Using the Abaqus CDP Model in Impact Simulations

Transcription

1 SAFIR project ( The Finnish Research Programme on Nuclear Power Plant Safety Using the Abaqus CDP Model in Impact Simulations Alexis Fedoroff Technical reseach centre of Finland (VTT), Nuclear safety.

2 Motivation 31/10/2018 2

3 Beyond design criteria structural assessments global behaviour of RC structures under impact local behaviour of RC structures under impact 31/10/2018 3

4 What are the challenges of using Abaqus CDP in impact simulations? The built-in Abaqus CDP is not suited for impact simulations. Needs some tayloring (user subroutines) Experiments on concrete at high speed are scarce. In FE simulations element removal is the simplest way to materialize changes in mesh topology. However, it is difficult to implement element removal a physically correct way. 31/10/2018 4

5 Benchmark simulation example 31/10/2018 5

6 Hard missile impact simulation (IRIS P1 benchmark) 1. Qualitative agreement (failure mode) 2. Quantitative agreement (time history for strains, missile speed, ) simulation experiment 31/10/2018 6

7 Assembly (quarter model) outline Part instance name Material model Continuum description Discretization method Element length concrete slab CDP + ED 3D Lagrangian 8-node reduced 10mm reinforcement MP + JCD + ED 1D Lagrangian 2-node 10mm u-channel LE 2D Lagrangian 4-node reduced 10mm missile LE 2D Lagrangian 4-node reduced 20mm frame - rigid body /10/2018 7

8 IRIS P1 benchmark at t=0ms 31/10/2018 8

9 IRIS P1 benchmark at t=1ms 31/10/2018 9

10 IRIS P1 benchmark at t=2ms 31/10/

11 IRIS P1 benchmark at t=3ms 31/10/

12 IRIS P1 benchmark at t=4ms 31/10/

13 IRIS P1 benchmark at t=5ms 31/10/

14 IRIS P1 benchmark at t=6ms 31/10/

15 IRIS P1 benchmark at t=7ms 31/10/

16 IRIS P1 benchmark at t=8ms 31/10/

17 IRIS P1 benchmark at t=9ms 31/10/

18 IRIS P1 benchmark at t=10ms 31/10/

19 IRIS P1 benchmark at t=11ms 31/10/

20 IRIS P1 benchmark at t=12ms 31/10/

21 IRIS P1 benchmark at t=13ms 31/10/

22 IRIS P1 benchmark at t=14ms 31/10/

23 Material modelling issues 31/10/

24 Physical phenomena in concrete under impact macroscopic scale microscopic scale rate dependence (compression) Quasi-static confinement dependence Void compaction Free water covection rate dependence (tension) Inertia effects Crack propagation inertia 31/10/

25 Enhance the Abaqus CDP model with userdefined field variable dependencies The yield condition F(σ,ft,fc)=0 depends on the evolution of the cohesive stresses (i.e. yield stresses) ft and fc. ft depends on the strain rate and fc depends on the confinement. 31/10/

26 Hillerborg regularization in tensile behavior Element size dependent stress-strain relation: fracture energy independent of element size ll σσ σσ 0 σσ 0 σσ GG ff uu εε εε = ll 1 2 ll 1 2 σσ σσ 0 llσσ 0 EE 2GG ff σσ 0 σσ σσ 0 σσ 0 EE 2GG ff llσσ 0 GG ff uu εε 1 2 εε = llσσ 0 2GG ff σσ 0 2 2GG ff 1 2 ll = ll 2EE σσ 0 EE llσσ 0 31/10/

27 Abaqus CDP model user defined field variables Field variable 1: confinement ratio CR (ii) at increment i CR (ii) = 0.4 σσ cnf tt ii max σσ tt [0,tt ii ] cnf tt ffcm σσ cnf = p q/3 Field variable 2: relative strain rate SR (ii) at increment i SR (ii) = 0.4 εεmax tt ii max tt [0,tt ii ] εεmax tt QS εε max 31/10/

28 Uniaxial tensile response 31/10/

29 Uniaxial confined compressive response 31/10/

30 Pure shear response 31/10/

31 Element deletion criterion 31/10/

32 Element deletion criterion can be based on: 1. the evolution of the internal hardening variables p p εε c εεc,cutoff p p εε t εεt,cutoff & CR CR lim 2. the evolution of pure shear strain content εεs εε s,cutoff & CR CR lim εεs = 2εεoct H(εεmax) 1 (εε mid + εε max 2 )2 +(εε min + εε max (εεmax) 2 +(εε mid ) 2 +(εε min ) 2 2 )2 3. the evolution of dissipated tensile fracture energy ll ch GG ff σσmax dεεmax 1 & CR CR lim 31/10/

33 ED1: deletion based on internal hardening variables 31/10/

34 IRIS P1 test: t=0.00ms Internal hardening variable based element deletion 31/10/

35 IRIS P1 test: t=1.00ms Internal hardening variable based element deletion 31/10/

36 IRIS P1 test: t=2.00ms Internal hardening variable based element deletion 31/10/

37 IRIS P1 test: t=3.00ms Internal hardening variable based element deletion 31/10/

38 IRIS P1 test: t=4.00ms Internal hardening variable based element deletion 31/10/

39 IRIS P1 test: t=5.00ms Internal hardening variable based element deletion 31/10/

40 Punch cone shape after impact 31/10/

41 Time evolution of missile tail velocity 31/10/

42 Permanent deformations at wall backside 31/10/

43 ED2: deletion based on shear strain 31/10/

44 IMPACT A12 test: t=0.00ms Shear strain based element deletion Dilation angle 30 Dilation angle 35 31/10/

45 IMPACT A12 test: t=0.25ms Shear strain based element deletion Dilation angle 30 Dilation angle 35 31/10/

46 IMPACT A12 test: t=0.50ms Shear strain based element deletion Dilation angle 30 Dilation angle 35 31/10/

47 IMPACT A12 test: t=1.00ms Shear strain based element deletion Dilation angle 30 Dilation angle 35 31/10/

48 IMPACT A12 test: t=2.00ms Shear strain based element deletion Dilation angle 30 Dilation angle 35 31/10/

49 IMPACT A12 test: t=3.00ms Shear strain based element deletion Dilation angle 30 Dilation angle 35 31/10/

50 IMPACT A12 test: t=4.00ms Shear strain based element deletion Dilation angle 30 Dilation angle 35 31/10/

51 Missile residual velocity measured residual velocity 31/10/

52 ED2: deletion based on fracture energy 31/10/

53 IMPACT A12 test: t=0.00ms Fracture energy based element deletion 31/10/

54 IMPACT A12 test: t=0.25ms Fracture energy based element deletion 31/10/

55 IMPACT A12 test: t=0.50ms Fracture energy based element deletion 31/10/

56 IMPACT A12 test: t=1.00ms Fracture energy based element deletion 31/10/

57 IMPACT A12 test: t=2.00ms Fracture energy based element deletion 31/10/

58 Missile residual velocity measured residual velocity 31/10/

59 Conclusions 31/10/

60 Conclusions ED1: unrealistic, many coefficients from the hat ED2: better results, but contains still many coefficients from the hat ED3: not bad results, no coefficients from the hat In CDP only tensile behavior is regularized. How about compression and shear? 31/10/