A localized mapped damage model for orthotropic materials

This paper presents an implicit orthotropic model based on the Continuum Damage Mechanics isotropic models. A mapping relationship is established between the behaviour of the anisotropic material and that of an isotropic one. The proposed model is used to simulate the failure loci of common orthotropic materials, such as masonry, fibre-reinforced composites and wood. The damage model is combined with a crack-tracking technique to reproduce the propagation of localized cracks in the discrete FE problem. The proposed numerical model is used to simulate the mixed mode fracture in masonry members with different orientations of the brick layers.

[1]  Jean-Louis Chaboche,et al.  ASPECT PHENOMENOLOGIQUE DE LA RUPTURE PAR ENDOMMAGEMENT , 1978 .

[2]  P. D. Soden,et al.  Biaxial test results for strength and deformation of a range of E-glass and carbon fibre reinforced composite laminates: failure exercise benchmark data , 2002 .

[3]  C. C. Wang,et al.  A new representation theorem for isotropic functions: An answer to Professor G. F. Smith's criticism of my papers on representations for isotropic functions , 1970 .

[4]  A. P. Karafillis,et al.  A general anisotropic yield criterion using bounds and a transformation weighting tensor , 1993 .

[5]  Z. Sobotka.  Theorie des plastischen Fließens von anisotropen Körpern , 1969 .

[6]  O. Hoffman.  The Brittle Strength of Orthotropic Materials , 1967 .

[7]  S. Pietruszczak,et al.  Numerical analysis of structural masonry: mesoscale approach , 2008 .

[8]  Stephen W. Tsai,et al.  A General Theory of Strength for Anisotropic Materials , 1971 .

[9]  Alberto Taliercio,et al.  Anisotropic damage model for the multiaxial static and fatigue behaviour of plain concrete , 1996 .

[10]  Miguel Cervera,et al.  Mesh objective tensile cracking via a local continuum damage model and a crack tracking technique , 2006 .

[11]  Richard Von Mises,et al.  Mechanik der plastischen Formänderung von Kristallen , 1928 .

[12]  Aw Page,et al.  THE BIAXIAL COMPRESSIVE STRENGTH OF BRICK MASONRY. , 1981 .

[13]  M. Cervera,et al.  Continuum damage model for orthotropic materials: Application to masonry , 2011 .

[14]  Y. R. Rashid,et al.  Ultimate strength analysis of prestressed concrete pressure vessels , 1968 .

[15]  J. Lemaitre,et al.  Mécanique des matériaux solides , 1996 .

[16]  Pw Kleeman,et al.  THE FAILURE OF BRICK MASONRY UNDER BIAXIAL STRESSES. , 1985 .

[17]  Charles B. Norris,et al.  Strength of orthotropic materials subjected to combined stresses. , 1962 .

[18]  R. Codina,et al.  Mixed stabilized finite element methods in nonlinear solid mechanics: Part I: Formulation , 2010 .

[19]  J. Oliver.  A consistent characteristic length for smeared cracking models , 1989 .

[20]  David A. Cendón,et al.  An embedded cohesive crack model for finite element analysis of brickwork masonry fracture , 2009 .

[21]  D. Green.  Wood: Strength and Stiffness , 2001 .

[22]  E. Oñate,et al.  An anisotropic elastoplastic constitutive model for large strain analysis of fiber reinforced composite materials , 2000 .

[23]  Isaac M Daniel,et al.  Engineering Mechanics of Composite Materials , 1994 .

[24]  Josef Betten,et al.  Creep Theory of Anisotropic Solids , 1981 .

[25]  F. Barlat,et al.  A six-component yield function for anisotropic materials , 1991 .

[26]  Miguel Cervera,et al.  Smeared crack approach: back to the original track , 2006 .

[27]  Sergio Oller,et al.  Nonlinear homogenization techniques to solve masonry structures problems , 2012 .

[28]  Miguel Cervera,et al.  Structural Analysis of Masonry Historical Constructions. Classical and Advanced Approaches , 2010 .

[29]  Sergio Oller,et al.  An anisotropic elastoplastic model based on an isotropic formulation , 1995 .

[30]  J. Oliver,et al.  A strain-based plastic viscous-damage model for massive concrete structures , 1998 .

[31]  D. C. Drucker,et al.  Soil mechanics and plastic analysis or limit design , 1952 .

[32]  Stephen W. Tsai,et al.  Anisotropic strength of composites , 1965 .

[33]  J. Mazars,et al.  The unilateral behaviour of damaged concrete , 1990 .

[34]  S. Oller,et al.  Composite Material Behavior Using a Homogenization Double Scale Method , 2005 .

[35]  Miguel Cervera,et al.  Viscoelasticity and damage model for creep behaviour of historical masonry structures , 2012 .

[36]  J. Lubliner,et al.  Definition of a general implicit orthotropic yield criterion , 2003 .

[37]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—I. Formulation , 1989 .

[38]  Z. Bažant,et al.  Crack band theory for fracture of concrete , 1983 .

[39]  Miguel Cervera,et al.  Mesh objective modeling of cracks using continuous linear strain and displacement interpolations , 2011 .

[40]  Liu I-Shih.  On representations of anisotropic invariants , 1982 .

[41]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—II. Computational aspects , 1987 .

[42]  E. Oñate,et al.  A large strain plasticity model for anisotropic materials - composite material application , 2001 .

[43]  SECTION 3.4 – Anisotropic Yield Conditions , 2001 .

[44]  Sergio Oller,et al.  Mixing anisotropic formulation for analysis of composites , 1996 .

[45]  S. G. Lekhnit︠s︡kiĭ.  Theory of elasticity of an anisotropic body , 1981 .

[46]  David R. Owen,et al.  Universal anisotropic yield criterion based on superquadric functional representation: Part 1. Algorithmic issues and accuracy analysis , 1993 .

[47]  E. Reyes,et al.  Cohesive crack model for mixed mode fracture of brick masonry , 2008 .

[48]  Miguel Cervera,et al.  Continuum FE models for the analysis of Mallorca Cathedral , 2013 .

[49]  P. Lourenço.  Computational strategies for masonry structures : Proefschrift , 1996 .

[50]  Frédéric Barlat,et al.  Plastic behavior and stretchability of sheet metals. Part I: A yield function for orthotropic sheets under plane stress conditions , 1989 .

[51]  M. Cervera,et al.  An orthotropic damage model for the analysis of masonry structures , 2013 .

[52]  Miguel Cervera,et al.  A crack-tracking technique for localized damage in quasi-brittle materials , 2010 .

[53]  M. Gurtin,et al.  Thermodynamics with Internal State Variables , 1967 .

[54]  Josef Betten,et al.  Applications of tensor functions to the formulation of yield criteria for anisotropic materials , 1988 .

[55]  L. Pelà.  Continuum damage model for nonlinear analysis of masonry structures , 2009 .

[56]  M. Kawa,et al.  Limit states for brick masonry based on homogenization approach , 2008 .

[57]  A. Huespe,et al.  A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM , 2006 .

[58]  R. Hill.  The mathematical theory of plasticity , 1950 .

[59]  R. Codina,et al.  Mixed stabilized finite element methods in nonlinear solid mechanics: Part II: Strain localization , 2010 .

[60]  R. Hill.  A theory of the yielding and plastic flow of anisotropic metals , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.