Stress InitializationStress Initialization

Sometimes it is important to induce a steady state preload before Sometimes it is important to induce a steady state preload before performing a transient dynamic analysis.performing a transient dynamic analysis.• Rotating fan or turbine blades, rotating flywheelsRotating fan or turbine blades, rotating flywheels• GravityGravity• Pressurized vessels or tiresPressurized vessels or tires• Stresses induced by a torqued boltStresses induced by a torqued bolt• Shrink-fit partsShrink-fit parts

Methods to induce preloads in LS-DYNAMethods to induce preloads in LS-DYNA• Explicit dynamic relaxationExplicit dynamic relaxation• Quasi-static transient analysis with mass dampingQuasi-static transient analysis with mass damping• Implicit static analysisImplicit static analysis

• 1. Implicit analysis > dynain file > 2. Explicit analysis1. Implicit analysis > dynain file > 2. Explicit analysis• Single analysis employing Implicit/Explicit switchingSingle analysis employing Implicit/Explicit switching• ‘‘Implicit dynamic relaxation’ Implicit dynamic relaxation’

Dynamic Relaxation (DR)Dynamic Relaxation (DR)

DR is an DR is an optionaloptional precurser transient analysis that takes place precurser transient analysis that takes place prior to the start of the regular transient analysis.prior to the start of the regular transient analysis.

DR is typically used to preload a model before onset of transient DR is typically used to preload a model before onset of transient loading. Preload stresses are typically elastic and loading. Preload stresses are typically elastic and displacements are small.displacements are small.

In DR, the computed nodal velocities are reduced each timestep In DR, the computed nodal velocities are reduced each timestep by the dynamic relaxation factor (default = .995). Thus the DR by the dynamic relaxation factor (default = .995). Thus the DR solution is essentially a heavily damped transient solution.solution is essentially a heavily damped transient solution.

The distortional kinetic energy is monitored. When this KE has The distortional kinetic energy is monitored. When this KE has been sufficiently reduced, i.e., the “convergence factor” has been sufficiently reduced, i.e., the “convergence factor” has become sufficiently small, the DR phase terminates and the become sufficiently small, the DR phase terminates and the solution automatically proceeds to the transient analysis phase.solution automatically proceeds to the transient analysis phase.

Alternately, DR can be terminated at a preset termination time.Alternately, DR can be terminated at a preset termination time.

Dynamic RelaxationDynamic Relaxation

DR is typically invoked by setting parameter SIDR in any load DR is typically invoked by setting parameter SIDR in any load curve (*DEFINE_CURVE) to 1 or 2.curve (*DEFINE_CURVE) to 1 or 2.

Loads (curves) tagged for DR are ramped and then held Loads (curves) tagged for DR are ramped and then held constant until the DR solution convergesconstant until the DR solution converges• make sure convergence occurs on the loading ‘plateau’make sure convergence occurs on the loading ‘plateau’

Maintain the load in subsequent transient analysis phase (use Maintain the load in subsequent transient analysis phase (use separate load curve without the ramp)separate load curve without the ramp)

DR converges

SIDR = 1 (DR phase) SIDR = 0 (transient phase)

*CONTROL_DYNAMIC_RELAXATION*CONTROL_DYNAMIC_RELAXATION

*CONTROL_DYNAMIC_RELAXATION parameters*CONTROL_DYNAMIC_RELAXATION parameters Iterations between convergence check (default=250)Iterations between convergence check (default=250)

• Also controls output interval for DRAlso controls output interval for DR Convergence tolerance (default 0.001)Convergence tolerance (default 0.001)

• Ratio of distorsional KE at convergence to peak distorsional KERatio of distorsional KE at convergence to peak distorsional KE• Smaller value results in converged solution nearer to steady Smaller value results in converged solution nearer to steady

state but run will take longer to get therestate but run will take longer to get there Dynamic relaxation factor (default=0.995)Dynamic relaxation factor (default=0.995)

• Reduction factor for nodal velocities each time stepReduction factor for nodal velocities each time step• If value is too small, model never reach steady state due to If value is too small, model never reach steady state due to

overdampingoverdamping Optional termination time for DR (default = infinity)Optional termination time for DR (default = infinity)

• DR will stop if time reaches DRTERM even if convergence DR will stop if time reaches DRTERM even if convergence criterion not satisfiedcriterion not satisfied

Time step scale factor used during DRTime step scale factor used during DR

*CONTROL_DYNAMIC_RELAXATION*CONTROL_DYNAMIC_RELAXATION

* * IDRFLGIDRFLG• Set to 1, activates DR (not required if DR is activated with Set to 1, activates DR (not required if DR is activated with

*DEFINE_CURVE) *DEFINE_CURVE) • Set to 2, will invoke a completely different and very fast Set to 2, will invoke a completely different and very fast

initialization approach … initialization approach … Initialization by Prescribed GeometryInitialization by Prescribed Geometry..• Requires supplemental input file containing nodal displacements and Requires supplemental input file containing nodal displacements and

rotations (“m=filename” on execution line). rotations (“m=filename” on execution line). • Such a file “drdisp.sif” is written at conclusion of standard DR run. Required Such a file “drdisp.sif” is written at conclusion of standard DR run. Required

file format is I8,6E15file format is I8,6E15• If nodal rotations are not included in file, method is invalid for beams and If nodal rotations are not included in file, method is invalid for beams and

shells.shells.

