(ISV) Model, Y. Sun, K. Maciejewski, H. Ghonem, 2008.

Numerical Application of Internal State Variable (ISV) Model
Yaofeng Sun, Kimberly Maciejewski, Hamouda Ghonem
Department of Mechanical Engineering & Applied Mechanics
University of Rhode Island, Kingston, RI, 02881
Objective
II. Simulation of Deformation Response of Single Steel Beam
Simulate deformation of a steel structure under
variable loading rate and temperature conditions using
finite element analysis (FE) with an internal state
variable (ISV) model to describe the visco-plastic
material behavior.
Single Steel Beam Model
Finite element modeling of steel structure for heat transfer analysis
Element type: plain strain (CPE4)
Element size: 0.02 m in transverse direction, 0.1 m in lengthwise direction
rate
Temperature
300 oC
700
oC
Pressure (MPa)
Element type: 2D and 4 nodes element (DC2D4) for heat transfer
Initial temperature: 25 oC
Surface heat flux: 110 KW/m2
Loading
I. Development of Abaqus UMAT subroutine
-Implementation of ISV model into Abaqus UMAT
-Validation of UMAT subroutine
-Heat Transfer Analysis
Pressure load
Matrix of simulation cases
Outline
III.Simulation of Deformation Response of Steel Structure
1.5 MPa/min
P
0.15
MPa/min
Duration: 60 minutes (1 hour)
load rate = P/t
T3-LR15
T7-LR15
T3-LR015
t Time (min)
T7-LR015
Material thermal properties
Mass Density
7800 kg/m3
Simulated deflection of single steel beam
II. Simulation of deformation response of single steel beam
-Load rate effect
-Temperature effect
III.Simulation of deformation response of steel structure
under fire condition
-Simulation strategy & Geometry modeling
-Heat transfer analysis
-Stress/Deformation analysis
Thermal Conductivity
50 J/(m·°C)
Specific heat
470 W/(kg·°C)
Temperature distribution in the middle bottom cell, and temperature
evolution at 3 nodes during heat transfer
Temperature Effect
Loading Rate Effect
Top
Middle
Bottom
I. Development of ABAQUS UMAT
 ij ,  ij , T , SDVk at time t
ABAQUS Solver:
 ij , T for time t  t
-Deformation/Stress Analysis
ABAQUS UMAT
Pass
Finite Element
Equilibrium Conditions
Return
 ij , SDVk
,  
Note:
III. Simulation of Deformation Response of Steel Structure
Finite element modeling of steel structure for deformation/stress analysis
ISV Model Equations
for time t  t
Material properties defined
in UMAT of ISV model.
UMAT is called for each Gauss point of the mesh at each time increment.
Read input parameter  ij ,  ij ,
T , SDVk for the time t , and
 ij , T for the time t  t
Determine temperature-dependent
material constants for the temperature
T  T based on their functions
of continuous temperature
4
T2
SDV are solution-dependent state variables, e.g. back stresses in ISV model.
Temperature field from
heat transfer analysis
Return to ABAQUS
ABAQUS
Call UMAT
T (oC)
P (MPa)
T1
Calculate
 ij ,  
Calculate SDVk
X ij1  ..., X ij2  ...R  ...
Calculate stress rate
 ij  E ije
Calculate SDV rate
X ij1  ... X ij2  ...R  ...
Calculate elastic strain
rate  ije   ij   ijp
 note :  ij   ij t 
Calculate viscoplastic strain
3  ij  X ij 
p
rate  ij  p
2 J 2 ( ij  X ij )
Calculate viscous stress
 v  J 2 ( ij  X ij )  R  k
Calculate
n
   v n 1 
v 

p    exp     
 K 
K


Deformation response of a
steel beam is loading-rate
independent at low
temperature 300°C, but
loading-rate dependent at
high temperature 700°C.
Deformation response of a
steel beam is significantly
affected by temperature. The
steel softens at elevated
temperature.
2
62
122
Time (min)
Load Step 1: Increasing mechanical pressure loading on beam
Load Step 2: Constant mechanical loading & varied temperature distribution
Load Step 3: Constant mechanical loading & constant temperature distribution
III. Simulation of Deformation Response of Steel Structure
Under Fire Condition
Samples of material constants as a function of temperature
Simulation strategy: Sequentially coupled thermal-stress analysis
Thermal
properties
Case 1: Monotonic test simulation
One 2D element model was
used for the validation with two
case studies
Nodes 1 & 2 are fixed
horizontally, and Nodes 1 & 4
vertically
Displacement loading is
applied on Nodes 3 & 4.
Thermal boundary
conditions & loading
Exaggerated view of predicted deformation of the steel structure
Viscoplastic deformation due to time
effect (strain-rate sensitivity)
Nodal temperature
distribution history
I. Development of ABAQUS UMAT
-Validation of UMAT Subroutine
Heat Transfer
Analysis
Load step 3
Load step 2
ABAQUS
UMAT
Stress/deformation
Analysis
Structural boundary
conditions & loading
Deflection increase due to
temperature rise (material softening)
Deflection increase due to
mechanical loading increase
Displacement (mm)
Displacement, Strain, Stress
0.01
Load step 1
Deflection evolution of the left and middle beams in the first floor
Structure geometry and finite element meshing
Conclusions
2000
• ISV model has been formulated as an ABAQUS UMAT
subroutine in a FE algorithm
Time (second)
• FE simulations were carried out on single and multi steel
members subjected to fire conditions
Case 2: Cyclic test simulation
Element size: 20mm in transverse direction
0.1m in lengthwise direction
Total number of elements: 6660
“Printing service provided by the RI-INBRE Centralized Research Core Facility supported by Grant # P20 RR 16457 from NCRR, NIH.”
• FE simulation results show that the integrated ISV model is
capable of describing steel members’ deformation as a
function of temperature including strain-rate/temperature
interaction

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