Introduction to LS - Dyna

                                                Introduction to LS-Dyna

What is Engineering? and the importance of CAE (Computer-Aided Engineering).

Engineering acts as a bridge between the researcher and the end-user. Example a researcher does some research about electromagnetic induction and an Engineer will design and produce a product like a table fan for the end-user. The Process of  Engineering Design starts from the necessity of the customer and ends after its functionality/performance. A lot of parameters should be taken into consideration during this process like Shape, Size, Material etc. Even after completion of the design, to make it successful, there will be always a Design Validation Plan (DVP) to validate (test) the design. Validation is to make sure that the designed product is successful to start the process of production and send it to the customer. Tests can be performed in 3 ways

1. Analytical method

2. Numerical method

3. Physical testing / Experimental Method

Analytical methods are used for simple geometries and simple problems and it is a formula based approach. The time required for Analytical method is very low. The final results are close to the actual results. Numerical methods use virtual prototypes and modifications can be done any number of types. The final results are just approximate to the final result. CAE involves working on these virtual prototypes. Physical testing involves physical prototypes testing which involves higher costs. The obtained results are final and then set to start mass production of the products.

Basics of FEA:

Discretization: The process of dividing the body into an equivalent number of finite elements associated with nodes is called discretization of an element in finite element analysis.

Discretization helps in reducing the infinite number of equations to a finite number of equations. 

Nodes and Elements: Nodes are the points where measurements take place in FEA. Elements bring a relation between each node. This relationship is governed by some of the linear and non-linear equations. 

Types of Analysis in LS-Dyna:

1. Linear Static Analysis: Linear static analysis refers to the load vector that does not change its magnitude and direction concerning time.

2. Nonlinear Static Analysis: The applied load is static but the material is non-linear.

3. Non-linear Dynamic Analysis:  If the load vector changes its magnitude and direction concerning time then that load is called Dynamic load. If the applied load is Dynamic and the material property is non-linear then the analysis is said to be Non-linear analysis. Examples: Crash, drop test, Impact etc.

 

 Static Analysis:  Static analysis refers to when static load causes non-permanent or permanent deformation. Permanent deformation refers to static non-linear analysis whereas non-permanent deformation refers to static linear analysis.

The relation between physics and mathematics in Numerical methods.

There are 2 types of Numerical methods.

1. Direct solving  methods

2. Iterative methods.

In direct solving methods inputs are required to start the simulations. The main input for direct solving is 'Least count'. For Iterative solving methods the user needs 'guess value' as an input. Generally, errors occur in Iterative methods and if there is a reduction in the errors then the solution is said to be Converging. Iterative methods were not used for time-dependent calculations.

Iterative methods for static analysis is for equilibrium condition. Iterative methods are best suitable for a single solution at a time. Single solutions are not possible in Direct solving methods.

Implicit code:

The iterative method used to solve a pure static problem then that code is called Implicit code. Optistruct, Ansys workbench is pure implicit codes. Ls Dyna, Abacus, Radioss has both Implicit and Explicit codes. Implicit codes are not used for progressive problems.

Explicit Code : 

An explicit code is a direct solving method used to solve a dynamic problem. In direct solving methods when the problem is progressive in nature Least count (minimum value) is necessary/defined. Direct solving methods are defined from Taylor's series. Direct solving methods are unidirectional and it must have a least count which is defined by the user. In explicit codes, the user-defined value is 'Timestep'. 

`star`If Explicit code is used to solve a static problem then that analysis is called Quasi-Static Analysis. 

Inputs possible in LS- Dyna: 

1. 3D stiffness matrix.

2. Inelastic

3. Non-linearity in Geometry, Material, Boundary conditions and Contacts.

4. Dynamic load (time-domain problems)

5. Transient (Entity which requires time for its definition)

 

1. 3D stiffness matrix

The above spring has two nodes `N_1` and `N_2` and spring stiffness `k`.