• LS-DYNA runs a short transient analysis of 100 timesteps to preload the LS-DYNA runs a short transient analysis of 100 timesteps to preload the model by imposing the nodal displacements and rotations.model by imposing the nodal displacements and rotations.

• Solution then proceeds with regular transient analysis.Solution then proceeds with regular transient analysis.

• Set to 5, activates implicit method for solution of preloaded stateSet to 5, activates implicit method for solution of preloaded state

Output related to Dynamic RelaxationOutput related to Dynamic Relaxation

ASCII output files are NOT written during DR phase, e.g., ASCII output files are NOT written during DR phase, e.g., GLSTAT, MATSUM, RCFORC, etc.GLSTAT, MATSUM, RCFORC, etc.

Binary database, d3drlf, is written by including command Binary database, d3drlf, is written by including command *DATABASE_BINARY_D3DRLF. Set output interval to 1. This *DATABASE_BINARY_D3DRLF. Set output interval to 1. This will cause a state to be written each time convergence is will cause a state to be written each time convergence is checked during DR (as controlled by NRCYCK in checked during DR (as controlled by NRCYCK in *CONTROL_DYNAMIC_RELAXATION)*CONTROL_DYNAMIC_RELAXATION)• Plotting time histories from d3drlf with LS-PrePost allows user Plotting time histories from d3drlf with LS-PrePost allows user

to confirm solution is near steady stateto confirm solution is near steady state ““relax” file is automatically written and contains record of relax” file is automatically written and contains record of

convergence history.convergence history. “ “drdisp.sif” contains nodal displacements and rotations at drdisp.sif” contains nodal displacements and rotations at

conclusion of DR phase.conclusion of DR phase.

Loads during Dynamic RelaxationLoads during Dynamic Relaxation

Initial velocities are ignored during DR and are imposed at the Initial velocities are ignored during DR and are imposed at the commencement of the regular transient analysis.commencement of the regular transient analysis.

Gravity loads and centrifugal loads (spinning bodies) are imposed Gravity loads and centrifugal loads (spinning bodies) are imposed using *LOAD_BODY_option. using *LOAD_BODY_option. • LCID and LCIDDR are separate curves for transient phase and DR LCID and LCIDDR are separate curves for transient phase and DR

phase, respectively.phase, respectively. Stresses due to torqued bolts can be imposed using Stresses due to torqued bolts can be imposed using

*LOAD_THERMAL_LOAD_CURVE.*LOAD_THERMAL_LOAD_CURVE.• Parts, e.g., bolts, which include coefficient of thermal expansion, Parts, e.g., bolts, which include coefficient of thermal expansion,

e.g., via *MAT_4 or *MAT_ADD_THERMAL_EXPANSION will have e.g., via *MAT_4 or *MAT_ADD_THERMAL_EXPANSION will have thermal stresses imposed.thermal stresses imposed.

• LCID and LCIDDR are separate curves for transient phase and DR LCID and LCIDDR are separate curves for transient phase and DR phase, respectively.phase, respectively.

Other load types or boundary conditions are applied during DR if Other load types or boundary conditions are applied during DR if SIDR flag in corresponding *DEFINE_CURVE is set to 1 or 2. SIDR flag in corresponding *DEFINE_CURVE is set to 1 or 2. Example: *LOAD_SEGMENT, Example: *LOAD_SEGMENT, *BOUNDARY_PRESCRIBED_MOTION.*BOUNDARY_PRESCRIBED_MOTION.

