies , 2004 .

[31]  Y. Benveniste,et al.  A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media , 2006 .

[32]  N. Laws,et al.  The determination of stress and strain concentrations at an ellipsoidal inclusion in an anisotropic material , 1977 .

[33]  G. Bonnet,et al.  Size-dependent Eshelby tensor fields and effective conductivity of composites made of anisotropic phases with highly conducting imperfect interfaces , 2010 .

[34]  J. Thorpe.  Elementary Topics in Differential Geometry , 1979 .

[35]  H. L. Quang,et al.  Size-dependent effective thermoelastic properties of nanocomposites with spherically anisotropic phases , 2007 .

[36]  Jan Drewes Achenbach,et al.  Effect of interfacial zone on mechanical behavior and failure of fiber-reinforced composites , 1989 .

[37]  M. B. Rubin,et al.  A Cosserat shell model for interphases in elastic media , 2004 .

[38]  Julien Yvonnet,et al.  A general and efficient computational procedure for modelling the Kapitza thermal resistance based on XFEM , 2011 .

[39]  Rintoul,et al.  Effect of the interface on the properties of composite media. , 1995, Physical review letters.

[40]  Zvi Hashin,et al.  Thin interphase/imperfect interface in conduction , 2001 .

[41]  Q. He,et al.  Estimation of the effective thermoelastic moduli of fibrous nanocomposites with cylindrically anisotropic phases , 2009 .

[42]  S. L. Crouch,et al.  Equivalent inhomogeneity method for evaluating the effective elastic properties of unidirectional multi-phase composites with surface/interface effects , 2010 .

[43]  M. E. Gurtin,et al.  A general theory of curved deformable interfaces in solids at equilibrium , 1998 .

[44]  Robert Lipton,et al.  Reciprocal Relations, Bounds, and Size Effects for Composites with Highly Conducting Interface , 1997, SIAM J. Appl. Math..

[45]  L. Walpole.  Elastic Behavior of Composite Materials: Theoretical Foundations , 1981 .

[46]  Y. Benveniste,et al.  An O(hN) interface model of a three-dimensional curved interphase in conduction phenomena , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[47]  Morton E. Gurtin,et al.  A continuum theory of elastic material surfaces , 1975 .

[48]  Robert Lipton,et al.  Variational methods, bounds and size effects for composites with highly conducting interface , 1997 .

[49]  Y. Benveniste,et al.  The effective mechanical behaviour of composite materials with imperfect contact between the constituents , 1985 .

[50]  S. L. Crouch,et al.  Multiple interacting circular nano-inhomogeneities with surface/interface effects , 2008 .

[51]  G. Dvorak,et al.  Solids containing spherical nano-inclusions with interface stresses: Effective properties and thermal-mechanical connections , 2007 .

[52]  G. Milton,et al.  New exact results for the effective electric, elastic, piezoelectric and other properties of composite ellipsoid assemblages , 2003 .

[53]  Z. Hashin.  Thin interphase/imperfect interface in elasticity with application to coated fiber composites , 2002 .

[54]  Z. Hashin.  Extremum principles for elastic heterogenous media with imperfect interfaces and their application to bounding of effective moduli , 1992 .

[55]  R. Lipton,et al.  Composites with imperfect interface , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[56]  Pradeep Sharma,et al.  Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities , 2003 .

[57]  Tungyang Chen.  An invariant treatment of interfacial discontinuities in piezoelectric media , 1993 .

[58]  S. Gu,et al.  Asymptotic Derivation of a Curved Piezoelectric Interface Model and Homogenization of Piezoelectric Composites , 2008 .

[59]  H. L. Quang,et al.  Variational principles and bounds for elastic inhomogeneous materials with coherent imperfect interfaces , 2008 .