If a displacement `U_1` is applied at node `N_1` and

if the stiffness `k to infty` then the displacement at node `N_2` will also be `U_1` 

if the stiffness `k to 0` then the displacement at node `N_2` will also be `0` 

The above two conditions are hypothetical because every material has some finite stiffness.

There are two kinds of stiffnesses 

1. Geometrical Stiffness

             a. Tensile stiffness

             b. Torsion Stiffness

                    `Z = I/y`

2. Material Stiffness

       a. Modulus of elasticity (E)

        b. Shear Modulus  (G)

 

 2. Inelastic

 A material is said to be inelastic when it loses its elasticity and enters into plastic/inelastic region. Usually, ductile materials like steels have both linear and non-linear regions.

Steel is recyclable and is available in abundance also it has higher energy absorption capacity compared to other materials. This makes steel so special in Automotive industries.  

3. Non-lineality: 

If the slope between input and output is not constant then it is called non-linearity. Typically there are  three types of non-linearity

a) Geometric non-linearity

b) Material non-linearity

c) Boundary condition non-linearity

 

Boundary condition non-linearity is further classified into two types

a) Load (inputs can be force, velocity, acceleration, temperature etc)

b) Constraint (single point constraint)

 

4. Dynamic load: 

A load which changes its magnitude and /or direction is called Dynamic load. LS-Dyna can understand dynamic loads.

5. Transient entities: 

Entities which requires time for its definition. example acceleration, velocity, force. .Entities which does not require time for its definition are called steady-state entities.

 

The procedure involved in LS- Dyna

1. Import the CAD model

2. Check for penetrations

3. Decide the type of elements (1D,2D,3D)

4. Decide timestep.

5. Identify boundary conditions

6. Material modelling

7. Run Analysis

8. Post-processing

9. Prepare report

 

Ls-Dyna can be used for both Direct solving numerical methods (Explicit) as well as Iterative numerical methods (Implicit) problems. It can be used for Quasi-static analysis as well. 99% of applications will be for Explicit analysis. 

Time Integration : 

Time is always positive and Explicit code suits best for Direct solving methods due to change in loading conditions concerning time.

Shock wave:  

Shock is defined as the rate of change of acceleration (a). Wave defines propagation means it propagates from one point to the other.  

Shock = `(da)/(dt)`

When a vehicle moving with constant velocity (v) hits a rigid wall then there is a drop in its velocity. This change in velocity is a non-linear fashion.  

Shock wave propagation speed: 

Three scientists Courant, Fredrich and Lewy defined it as ' Any solid material cannot exceed acoustic wave speed in that material'. 

Speed of sound of any material is given by 

`C_(sound speed) = sqrt(E/rho)`

`E` = Young's modulus of Elasticity

`rho` = Density of solid material

 

When a shock wave flowing from one node to the other and this shock causes deformation at the nodes when stiffness `k to 0`.

 Distance between two nodes = `N_2 - N_1`

C = `sqrt (E/rho)`

Time step : 

The time required (`triangle t`) for a shock wave to travel from one node to the other in an element is called as time step (least count)

 `triangle t = (N_2 - N_1)/(sqrt(E/rho)`

`l_e` = edge length

`l_c` = characteristic length

`l_c` = `N_2 - N_1`  for 1D elements

`l_c` = Area/Largest diagonal ;  For 2D elements having four nodes 

`l_c` = Volume/largest face area; For 3D elements.

 

 

Deformation for rigid bodies is zero and displacement is maximum. 

Types of Time steps:   

A) Time step (`triangle t`) = least count (defined by the user - Input)

User input time step control can be decided by three factors

1. Hardware available

2. Accuracy required

3. Time available to solve

The decrease in the value of `triangle t`(Least count) results in higher accuracy and time with an increased cost.

In order to reduce the timestep, Fine mesh is used instead of coarse mesh. 

 

B) Time step (`triangle t`) = least count (solver defined).

