A large strain finite volume method for orthotropic bodies with general material orientations

Abstract This paper describes a finite volume method for orthotropic bodies with general principal material directions undergoing large strains and large rotations. The governing and constitutive relations are presented and the employed updated Lagrangian mathematical model is outlined. In order to maintain equivalence with large strain total Lagrangian methods, the constitutive stiffness tensor is updated transforming the principal material directions to the deformed configuration. Discretisation is performed using the cell-centred finite volume method for unstructured convex polyhedral meshes. The current methodology is successfully verified by numerically examining two separate test cases: a circular hole in an orthotropic plate subjected to a traction and a rotating orthotropic plate containing a hole subjected to a pressure. The numerical predictions have been shown to agree closely with the available analytical solutions. In addition, a 3-D composite component is examined to demonstrate the capabilities of the developed methodology in terms of a variable material orientation and parallel processing.

[1]  M. Wheel,et al.  A finite volume method for analysing the bending deformation of thick and thin plates , 1997 .

[2]  Philip Cardiff,et al.  Development of the Finite Volume Method for Hip Joint Stress Analysis , 2012 .

[3]  Transferability of Adhesive Fracture Toughness Measurements between Peel and TDCB Test Methods for a Nano-Toughened , 2011 .

[4]  I. Bijelonja,et al.  A finite volume method for incompressible linear elasticity , 2006 .

[5]  I. Demirdžić,et al.  Finite volume method for thermo-elasto-plastic stress analysis , 1993 .

[6]  I. Demirdžić,et al.  Finite volume analysis of stress and deformation in hygro-thermo-elastic orthotropic body , 2000 .

[7]  Chris Bailey,et al.  A control volume procedure for solving the elastic stress-strain equations on an unstructured mesh , 1991 .

[8]  N. Murphy,et al.  Fracture Properties of PCBN as a Function of Loading Rate and Temperature , 2010 .

[9]  Hrvoje Jasak,et al.  Application of the finite volume method and unstructured meshes to linear elasticity , 2000 .

[10]  H. Jasak Tuković,et al.  UPDATED LAGRANGIAN FINITE VOLUME SOLVER FOR LARGE DEFORMATION DYNAMIC RESPONSE OF ELASTIC BODY , 2007 .

[11]  Philip Cardiff,et al.  Development of a Finite Volume Based Structural Solver for Large Rotation of Non-Orthogonal Meshes , 2012 .

[12]  A. Kinloch,et al.  Rate dependent fracture behaviour of adhesively bonded joints , 2003 .

[13]  G. Venizelos,et al.  High strain rate properties of selected aluminium alloys , 2000 .

[14]  Tn Venkatesh,et al.  Super-linear speed-up of a parallel multigrid Navier-Stokes solver on Flosolver , 2005 .

[15]  A. Ivanković,et al.  Investigating the behaviour of fluid-filled polyethylene containers under base drop impact: A combined experimental/numerical approach , 2009 .

[16]  W. S. Teo,et al.  Modelling the fracture behaviour of adhesively-bonded joints as a function of test rate , 2011 .

[17]  Philip Cardiff,et al.  Development of a finite volume contact solver based on the penalty method , 2012 .

[18]  Hrvoje Jasak,et al.  Dynamic Mesh Handling in OpenFOAM , 2009 .

[19]  J. G. Williams,et al.  Cohesive zone models and the plastically deforming peel test , 2003, The Journal of Adhesion.

[20]  S. Kelly,et al.  Fluid, solid and fluid–structure interaction simulations on patient-based abdominal aortic aneurysm models , 2012, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[21]  François Pellegrini,et al.  PT-Scotch: A tool for efficient parallel graph ordering , 2008, Parallel Comput..

[22]  I. Demirdzic,et al.  Numerical method for coupled fluid flow, heat transfer and stress analysis using unstructured moving meshes with cells of arbitrary topology , 1995 .

[23]  S. Muzaferija,et al.  Adaptive finite volume method for flow prediction using unstructured meshes and multigrid approach , 1994 .

[24]  A Karac,et al.  Validation of a fluid-structure interaction numerical model for predicting flow transients in arteries. , 2009, Journal of biomechanics.

[25]  S. Kelly,et al.  A two-system, single-analysis, fluid—structure interaction technique for modelling abdominal aortic aneurysms , 2010, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[26]  A. Ivankovic,et al.  Finite volume method and multigrid acceleration in modelling of rapid crack propagation in full-scale pipe test , 1997 .

[27]  G. P. Venizelos,et al.  Rapid crack propagation in plastic pipe: predicting full-scale critical pressure from S4 test results , 1998 .

[28]  I. Demirdzic,et al.  FINITE-VOLUME APPROACH TO THERMOVISCOELASTICITY , 2005 .

[29]  M. Wheel,et al.  A geometrically versatile finite volume formulation for plane elastostatic stress analysis , 1996 .

[30]  J. G. Williams,et al.  Application of the finite volume method to the analysis of dynamic fracture problems , 1994 .

[31]  J. Williams,et al.  Numerical Analysis of the Three Point Bend Impact Test for Polymers , 2005 .

[32]  C. J. Greenshields,et al.  A FLUID–STRUCTURE MODEL FOR FAST BRITTLE FRACTURE IN PLASTIC PIPES , 2000 .

[33]  Hrvoje Jasak,et al.  A tensorial approach to computational continuum mechanics using object-oriented techniques , 1998 .

[34]  Kuntinee Maneeratana,et al.  Development of the finite volume method for non-linear structural applications , 2000 .

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

[36]  J. Fainberg,et al.  Finite volume multigrid solver for thermo-elastic stress analysis in anisotropic materials , 1996 .

[37]  J. Mohan,et al.  An Experimental and Numerical Investigation of the Mixed-Mode Fracture Toughness and Lap Shear Strength of Aerospace Grade Composite Joints , 2011 .

[38]  I. Bijelonja,et al.  A finite volume method for large strain analysis of incompressible hyperelastic materials , 2005 .

[39]  S. Muzaferija,et al.  BENCHMARK SOLUTIONS OF SOME STRUCTURAL ANALYSIS PROBLEMS USING FINITE‐VOLUME METHOD AND MULTIGRID ACCELERATION , 1997 .