Continuum damage dynamics of a large-scale flexible multibody system comprised of composite beams

Herein, a continuum damage dynamic model of a large-scale flexible multibody system comprising composite beams is proposed based on the framework of the absolute nodal coordinate formulation. To accurately model the continuum damage dynamics of a multibody system, the Hashin criterion is adopted to describe damage initiation during dynamics. A type of nonlinear evolution law is used to characterize the value of material damage. Furthermore, a material stiffness degradation rule is introduced to describe the process of structural damage. A formulation for the damage element elastic force and its Jacobian are derived based on the second Piola–Kirchhoff stress tensor. Two dynamic numerical examples, including a deployment dynamic analysis of the spatial beam structural unit, are conducted to verify the availability and applicability of the proposed model.

[1]  J. Rong,et al.  Dynamic Analysis of Spatial Truss Structures Including Sliding Joint Based on the Geometrically Exact Beam Theory and Isogeometric Analysis , 2020 .

[2]  Mohil Patel,et al.  Locking alleviation in the large displacement analysis of beam elements: the strain split method , 2018 .

[3]  Niklas Gloeckner,et al.  Computational Continuum Mechanics , 2016 .

[4]  Jinyang Zheng,et al.  Failure analysis of carbon fiber/epoxy composite cylindrical laminates using explicit finite element method , 2014 .

[5]  Pedro P. Camanho,et al.  Failure Models and Criteria for Frp Under In-Plane or Three-Dimensional Stress States Including Shear Non-Linearity , 2013 .

[6]  Qiang Tian,et al.  Dynamics of a large scale rigid–flexible multibody system composed of composite laminated plates , 2011 .

[7]  Yunqing Zhang,et al.  Simulation of planar flexible multibody systems with clearance and lubricated revolute joints , 2010 .

[8]  Ahmed A. Shabana,et al.  Computational Dynamics, Third Edition , 2009 .

[9]  Yunqing Zhang,et al.  Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints , 2009 .

[10]  Qiang Tian,et al.  Simulation of a viscoelastic flexible multibody system using absolute nodal coordinate and fractional derivative methods , 2009 .

[11]  D. García-Vallejo,et al.  Three-dimensional formulation of rigid-flexible multibody systems with flexible beam elements , 2008 .

[12]  Maqueda Sanchez,et al.  Use of nonlinear constitutive models in the absolute nodal coordinate formulation , 2008 .

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

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

[15]  M. Arnold,et al.  Convergence of the generalized-α scheme for constrained mechanical systems , 2007 .

[16]  Ahmed A. Shabana,et al.  Poisson modes and general nonlinear constitutive models in the large displacement analysis of beams , 2007 .

[17]  J. G. Jalón.  Twenty-five years of natural coordinates , 2007 .

[18]  J. Domínguez,et al.  An Internal Damping Model for the Absolute Nodal Coordinate Formulation , 2005 .

[19]  A. Shabana,et al.  EFFICIENT INTEGRATION OF THE ELASTIC FORCES AND THIN THREE-DIMENSIONAL BEAM ELEMENTS IN THE ABSOLUTE NODAL COORDINATE FORMULATION , 2005 .

[20]  Johannes Gerstmayr,et al.  The Absolute Coordinate Formulation with Elasto-Plastic Deformations , 2004 .

[21]  Hiroyuki Sugiyama,et al.  Application of Plasticity Theory and Absolute Nodal Coordinate Formulation to Flexible Multibody System Dynamics , 2004 .

[22]  Peter Linde,et al.  Modelling and Simulation of Fibre Metal Laminates , 2004 .

[23]  Peter Eberhard,et al.  Flexible Multibody Systems with Large Deformations and Nonlinear Structural Damping Using Absolute Nodal Coordinates , 2003 .

[24]  R. Y. Yakoub,et al.  Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Applications , 2001 .

[25]  A. Shabana,et al.  Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems , 2000 .

[26]  W Sleight David,et al.  Progressive Failure Analysis Methodology for Laminated Composite Structures , 1999 .

[27]  Ahmed A. Shabana,et al.  Flexible Multibody Dynamics: Review of Past and Recent Developments , 1997 .

[28]  A. Shabana.  An Absolute Nodal Coordinate Formulation for the Large Rotation and Deformation Analysis of Flexible Bodies , 1996 .

[29]  K. Bathe.  Finite Element Procedures , 1995 .

[30]  Fu-Kuo Chang,et al.  An Accumulative Damage Model for Tensile and Shear Failures of Laminated Composite Plates , 1995 .

[31]  Javier García de Jalón,et al.  Kinematic and Dynamic Simulation of Multibody Systems , 1994 .

[32]  Javier García de Jalón,et al.  Kinematic and Dynamic Simulation of Multibody Systems: The Real Time Challenge , 1994 .

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

[34]  Seng C. Tan,et al.  A Progressive Failure Model for Composite Laminates Containing Openings , 1991 .

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

[36]  Fu-Kuo Chang,et al.  The In Situ Ply Shear Strength Distributions in Graphite/Epoxy Laminated Composites , 1987 .

[37]  Z. Hashin.  Analysis of Composite Materials—A Survey , 1983 .

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

[39]  F. Sidoroff,et al.  Damage Induced Elastic Anisotropy , 1982 .

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