 

2D Elements : 

In the Automotive industry, most of the parts are made of sheet metal. Sheet metals have a constant thickness throughout its length. 2D mesh/elements are widely used because of the larger area compared to its thickness. 

The characteristic length of the 2D element is given by

`l_e = l_c/(sqrt2)`

The unit system in LS-Dyna is

General SI unit system 

Mass - kg  ; Length - m  ; Time - Sec; Temp - K; Force - N; Stress - `(N/(m^2))`; 

Density - `((kg)/(m^3))`

1 Megapascal = 1 `(N/(mm^2))`

Widely used LS Dyna Unit systems

LS Dyna unit system 1:

Mass - T  ; Length - mm  ; Time - Sec; Temp - K; Force - N; Stress - `(N/(mm^2))`; 

Density - `((kg)/(m^3))`, `((T)/(mm^3))`

1 Megapascal = 1 `(N/(mm^2))`

LS Dyna unit system 2:

Mass - kg  ; Length - mm  ; Time - ms; Temp - K; Force - KN; Stress - `((KN)/(mm^2))`; 

Density - `((kg)/(m^3))`

1 Gigapascal = 1 `((KN)/(mm^2))`

 

Types of Elements:  

There are mainly 4 kinds of elements used in Explicit solvers. They are

1. 1D elements

2. 2D elements

3. 3D elements

4. 0D elements

0D elements:

An element which is defined using one node is called 0D elements. Lumped mass (concentrated mass) is an example of a 0D element. The 0D element takes only mass into consideration and ignores the stiffness. During crash analysis objects like batteries, structural deformation is not important so the stiffness of the battery is ignored and only the mass is taken into consideration. The non-structural mass can be simulated at the centre of gravity of that particular assembly. Sensors used in Airbags and Seatbelt slipring are defined as 0D elements.

1D elements:

 1D elements are classified as 

a) Rigid 1D elements

b) Deformable 1D elements

Rigid elements there will be no relative motion between each node. Rigid elements have all rotational degrees of freedom

 1D elements are used if one of the dimensions is very large in comparison
to the other two. 

Element shape – Line
Additional data from user - The remaining two dimensions, the cross-sectional area.
Element type – Rod, bar, beam, pipe, axisymmetric shell etc.
Practical applications - Long shafts, beams, pin joint, connection elements

Beam elements are used for bolting connections, Rebar, Welding (spot welds), Wire mesh. 

deformable 1D elements are defined as length and cross-section. They can be circular, triangular,     orbitary, Rectangular etc. 

 

2D elements:

There are 2 types of 2D elements

1. Triangular elements

2. Quad/Rectangular elements

If there are no mid nodes in between pre-defined nodes then those elements are called 1st order elements. If there are any nodes then they are called 2nd order elements. 

2nd order elements are used mostly in 3D elements.

Practical Applications: All sheet metals, Plastic parts with less thickness, 

3D elements: 

First Order

Tetrahedral elements (4 sides) - 4 nodes and 4 triangular faces

Pentahedral elements (5 faces) - 6 nodes and 5 faces ( 2 triangular and 3 Quad) 

Hexahedral elements (6 faces) -  8 nodes and 6 faces (6 Quad)

Second-order

Tetrahedral elements (4 sides) - 4 + 6 nodes and 4 triangular faces

Pentahedral elements (5 faces) - 6 + 9 nodes and 5 faces ( 2 triangular and 3 Quad) 

Hexahedral elements (6 faces) -  8 +12 nodes and 6 faces (6 Quad)

Element Formulation:

The relation between 2 or more nodes is called element formulation. 

It is known that nodes carry mass and element carry stiffness. Relative motion between nodes becomes zero when stiffness k becomes infinity. In order to avoid that always a finite stiffness value has to be defined. 