Shrink-fit parts (see slide on *contact_interference)Shrink-fit parts (see slide on *contact_interference)

Preloading a cross-section to a known stress Preloading a cross-section to a known stress

*INITIAL_STRESS_SECTION will preload a cross-*INITIAL_STRESS_SECTION will preload a cross-section of section of solidsolid elements to a prescribed stress value elements to a prescribed stress value• Preload stress (normal to the cross-section) is defined via Preload stress (normal to the cross-section) is defined via

*DEFINE_CURVE (stress vs. time)*DEFINE_CURVE (stress vs. time)• This curve is typically flagged with SIDR=1 so that dynamic This curve is typically flagged with SIDR=1 so that dynamic

relaxation is invoked for applying the preloadrelaxation is invoked for applying the preload• Stress should be ramped from zeroStress should be ramped from zero

• Physical location of cross-section is defined via Physical location of cross-section is defined via *DATABASE_CROSS_SECTION*DATABASE_CROSS_SECTION

• A part set, together with the cross-section, identify the A part set, together with the cross-section, identify the elements subject to the prescribed preload stresselements subject to the prescribed preload stress

• Contact damping and/or *damping_part_stiffness may be Contact damping and/or *damping_part_stiffness may be required to attain convergence during the dynamic required to attain convergence during the dynamic relaxation analysisrelaxation analysis

*INITIAL_STRESS_SECTION *INITIAL_STRESS_SECTION

*CONTACT_..._INTERFERENCE*CONTACT_..._INTERFERENCE

For shrink-fit parts. The unstressed, pre-fit geometry which includes For shrink-fit parts. The unstressed, pre-fit geometry which includes interferences (penetrations) is specified. interferences (penetrations) is specified.

Contact forces are ramped up during DR to remove the Contact forces are ramped up during DR to remove the interferences.interferences.

Shell thickness offsets are considered.Shell thickness offsets are considered. Specify the contact using two segment sets having correct Specify the contact using two segment sets having correct

orientation (or by a node set and a correctly oriented segment set).orientation (or by a node set and a correctly oriented segment set). To avoid sudden, large contact forces, the contact stiffness should To avoid sudden, large contact forces, the contact stiffness should

be ramped. Contact stiffness scaling factors are specified via be ramped. Contact stiffness scaling factors are specified via curves LCID1 (DR phase) and LCID2 (Transient phase). curves LCID1 (DR phase) and LCID2 (Transient phase).

Types:Types:• *Contact_nodes_to_surface_interference*Contact_nodes_to_surface_interference• *Contact_one_way_surface_to_surface_interference*Contact_one_way_surface_to_surface_interference• *Contact_surface_to_surface_interference*Contact_surface_to_surface_interference

*CONTACT_..._INTERFERENCE*CONTACT_..._INTERFERENCE

Time

Stiff.scalefactor

Stiff.scalefactor

Time

Dynamic relaxation (LCID1) + Transient Phase (LCID2)

Transient Phase Only (LCID2) if LCID1=0

Time

Stiff.scalefactor

OROR

1.0 1.0

1.0

Transient Stress Initialization Transient Stress Initialization

As an alternative to using DR, in some cases the As an alternative to using DR, in some cases the preload can be established in the early part of the preload can be established in the early part of the regular transient simulation.regular transient simulation.• Not appropriate for problems whose transient response is Not appropriate for problems whose transient response is

driven by initial velocity.driven by initial velocity.• Immediately ramp up preloads quasi-statically and then Immediately ramp up preloads quasi-statically and then

hold steady.hold steady.• Use time-dependent mass damping (*DAMPING_GLOBAL) Use time-dependent mass damping (*DAMPING_GLOBAL)

to impose near-critical damping until preload is to impose near-critical damping until preload is established.established.

• Drop damping constant to zero after preload is established Drop damping constant to zero after preload is established and transient loading is ready to be applied.and transient loading is ready to be applied.

• Apply transient loads AFTER preload is established. Apply transient loads AFTER preload is established. • Use nonzero birthtime or nonzero arrival time for transient Use nonzero birthtime or nonzero arrival time for transient

loadsloads

Transient Stress Initialization Transient Stress Initialization

Load

Time

Preload Transient Load

Mass Damping

Coef

Time

Load

Time

t1

t2

t2

t1

Stress Initialization via Implicit AnalysisStress Initialization via Implicit Analysis

Recall that true static analysis is possible by invoking Recall that true static analysis is possible by invoking implicit analysis in LS-DYNA. Static analysis is well-suited implicit analysis in LS-DYNA. Static analysis is well-suited to inducing preload.to inducing preload.

Implicit analysis is invoked via the command Implicit analysis is invoked via the command *CONTROL_IMPLICIT_GENERAL.*CONTROL_IMPLICIT_GENERAL.

Details of implicit analysis are beyond the scope of this Details of implicit analysis are beyond the scope of this course. See Appendix in the LS-DYNA User’s Manual.course. See Appendix in the LS-DYNA User’s Manual.

