Isogeometric analysis of continuum damage in rotation-free composite shells

Abstract A large-deformation, isogeometric rotation-free Kirchhoff–Love shell formulation is equipped with a damage model to efficiently and accurately simulate progressive failure in laminated composite structures. The damage model consists of Hashin’s theory of damage initiation, a bilinear material model for damage evolution, and an appropriately chosen Gibbs free-energy density. Four intralaminar modes of failure are considered: Longitudinal and transverse tension, and longitudinal and transverse compression. The choice of shell formulation and modes of failure modeled make the proposed methodology valid in the regime of relatively thin shell structures where damage occurs without significant evidence of delamination. The damage model is extensively validated against experimental data and its use is also illustrated in the context of multiscale composite damage analysis.

[1]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[2]  Frederica Darema,et al.  Dynamic Data Driven Applications Systems: A New Paradigm for Application Simulations and Measurements , 2004, International Conference on Computational Science.

[3]  Jacob Fish,et al.  Computational damage mechanics for composite materials based on mathematical homogenization , 1999 .

[4]  R. Echter,et al.  A hierarchic family of isogeometric shell finite elements , 2013 .

[5]  Robert L. Taylor,et al.  A constitutive model for anisotropic damage in fiber-composites , 1995 .

[6]  R. Brockman,et al.  Strength Prediction in Open Hole Composite Laminates by Using Discrete Damage Modeling , 2011 .

[7]  Yuri Bazilevs,et al.  3D simulation of wind turbine rotors at full scale. Part II: Fluid–structure interaction modeling with composite blades , 2011 .

[8]  Somnath Ghosh,et al.  Statistically Equivalent Representative Volume Elements for Unidirectional Composite Microstructures: Part II - With Interfacial Debonding , 2006 .

[9]  Thomas J. R. Hughes,et al.  A large deformation, rotation-free, isogeometric shell , 2011 .

[10]  Pedro P. Camanho,et al.  A continuum damage model for composite laminates: Part II – Computational implementation and validation , 2007 .

[11]  Thomas J. R. Hughes,et al.  Encyclopedia of computational mechanics , 2004 .

[12]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[13]  Thomas J. R. Hughes,et al.  An isogeometric analysis approach to gradient damage models , 2011 .

[14]  Jacob Fish,et al.  Two-scale damage modeling of brittle composites , 2001 .

[15]  P. D. Soden,et al.  A COMPARISON OF THE PREDICTIVE CAPABILITIES OF CURRENT FAILURE THEORIES FOR COMPOSITE LAMINATES , 1998 .

[16]  Thomas J. R. Hughes,et al.  Blended isogeometric shells , 2013 .

[17]  E. Ramm,et al.  Models and finite elements for thin-walled structures , 2004 .

[18]  Silvestre T. Pinho,et al.  Modelling failure of laminated composites using physically-based failure models , 2005 .

[19]  Z. Hashin,et al.  A Fatigue Failure Criterion for Fiber Reinforced Materials , 1973 .

[20]  Cv Clemens Verhoosel,et al.  A phase-field description of dynamic brittle fracture , 2012 .

[21]  J. Chaboche,et al.  Two-scale viscoplastic and damage analysis of a metal matrix composite , 1996 .

[22]  Thomas J. R. Hughes,et al.  Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .

[23]  Cv Clemens Verhoosel,et al.  An isogeometric continuum shell element for non-linear analysis , 2014 .

[24]  Yuri Bazilevs,et al.  A computational procedure for prebending of wind turbine blades , 2012 .

[25]  S. Xia,et al.  A nonlocal damage theory , 1987 .

[26]  Thomas J. R. Hughes,et al.  Isogeometric shell analysis: The Reissner-Mindlin shell , 2010 .

[27]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[28]  Michael R Wisnom,et al.  An experimental investigation into the tensile strength scaling of notched composites , 2007 .

[29]  Thomas J. R. Hughes,et al.  An isogeometric approach to cohesive zone modeling , 2011 .

[30]  L. J. Sluys,et al.  On gradient-enhanced damage and plasticity models for failure in quasi-brittle and frictional materials , 1995 .

[31]  Z. Bažant,et al.  Nonlocal damage theory , 1987 .

[32]  Susanne Ebersbach,et al.  Engineering Mechanics Of Composite Materials , 2016 .

[33]  René de Borst,et al.  The incorporation of gradient damage models in shell elements , 2014 .

[34]  Yuri Bazilevs,et al.  Toward a Computational Steering Framework for Large-Scale Composite Structures Based on Continually and Dynamically Injected Sensor Data , 2012, ICCS.

[35]  J. Reddy Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[36]  T. Belytschko,et al.  X‐FEM in isogeometric analysis for linear fracture mechanics , 2011 .

[37]  Yuri Bazilevs,et al.  The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches , 2010 .

[38]  Roland Wüchner,et al.  Isogeometric shell analysis with Kirchhoff–Love elements , 2009 .

[39]  Eugenio Oñate,et al.  Rotation-free triangular plate and shell elements , 2000 .

[40]  Roland Wüchner,et al.  Computational methods for form finding and optimization of shells and membranes , 2005 .

[41]  Ireneusz Lapczyk,et al.  Progressive damage modeling in fiber-reinforced materials , 2007 .

[42]  S. Murakami,et al.  Mechanical Modeling of Material Damage , 1988 .

[43]  C. Sun,et al.  Prediction of composite properties from a representative volume element , 1996 .

[44]  Cv Clemens Verhoosel,et al.  An isogeometric solid‐like shell element for nonlinear analysis , 2013 .

[45]  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 .

[46]  Cv Clemens Verhoosel,et al.  Numerical homogenization of cracking processes in thin fibre-epoxy layers , 2010 .

[47]  Michael Ortiz,et al.  Fully C1‐conforming subdivision elements for finite deformation thin‐shell analysis , 2001, International Journal for Numerical Methods in Engineering.

[48]  Roland Wüchner,et al.  Upgrading membranes to shells-The CEG rotation free shell element and its application in structural analysis , 2007 .

[49]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

[50]  P. D. Soden,et al.  Lamina properties, lay-up configurations and loading conditions for a range of fibre-reinforced composite laminates , 1998 .

[51]  P. D. Soden,et al.  Predicting failure in composite laminates: the background to the exercise , 1998 .

[52]  Mgd Marc Geers,et al.  Strain-based transient-gradient damage model for failure analyses , 1998 .

[53]  Glaucio H. Paulino,et al.  Influence of the Cohesive Zone Model Shape Parameter on Asphalt Concrete Fracture Behavior , 2008 .

[54]  N. J. Pagano,et al.  Statistically Equivalent Representative Volume Elements for Unidirectional Composite Microstructures: Part I - Without Damage , 2006 .

[55]  Z. Bažant,et al.  Nonlocal Continuum Damage, Localization Instability and Convergence , 1988 .

[56]  Roland Wüchner,et al.  Optimal shapes of mechanically motivated surfaces , 2010 .

[57]  Pedro P. Camanho,et al.  A continuum damage model for composite laminates: Part I - Constitutive model , 2007 .

[58]  S. Li,et al.  Two scale response and damage modeling of composite materials , 2004 .

[59]  Michael R Wisnom,et al.  An experimental and numerical investigation into the damage mechanisms in notched composites , 2009 .