 Single point integration and Hourglass effect:

Since the solver can only read the nodes, Transforming local displacement to the centroid and extrapolate it to the other node. This will create a proper deformation based on two stiffnesses 1. Material stiffness and 2. Geometric stiffness. 

There will be always a local deformation and then converts to centroidal deformation and finally back to local deformation. One is called Transformation matrix and the other is called extrapolation matrix. This happens in a local coordinate system of a matrix. If this happens in a global coordinate system then it is Shape function. 

Single point integration always has the correct magnitudes and it may have opposite directions.  

This change in direction causes errors in the solution. This effect is called Hourglass Effect. It is also called Zero energy mode. 

Full Integration :

In order to reduce or eliminate the Hourglass Effect one of the most commonly used methods is using Full integration. In full integration instead of referring just one point, 2 points can be used for one node. This brings two transformations and two extrapolations for one nodal displacement. This increases the time to solve and finally, the Hourglass becomes Zero. 

Hourglass energy should be less than 10% of total energy. Hourglass is not possible in tria and tetra elements and is possible only in Quad elements. 

`star` ELEFORM = 16 - Full integration.

`star` Hourglass Effect can also be removed by using Control Cards which was provided by LS -Dyna.

`star` If the element size is more than 100 mm then single-point integration is used. Examples in Shipbuilding and Civil structures applications. All Automotive applications use full integration.

 

                                             Materials in LS- Dyna

 

Materials are classified into 2 types 

1. Hypothetical elements

    a) Rigid

    b) Elastic

    c) Null

2. Real elements

    a) Elasto-plastic

    b) Foam

 

a) Rigid (MAT - 20) : 

If Rigid material is assigned to a part then the relative motion between the nodes is Zero. Which means deformation of the object does not happen at any type of load application. CMO defines the coordinate system in which the rigid body is aligned (Global coordinate or local coordinate). CON1 and CON2 define translation and rotational constraints. 

 

b) Null (MAT - 9): Zero stiffness or cover material

Null materials are used as covering material over the top of 3D elements for better contact. Null materials are widely used in Foams, Dummy, Engine block. Null materials will have thickness less than 0.3 mm. 

c) Elastic (Mat- )

In the elastic material the stress vs strain graph keeps goes on infinity without any change in curve. This is used in Modal analysis. 

 

Real Materials : 

`star` Piecewise - linear plasticity (MAT 24): 

The linear region defines Elasticity, whereas non-linear region defines Plasticity.  This applies to both metals and non-metals. `E, rho, mu`values were defined and Effective plastic strain (EPS) vs Effective stress curve was also defined. 

0.5% of the total strain = elastic strain. The starting point of the plastic curve is called the yield point and the corresponding stress is called yield stress. Effective plastic strain =0 at the yield point. Total strain at yield point = 0.5% of the total strain. This is the process in curve truncation.

Simple Foam material (MAT 57) :

 These materials are used for compression tests. 

                                                        CONTACT Interface / Modeling

Contacts are termed as surface interactions. Contacts are all about surfaces they can be inner surface, the outer surface, Convex surface, Concave surface, etc. Contacts are Non-permanent and Uni-directional way of transferring force. For example, if a body that was used to push another body cannot be used to push each other with the same arrangement. The direction in which it was acting is only in one direction. In-vehicle crash analysis there is a transfer of energy from the vehicle to the body it is hitting without having a permanent connection. 

Contacts can be classified into two types.

1.  Penalty Formulation

2. Constrained Formulation

 Penalty deals with Damage whereas Constrained deals with motion. 

1. Penalty (Damage) based contact: They are further classified into two types.

a) Old type of contact (Non -Automatic)

Contact Algorithm.

If two plates of thickness `t_1` and `t_2`are in contact and the gap between these two shell mesh are equal to `(t_1+t_2)/2`. If the gap is less than `(t_1+t_2)/2` then there will be penetration. Ls Dyna will detect the contact if the gap is less than `(t_1+t_2)/2` The solver will check it in every time step. The contact algorithm gets activated if it is less than `(t_1+t_2)/2`. The contact Algorithm activates a Nonpermanent Uni directional spring and the part with lower stiffness will get damaged. This purely depends on Geometrical stiffness and Material stiffness of the parts that are going to get in contact.  

