ECCM 2010 Towards a multiscale analysis of delamination in dynamics Chloé Dupleix-Couderc (1), (2), Olivier Allix (1), Fabrice Gatuingt (1), Benoît Malherbe (2) (1) LMT-Cachan (ENS Cachan/CNRS/Université Paris 6/PRES UniverSud Paris) 61 av. du Président Wilson, F-94230 Cachan, France (2) Airbus France 316 route de Narbonne, F-31000 Toulouse, France Thursday, May 20 th 2010
Outline Industrial context Technical issues Towards a multi-scale method for delamination Conclusions Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 2 /19
Industrial context Aircraft vulnerability: Dynamics problems: Tyres debris impact, bird strike Crash Verification of safety requirements Avoid perforation Damage assessment Important use of numerical simulation Design of composite structures: At first: use of criteria New industrial demand: need of a precise description of local degradation phenomena To improve the design To reduce the margin Cockpit Bird strike Examples of structures dimensioned for impact LGB area Tyre debris CWB rear spar Tyre debris Inlet Bird strike Need to have accurate numerical results for composite structures Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 3 /19
Phenomena to represent Example: tyre debris impact on composite shell structure Impacted structure Structure description Material description In-plane dimension: ~1.2m x 1m Oriented plies Ply thickness: ~0.1mm Accurate representation of delamination: Analysis of degradation looking at ply scale Delaminated area Delamination model: interface model between plies Test results Local phenomena observed Matrix cracks Local delamination Delaminated area: ~m 2 Local degradation characteristic length: ~mm [de Borst], [Allix], [Ladevèze] Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 4 /19
Meso-scale model Application to an industrial structure Structure dimension: ~1 m2, 40 plies Simulation length: ~20 ms Use of a meso-scale model: Each ply is meshed separately: 1 element per ply Additional interface elements between plies Time steps: ~10-5 ms Dofs: ~ 3 billions Unrealistic with actual computers Development of a specific numerical approach For transient dynamics problems Considering industrial structure dimension Able to predict accurately the delaminated area Reducing the CPU cost Example of problem to solve Classic shell model : Multi-layer shell elements Time steps: ~ 10-4 ms Dofs: ~100000 dofs Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 5 /19
Outline Industrial context Technical issues Towards a multi-scale method for delamination Conclusions Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 6 /19
Problem analysis Example: 2D composite bean with evolutive effort Structure: 10 plies of composite linear elements for plies (Q4), interface elements with damage behavior [Allix] 2D model Results: evolution of delamination in the structure F A fine description is not useful everywhere in the structure for all time steps t The model used can evolve Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 7 /19
Problem analysis What we would like to do... t0 t1 t2 Elastic behavior, no delamination Initiation of delamination Propagation Global kinematic of the problem: shell Accurate shell description needed Fine representation locally Use of a local model Multiscale method to couple the scales, both in time and space Coupling shell and 3D model Use of 3D shell theory Evolution of the model to follow the delamination Criterion Multiscale method able to evolve Fine model not needed in delaminated areas Model to represent discontinuities Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 8 /19
Technical issues Shell representation Mainly 2D shell elements Global scale Correct coupling with 3D model For 3D shell elements, specific developments required to avoid «locking» and to represent well the shell kinematic: Adaptation of 3D classic element [Hughes & al. 1981], [Simo & al. 1990] Modification of classic shell theory [Parisch 1995] Shape function with high order Multi-scale methods Time methods: Useful to couple different time steps [Belyschko 1979] Coupling the space scale Allowing the use of different time steps Or different integration scheme [Belytschko 1985], [Gravouil & Combescure 2001] Space methods: For static problems: different type depending on transmitted information between sub-domains: BDD [Mandel 1993], FETI [Farhat & Roux 1991], LATiN [Ladevèze 1990] And their application to dynamics problem [Farhat 1993], [Boucard & al.] Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 9 /19
Outline Industrial context Technical issues Towards a multi-scale method for delamination Conclusions Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 10/19
Definition of a global shell scale 3D shell elements: Choose an element with no locking effects Use of an element with high order shape functions: Accurate description of both displacements and stress field in thickness Cubic shape functions element: Q16 Reference problem: bending problem in static Stress field (L/e~7) Sxx Error (%) Stress field (L/e~30) Sxx Error (%) Szz (analytical: 0) Szz (analytical: 0) Even with high L/e ratio, stress and displacements are still accurate Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 11/19
Definition of a global shell scale 3D shell elements: Choose an element with no locking effects Use of an element with high order shape functions: Accurate description of both displacements and stress field in thickness Cubic shape functions element: Q16 Reference problem: bending problem in static Deformed shape for different L/e ratio Even with high L/e ratio, stress and displacements are still accurate Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 11/19
Multi time step method [Gravouil & Combescure 2001] Main characteristic: Enable to couple incompatible meshes Enable to couple different resolution scheme and different time steps Resolution scheme Problem split in 2 parts: for time step t n+1 : Solution of a «free» problem: Consider each sub-domain separately Solution of a «link» problem: M k ÜLink k = Flink k Connecting all the sub-domains Continuity of velocity quantities Ü k = Ü k free + Ü k link M k Ü k free + K k p U k = F k ext with F k Link = C k Λ k F k ext A B C Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 12/19
