Nonlinear Analysis: Impact

1. Nonlinear Analysis: Impact

2. Objectives Section 3 – Nonlinear Analysis Module 6 – Impact Page 2 The objective of this module is to introduce the concepts and modeling considerations necessary to include impact in a Mechanical Event Simulation using Autodesk Simulation Multiphysics software. • General approaches to modeling contact in Autodesk Simulation Multiphysics are discussed first. • The special case of impact (high speed contact) will then be addressed. • Steps needed to perform a nonlinear dynamic analysis (MES with Nonlinear Material Models) will be presented.

3. Introduction Section 3 – Nonlinear Analysis Module 6 – Impact Page 3 • All real world problems involve contact. • In some cases we can idealize the problem and model the effect of the contact. • Assume fixed or pinned ends on beams • Substitute a load associated with one body acting on another • In other cases the contact forces cannot be determined in advance, and the interaction between bodies during the event must be determined during the analysis. Two automobiles after a close encounter. Impact is a special case of contact in which dynamic forces are involved.

4. Challenges Section 3 – Nonlinear Analysis Module 6 – Impact Page 4 • Computing the effect of contact between separated bodies coming together during a mechanical event is complicated. • There are sudden changes in stiffness, and • The forces exerted on one body by another must be determined. There are two primary classes of methods used to solve contact problems with finite element technology. The first class is known as penalty based methods, and the second class is Lagrangian multiplier based methods. Penalty based methods use contact stiffnesses and restoring forces. This is the approach used in Autodesk Simulation. Lagrangian multiplier based methods use constraints and introduce additional degrees of freedom.

5. Autodesk Simulation Multiphysics Contact Types Section 3 – Nonlinear Analysis Module 6 – Impact Page 5 • Category 1 – No relative motion allowed • Bonded • Welded • Category 2 – Relative motion allowed • Free/No Contact • Surface Contact • Sliding/No Separation • Separation/No Sliding • Edge Contact • Autodesk Simulation provides a wide range of contact types to model the interaction between parts. • The contact types can be broken into two major categories. • Category 1 – no relative motion between parts. • Category 2 – relative motion between parts is allowed. Each contact category and contact type will be discussed in subsequent slides.

6. Category 1: No Relative Motion Allowed Section 3 – Nonlinear Analysis Module 6 – Impact Page 6 • In bonded and welded joints, parts will start and remain in contact throughout the event. • During the meshing operation, Autodesk Simulation creates a “foot print” of the common edges and surfaces on both parts. • When the surface mesh is created, the “foot print” on each part will be meshed the same. Edge and surface matching is the default technique used when bonded or welded joints are specified. The footprint of one part on another is performed automatically and the footprint is not available to the user unless “surface knitting” is turned on.

7. Category 1: Surface Knitting Section 3 – Nonlinear Analysis Module 6 – Impact Page 7 • Surface knitting is a process of creating “foot prints” of common surfaces on mating parts. • The foot prints show up as additional surfaces that can be used to specify contact pairs or loads that act only on a portion of a surface. • In the top figure the two red brackets and fillet welds share common surfaces with the plate. • When the bracket and welds are made invisible, the foot prints on the plate can be selected as surfaces. Fillet Weld Common Surfaces Bracket Common Surfaces

8. Category 1: Activating Surface Knitting Section 3 – Nonlinear Analysis Module 6 – Impact Page 8 Select • Surface Knitting is not a default option. • Surface Knitting can be turned on in the CAD Import options box.

9. Category 1: Bonded Joints Section 3 – Nonlinear Analysis Module 6 – Impact Page 9 • All nodes having the same coordinates are given a common node during the volume mesh generation phase. • The common node forces the displacement to be the same for each point on the shared surfaces. • This makes the joint behave as if the shared surfaces are bonded or glued together. Nodes located at the same point on two different surfaces are forced to move together in a bonded joint. Surface A Surface B Surfaces A and B are in contact but are shown separated for clarity.

10. Category 1: Welded Joints Section 3 – Nonlinear Analysis Module 6 – Impact Page 10 • A welded joint is similar to a bonded joint except only the common nodes around the perimeter of the shared surfaces are joined by a common node. • The nodes on the interior of the shared surfaces are allowed to move independently. • Although referred to as a welded joint it does not attempt to model the geometry of an actual weld. Nodes located at the same point on the edge of two different surfaces are forced to move together in a welded joint. Surface A Edge Nodes Edge Nodes Surface B Surfaces A and B are in contact but are shown separated for clarity.

11. Category 1: Smart Bonding Section 3 – Nonlinear Analysis Module 6 – Impact Page 11 • The default method in Autodesk Simulation Multiphysics for bonded and welded joints is to use matched meshes as discussed in previous slides. • Smart bonding is an alternate method that allows unmatched surface meshes to be bonded together. • This option is selected in the Analysis Parameters dialog box. Smart bonding can be turned on here.

