SAFIR project (http://safir2018.vtt.fi/) The Finnish Research Programme on Nuclear Power Plant Safety 2015-2018 Using the Abaqus CDP Model in Impact Simulations Alexis Fedoroff Technical reseach centre of Finland (VTT), Nuclear safety.
Motivation 31/10/2018 2
Beyond design criteria structural assessments global behaviour of RC structures under impact local behaviour of RC structures under impact 31/10/2018 3
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
Benchmark simulation example 31/10/2018 5
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
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 - - 31/10/2018 7
IRIS P1 benchmark at t=0ms 31/10/2018 8
IRIS P1 benchmark at t=1ms 31/10/2018 9
IRIS P1 benchmark at t=2ms 31/10/2018 10
IRIS P1 benchmark at t=3ms 31/10/2018 11
IRIS P1 benchmark at t=4ms 31/10/2018 12
IRIS P1 benchmark at t=5ms 31/10/2018 13
IRIS P1 benchmark at t=6ms 31/10/2018 14
IRIS P1 benchmark at t=7ms 31/10/2018 15
IRIS P1 benchmark at t=8ms 31/10/2018 16
IRIS P1 benchmark at t=9ms 31/10/2018 17
IRIS P1 benchmark at t=10ms 31/10/2018 18
IRIS P1 benchmark at t=11ms 31/10/2018 19
IRIS P1 benchmark at t=12ms 31/10/2018 20
IRIS P1 benchmark at t=13ms 31/10/2018 21
IRIS P1 benchmark at t=14ms 31/10/2018 22
Material modelling issues 31/10/2018 23
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 31/10/2018 24
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. 31/10/2018 25
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 31/10/2018 26
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 + 0.6 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 + 0.6 max tt [0,tt ii ] εεmax tt QS εε max 31/10/2018 27
Uniaxial tensile response 31/10/2018 28
Uniaxial confined compressive response 31/10/2018 29
Pure shear response 31/10/2018 30
Element deletion criterion 31/10/2018 31
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 31/10/2018 32
ED1: deletion based on internal hardening variables 31/10/2018 33
IRIS P1 test: t=0.00ms Internal hardening variable based element deletion 31/10/2018 34
IRIS P1 test: t=1.00ms Internal hardening variable based element deletion 31/10/2018 35
IRIS P1 test: t=2.00ms Internal hardening variable based element deletion 31/10/2018 36
IRIS P1 test: t=3.00ms Internal hardening variable based element deletion 31/10/2018 37
IRIS P1 test: t=4.00ms Internal hardening variable based element deletion 31/10/2018 38
IRIS P1 test: t=5.00ms Internal hardening variable based element deletion 31/10/2018 39
Punch cone shape after impact 31/10/2018 40
Time evolution of missile tail velocity 31/10/2018 41
Permanent deformations at wall backside 31/10/2018 42
ED2: deletion based on shear strain 31/10/2018 43
IMPACT A12 test: t=0.00ms Shear strain based element deletion Dilation angle 30 Dilation angle 35 31/10/2018 44
IMPACT A12 test: t=0.25ms Shear strain based element deletion Dilation angle 30 Dilation angle 35 31/10/2018 45
IMPACT A12 test: t=0.50ms Shear strain based element deletion Dilation angle 30 Dilation angle 35 31/10/2018 46
IMPACT A12 test: t=1.00ms Shear strain based element deletion Dilation angle 30 Dilation angle 35 31/10/2018 47
IMPACT A12 test: t=2.00ms Shear strain based element deletion Dilation angle 30 Dilation angle 35 31/10/2018 48
IMPACT A12 test: t=3.00ms Shear strain based element deletion Dilation angle 30 Dilation angle 35 31/10/2018 49
IMPACT A12 test: t=4.00ms Shear strain based element deletion Dilation angle 30 Dilation angle 35 31/10/2018 50
Missile residual velocity measured residual velocity 31/10/2018 51
ED2: deletion based on fracture energy 31/10/2018 52
IMPACT A12 test: t=0.00ms Fracture energy based element deletion 31/10/2018 53
IMPACT A12 test: t=0.25ms Fracture energy based element deletion 31/10/2018 54
IMPACT A12 test: t=0.50ms Fracture energy based element deletion 31/10/2018 55
IMPACT A12 test: t=1.00ms Fracture energy based element deletion 31/10/2018 56
IMPACT A12 test: t=2.00ms Fracture energy based element deletion 31/10/2018 57
Missile residual velocity measured residual velocity 31/10/2018 58
Conclusions 31/10/2018 59
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? 31/10/2018 60