In the old type of contact master segment always searches for the slave segment. In the case of LS-Dyna contacts, all the slave segments always comprise of nodes. The old type of contacts is completely user-defined. Search algorithm starts working only if the slave segment gets in contact with the master segment. 

                             `ast`CONTACT_NODES_TO_SURFACE

This contact is non-automatic and also the normals of the master and slave segments must face each other. 

                            `ast`CONT_SURFACE_TO_SURFACE 

This type of contact is a combination of two NODES to Surface contact in a one-time step. During this checking process at every time step, the solver will do a reversal of Slave and Master segments automatically. 

The rigid body is defined as Master segment whereas the deformable part is defined as Slave segment. The part with higher stiffness is defined as Master segment whereas the deformable part with lower stiffness is defined as Slave segment. If both the materials are the same then the moving (motion) part is defined as the master. 

These Old type of contacts are still been used 

 

b) Automatic type of contact: 

                            `ast`CONT_AUTO_NODES_TO_SURFACE 

 The contact will be done automatically by the solver itself. The normals should be defined by the user and the segments defied are automatic. 

  2. Constrained based contact:

This type of contact is used without connecting the actual nodes of the body and having a mathematical connection between them. These type of contacts are used to connect Rigid to  Deformable-body, Rigid to rigid and Deformable to Deformable bodies.      

`ast`CONT_EXTRA_NODE  ( Deformable to Rigid)

`ast`CONT_RIGID_BODY  ( Rigid to Rigid)

Two rigid bodies cannot share a common node. 

`ast`CONT_TIED_NODES_TO_SURFACE (Deformable to Deformable)

 

                                                  Control Cards 

 Control cards are extremely important for the smooth functioning of the solver. 90% of the control cards are default cards. 

 

 `ast`CONTROL_ACCURACY (Default)

`ast`CONTROL_BULK_VISCOSITY (Default)

`ast`CONTROL_CONTACT ; SHLTHK = 2 , IGNORE = 2

`ast`CONTROL_ENERGY ; HGEN = 2, SLNTEN = 2, RYLEN = 2

`ast`CONTROL_HOURGLASS (Default)

`ast`CONTROL_SHELL (Default)

`ast`CONTROL_SOLID (Default)

`ast`CONTROL_TERMINATION (Default)

`ast`CONTROL_TIMESTEP ( ISDO = 1; D2DMS = -3`e^(-7)`= 0.3 micro seconds; Default)

 

                                                  Database Cards / Output Requests (Special)

 

 ASCII Input: It is used to convert all the output files to be read in any type of post-processor.

`ast` Database_Option : Default DT value is defined in a way that it can generate the output for every mentioned DT value time step. All necessary outputs should be selected in the Database cards. Default_Binary is defined as '3'. 

ABSTAT (Airbag statistic),

BNDOUT(Boundary output),

DEFORC (Discrete element formulation), 

ELOUT (Elemental output),

GLSTAT (Global statics) ,

JNTFORC (Joint force), 

MATSUM (Internal part internal energy),

NODOUT (Motion will be analysed),   

  RBDOUT (Rigid body output with part having MAT 20 material), 

  RCFORC (Resultant interface forces due to contacts),

SBTOUT (Seatbelt output),   

  SECFORC (Section Force),

SLEOUT (Sliding interface energy),

SPCFORC (Single point constraint reaction force),

SWFORC (Spot weld nodal constraint reaction forces),   

 

`ast`DATABASE_BINARY_D3PLOT: Creates animation file. 

`ast`DATABASE_BINARY_D3DUMP: This allows in restarting the solver due to power failures from the point it was stopped.