12. Category 2: Relative Motion Allowed Section 3 – Nonlinear Analysis Module 6 – Impact Page 12 • Category 2 contact options allow parts to move relative to each other. • If contact is involved, the parts can move apart or slide relative to each other, but they cannot pass through each other. • The Free/No Contact option allows parts to act independently. This option will allow two parts to pass through each other or occupy the same space. • Category 2 – Relative motion allowed • Free/No Contact • Surface Contact • Sliding/No Separation • Separation/No Sliding • Edge Contact

13. Category 2: Surface Contact Section 3 – Nonlinear Analysis Module 6 – Impact Page 13 • Surface contact does not require that the parts be in contact at the start of the analysis. • Parts may separate or come into contact during the analysis. • The master surface – slave node concept is used to implement surface contact. • The direction of the contact stiffness and contact force is normal to the master surface. Part containing Master Surfaces Master Surface Part containing slave nodes Slave Node Penetration Contact Stiffness, Kc Master Surface Contact Force

14. Category 2: Friction in Surface Contact Section 3 – Nonlinear Analysis Module 6 – Impact Page 14 • A tangential stiffness is used to facilitate calculation of friction forces tangent to the master surface. • The tangential stiffness is a percentage (1% to 100%) of the contact stiffness. • If the tangential force, , is greater than the maximum force that static friction can resist, the tangent stiffness is reduced to a small number and the sliding force is set equal to the kinematic friction force. Slave Node Contact Stiffness, Kc Penetration Tangential Stiffness, Kt Master Surface Sliding Displacement Contact Force Friction Force Constrained Motion Sliding Motion Coefficient of Static Friction, ms Coefficient of Kinematic Friction, mk

15. Category 2: Selecting Friction Surface Contact Section 3 – Nonlinear Analysis Module 6 – Impact Page 15 Contact Controls & Parameters for Surface Contact in an MES Analysis with Non-linear Materials • Friction can be selected in the contact Settings menu obtained by right clicking on the Contact specification in the browser. • If the Frictional Contact option is specified, the static and sliding coefficients of friction must be specified. • The tangential stiffness ratio (percentage) can also be set. (Values from 1% to 100% are typically used.)

16. Category 2: Special Cases Section 3 – Nonlinear Analysis Module 6 – Impact Page 16 • Edge contact is similar to surface contact except only edges or perimeters of the parts are allowed to make contact. • The interior portions of the surface behave like the free/no contact options. • Sliding/No Separation and Separation/No Sliding are special cases of surface contact. • Sliding/No Separation is equivalent to a bonded joint in the normal direction with zero friction in the tangential direction. • Separation/No Sliding is equivalent to surface contact with infinite friction.

17. Category 2: Surface Contact Iteration Strategies Section 3 – Nonlinear Analysis Module 6 – Impact Page 17 • If all of the contact changes during an equilibrium iteration are made at once in a static analysis the solution may bounce between different contact states and not converge. • Autodesk Simulation provides three options that can be used to control this phenomena. • The most conservative approach, Individual Points, is also the slowest. • The least conservative approach, Multiple, is the fastest if the solution will converge. • Individual Points Activates/deactivates each contact point. Considers multiple contact points simultaneously if all have identical states. • Mixed Simultaneously activates all inactive contact points in compression. Deactivates those in tension one at a time. • Multiple Simultaneously activates or deactivates all gaps requiring a change of state.

18. Category 2: Selecting Iteration Strategies Section 3 – Nonlinear Analysis Module 6 – Impact Page 18 • The iteration strategy can only be selected during a static linear analysis. • The option is found by selecting the Contact tab on the Analysis Parameters menu. • Autodesk Simulation automatically chooses the most optimum iteration strategy for other analysis types.

19. Example Problem Section 3 – Nonlinear Analysis Module 6 – Impact Page 19 Steel Cylinder • The cantilevered beam shown in the figure is the same one used in Module 4: Viscoelastic Materials. • It consists of aluminum top and bottom plates that are bonded together using an industrial adhesive ISR70-03. • A steel cylinder, dropped from a height of six inches, impacts the free end of the beam. • All parts are modeled as 2D plane strain elements. Gravity Vector 6 inch Sandwich Beam Clamped Boundary Condition Details on setting up a 2D mesh from a 3D CAD model are contained in Video 3A. Details on specifying the viscoelastic material properties are contained in Module 4.

20. Example Problem – Contact Specifications Section 3 – Nonlinear Analysis Module 6 – Impact Page 20 • The contact between the top and bottom plates and the middle adhesive layer are modeled as a bonded joint. • This is the default contact specification. • The contact between the cylinder and the top surface of the top plate is modeled as surface contact. Bonded Contact Surface Contact

21. Example Problem: Surface Contact Settings Section 3 – Nonlinear Analysis Module 6 – Impact Page 21 • The Contact problem type is set to High Speed Contact (Impact). • The Contact method is set to Frictionless Contact since the problem doesn’t involve sliding type motion. • The Contact type is set to Surface to Surface. The point to point or point to surface options are generally used when corners are involved.

22. Example Problem: Analysis Parameters Section 3 – Nonlinear Analysis Module 6 – Impact Page 22 • The event duration is set to 0.6 seconds. This is based on a previous analysis. • A capture rate of 500 time steps per second is adequate for most of the analysis. Autodesk Simulation will automatically decrease the time step during contact between the cylinder and beam. • The load curve is set to have multipliers of 1 for all time steps. This results in the gravity load being applied as a step input.

23. Example Problem: Impact Response Section 3 – Nonlinear Analysis Module 6 – Impact Page 23 Graphs showing the displacement response of the cylinder and the tip of the cantilever. • The top graph shows the vertical displacement as a function of time for the cylinder. • The bottom graph shows the vertical displacement as a function of time for the tip of the cantilever. • The sudden increase in displacement due to the impact event is clearly seen in the bottom graph.

24. Module Summary Section 3 – Nonlinear Analysis Module6 – Impact Page 24 • This module has provided an overview of topics associated with performing an impact analysis using Autodesk SimulationMultiphysics software. • The two primary categories of contact found in Autodesk Simulation were presented. • An example that shows how to set up an Mechanical Event Simulation with nonlinear materials and impact was presented.