Stress Initialization via Implicit AnalysisStress Initialization via Implicit Analysis

Approach 1: Two separate analyses.Approach 1: Two separate analyses.• Make an implicit (or explict) simulation of the preload. In the Make an implicit (or explict) simulation of the preload. In the

input deck specify *interface_springback_lsdyna. This creates input deck specify *interface_springback_lsdyna. This creates an ASCII file called an ASCII file called dynaindynain when the simulation is finished. The when the simulation is finished. The dynaindynain file contains keyword commands describing the file contains keyword commands describing the deformed geometry, stresses, and plastic strains. Merge these deformed geometry, stresses, and plastic strains. Merge these commands into the original deck, deselect the implicit cards, commands into the original deck, deselect the implicit cards, modify the loads, and run a second, explicit simulation.modify the loads, and run a second, explicit simulation.

• The dynain file does not include contact forces nor does it The dynain file does not include contact forces nor does it contain nodal velocities. Thus these quantities from the preload contain nodal velocities. Thus these quantities from the preload analysis do not carry over to the second analysis.analysis do not carry over to the second analysis.

• Taking data from the d3plot database, LS-PrePost can output a Taking data from the d3plot database, LS-PrePost can output a dynain file via Output > Format: Dynain Ascii > Write.dynain file via Output > Format: Dynain Ascii > Write.

Stress Initialization via Implicit AnalysisStress Initialization via Implicit Analysis

Approach 2: Single, switched analysis.Approach 2: Single, switched analysis.• Use one input deck where switching between implicit and Use one input deck where switching between implicit and

explicit is determined by a curve. The abscissa of the curve is explicit is determined by a curve. The abscissa of the curve is time and the ordinate is set to 1.0 for implicit and to 0.0 for time and the ordinate is set to 1.0 for implicit and to 0.0 for explicit (curve is a step function). This switching is activated explicit (curve is a step function). This switching is activated by setting IMFLAG at *control_implicit_general to -|curve ID|. by setting IMFLAG at *control_implicit_general to -|curve ID|. Switching from one analysis to the other is seamless and has Switching from one analysis to the other is seamless and has no CPU or I/O overhead.no CPU or I/O overhead.

Exercise 4a and 4bExercise 4a and 4b

Stress initialization of spinning barStress initialization of spinning bar

Mapping Strains/Thicknesses from Metal Mapping Strains/Thicknesses from Metal Stamping SimulationsStamping Simulations

Material Modeling for MetalsMaterial Modeling for Metals

Need for strain/thickness mappingNeed for strain/thickness mapping

Forming sheet metal components causes the material to hardenForming sheet metal components causes the material to harden

After Springback, the accumulated plastic strain increases the yield After Springback, the accumulated plastic strain increases the yield for any further loadingfor any further loading

The assumption of constant thickness distribution may be inadequate The assumption of constant thickness distribution may be inadequate for critical components as the thinning of sheet metal occurs during for critical components as the thinning of sheet metal occurs during stamping operationstamping operation

Initial mapping of plastic strain and thickness from one mesh to Initial mapping of plastic strain and thickness from one mesh to another is now handled trivially using LS-DYNA another is now handled trivially using LS-DYNA • Offers a method of mapping the strains and thickness that may be Offers a method of mapping the strains and thickness that may be

obtained from a metal stamping simulationobtained from a metal stamping simulation• In v. 970, stresses and other history variables can also be mapped.In v. 970, stresses and other history variables can also be mapped.

From forming/springback simulation, write final stresses/strains/thickness at From forming/springback simulation, write final stresses/strains/thickness at integration points usingintegration points using• *INTERFACE_SPRINGBACK_LSDYNA*INTERFACE_SPRINGBACK_LSDYNA• this outputs a file “dynain” consisting ofthis outputs a file “dynain” consisting of

• *INITIAL_STRESS_SHELL *INITIAL_STRESS_SHELL • *INITIAL_STRAIN_SHELL*INITIAL_STRAIN_SHELL• *ELEMENT_SHELL_THICKNESS*ELEMENT_SHELL_THICKNESS• *NODE (deformed geometry)*NODE (deformed geometry)

The stamping simulation mesh may be much finer than the crash simulation The stamping simulation mesh may be much finer than the crash simulation meshmesh

Additionally, the stamped part may be oriented differently in the crash modelAdditionally, the stamped part may be oriented differently in the crash model

The mesh disparity as well as different orientation necessitates the need to The mesh disparity as well as different orientation necessitates the need to map the variablesmap the variables

Need for strain/thickness mappingNeed for strain/thickness mapping

*INCLUDE_STAMPED_PART*INCLUDE_STAMPED_PART

Filename of “dynain” file Filename of “dynain” file containing information to be containing information to be mappedmapped

Crash Part IDCrash Part ID Variables to mapVariables to map

• ThicknessThickness

• Eff plastic strainEff plastic strain

• Strain tensorStrain tensor

• Stress tensorStress tensor

Orientation nodes from both Orientation nodes from both modelsmodels

n1

crash

stamp

n2

n3

n1

n2

n3