Application to delamination Use of meso-model with multi-time steps method Mesh (2 plies): Reference Multi-time steps Results: Q4 (1 element per ply) and interface Q4 (1 element per ply) and interfaces, Q16 elements Delaminated area at t end (reference) Delamination propagation in interface Refined mesh (7 elements/ply) Corser mesh (5 elements/ply) Good representation of propagation Damage evolution vs time Similar delamination propagation Propagation across sub-domains interfaces Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 13/19
Application to delamination Use of meso-model and Q16 element Mesh (10 plies): Mesh Time steps Dofs Reference Q4 (1 element per ply) and interfaces t 26680 Multi-time steps/q16 Results: Q4 (1 element per ply) and interfaces, Q16 elements t T = 2 t 10744 Fine Q4 mesh Q16 mesh Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 14/19
Application to delamination Use of meso-model and Q16 element Mesh (10 plies): Mesh Time steps Dofs Reference Q4 (1 element per ply) and interfaces t 26680 Multi-time steps/q16 Results: Q4 (1 element per ply) and interfaces, Q16 elements t T = 2 t 10744 Fine Q4 mesh Q16 mesh Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 14/19
Application to delamination Use of meso-model and Q16 element Mesh (10 plies): Mesh Time steps Dofs Reference Q4 (1 element per ply) and interfaces t 26680 Multi-time steps/q16 Results: Q4 (1 element per ply) and interfaces, Q16 elements Delamination propagation t T = 2 t Damage in interface (t fixed) 10744 Fine Q4 mesh Q16 mesh Delamination at t Good approximation of initiation and propagation Similar damage evolution Differences when delamination reach the shell representation Same accuracy, reducing dofs and time computation Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 14/19
Definition of a multi-scale method Outcome: Delamination propagation is still accurate using a multi-time step method Global kinematic is still accurate using an equivalent shell element Method objectives: Use of a global shell kinematics on the whole structure: Better approximation of the global solution Use of a refined model locally Add to the global mesh a refined mesh Use of different time-step in the 2 models Adaptation of the multi-time step method U m Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 15/19
Method definition t=tn Information transfer between scales: In the thickness From global to local: velocity continuity From local to global: residual forces Method description: Solution of the global problem for t=t n+1 t=tj+ t t=t n + T Solution of the local problem for t=t j Free problem Link problem: global velocity imposed on frontiers t n t n+1 t j t j+1 Calcul of residual stress field on Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 16/19
Method definition t=tn Information transfer between scales: In the thickness From global to local: velocity continuity From local to global: residual forces Method description: Solution of the global problem for t=t n+1 t=tj+ t t=t n + T Solution of the local problem for t=t j Free problem Link problem: global velocity imposed on frontiers t n t n+1 t j t j+1 M G Ü G n+1 = F ext K G p U G n+1 Calcul of residual stress field on Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 16/19
Method definition t=tn Information transfer between scales: In the thickness From global to local: velocity continuity From local to global: residual forces Method description: Solution of the global problem for t=t n+1 t=tj+ t t=t n + T Solution of the local problem for t=t j Free problem Link problem: global velocity imposed on frontiers t n t n+1 u G j+1 Γ t j t j+1 Calcul of residual stress field on M l Ü l,f j+1 = K l p U l j+1 M l Ü l,l j+1 = CΛ j+1 Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 16/19
Method definition t=tn Information transfer between scales: In the thickness From global to local: velocity continuity From local to global: residual forces Method description: Solution of the global problem for t=t n+1 t=tj+ t t=t n + T Solution of the local problem for t=t j Free problem Link problem: global velocity imposed on frontiers t n t n+1 t j t j+1 u G n+1 Γ Calcul of residual stress field on Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 16/19
Method definition Information transfer between scales: In the thickness From global to local: velocity continuity t=tn From local to global: residual forces Method description: Solution of the global problem for t=t n+1 t=tj+ t t=t n + T Solution of the local problem for t=t j Free problem Link problem: global velocity imposed on frontiers t n t n+1 t j t j+1 r n+1 Calcul of residual stress field on Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 16/19
Method definition t=tn Information transfer between scales: In the thickness From global to local: velocity continuity From local to global: residual forces Method description: Solution of the global problem for t=t n+1 t=tj+ t t=t n + T Solution of the local problem for t=t j Free problem Link problem: global velocity imposed on frontiers M G Ü G n+1 = F ext K G p U G n+1 + F r t n t n+1 t j t j+1 r n+1 Calcul of residual stress field on Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 16/19
Example Example: elastic bending beam Mesh: F Global: Q16 elements t Local: refined Q4 mesh Information transfer from global to local only (velocity continuity) Results: Displacements: Strain field Exx Global mesh result Local mesh result Deformed shape (amplified) Exz Similar displacements and strain field Ongoing work: Complete multi-scale method: residual stress transfer from local to global Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 17/19
Outline Industrial context Technical issues Towards a multi-scale method for delamination Conclusions Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 18/19
Conclusions Multi-time steps method applied to: Composite model Coupling different type of elements Good accuracy in both case in predicting delamination initiation and propagation Definition of a multi-scale method for delamination prediction Use of a global shell scale on the whole structure Coupling a local scale with the global scale: use of different time steps information transfer in the thickness Improvements to be done: Substitution of fine model in already delaminated areas: Use of strong discontinuities representation? Other method? Automatic addition of local model Chloé Dupleix-Couderc Towards a multiscale analysis of delamination in dynamics 19/19