Category: Blog

A nonlinear static problem can be unstable as a result of global buckling or material softening. If the load-displacement response of the model seems to be reaching a load maximum and there is the possibility of global instability or negative stiffness, two approaches to solving the problem can be used — static or dynamic analysis.

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If the structure is reaching a buckling load in a static analysis, perform a Riks analysis

The Riks method assumes that the global instability can be controlled by modification of the applied loads. This means the loss in stability cannot be too severe; that is, there cannot be a sharp bifurcation in the load-displacement curve. Therefore, structures such as flat sheets, cylinders, and spheres that have a sudden significant loss of stiffness after buckling must have some imperfection built into the original geometry.

This can be done by using the *IMPERFECTION option to modify the original geometry by adding imperfections. The best approach is to use experimentally determined imperfections; however, since these measurements may not be available, the *IMPERFECTION option can use combinations of the eigen modes from a previous buckling analysis as the imperfections to the original geometry.

If the Riks method fails to converge near a limit or bifurcation point (buckling load), the problem may be that the loss in stiffness is too severe. Instability problems that exhibit a sharp transition often require a limit on the maximum incremental arc length to get past the transition point or to have larger imperfections built into the geometry.

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If a dynamic analysis is desired

Abaqus/Explicit should be considered as the most robust approach, particularly in the presence material failure, extreme deformation, or rapid changes in contact state. If the loss in stability is not too severe, or only the load maximum is to be computed rather than a fully collapsed configuration, then a dynamic analysis in Abaqus/Standard may be completed with less run time. Choose the APPLICATION parameter on DYNAMIC to control the amount numerical damping that is applied to the integration operator. If a dynamic analysis is used in Abaqus/Explicit, the structure will vibrate once it has passed the instability and you must decide how to damp the vibrations if a quasi-static solution is required.

Global instabilities can also be stabilized in a static analysis with viscous forces. Although not intended as a primary solution technique for global instabilities, automatic stabilization can be used in the static, coupled temperature-displacement, soils and quasi-static procedures. Automatic stabilization will add viscous damping to the structure, which may allow the solution to go beyond the instability point.

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Discrete dashpots can also be used to stabilize a problem of this type

With either technique, the energy dissipated by the artificial viscous forces (output variable ALLVD for discrete dashpots or ALLSD for automatic stabilization) should remain small compared to the total internal energy (output variable ALLIE) in the problem. The nodal viscous forces should also be small when compared with typical forces in the problem (use nodal output variable VF).

 

The computation of effect and motion of a large group spherical particles, where the particles interact with one another and with other surfaces/flow is known as discrete element method (DEM). Granular particles can be simulated in Abaqus using DEM in Abaqus/Explicit Analysis. Abaqus also has another technique to model particles and the technique is known as Smoothed Particle Hydrodynamics (SPH). The major difference between DEM and SPH is that in SPH technique, the particles collectively have continuum behaviour whereas in the DEM technique, the particles cannot undergo a large complex deformation by themselves. Also, DEM technique is a much simpler method.

DEM particles are rigid single-node elements with a certain radius. Particle nodes have degrees of freedom for translational motion and rotation, so considering friction, the latter can significantly affect behaviour, through general contact method. For DEM particles, a contact penalty process is used, which introduces flexibility into the particle system. This correspondence can be used to model the macroscopic stiffness of the filled granular material. Alternatively, the Hertz contact method can be used for particle interaction.

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DEM debris may be initialised in the beginning of the analysis, or may be generated all through the analysis. When generated, a random radius, primarily based totally on a user-specified chance density function, may be assigned to every particle. To analyse more complicated shapes in place of easy spheres, more than one DEM debris may be mixed in a cluster the usage of MPC constraints. Clusters aren’t well suited with the particle generator.

Each DEM particle is modelled with a single node element type of PD3D.  The PD3D element type have displacement and rotational degrees of freedom. When friction is considered for a study, the rotational degree of freedom of the discrete element particles has a considerable effect on the contact interactions.

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Interaction between Particles

Let us consider three instances of particles in contact as shown in the above figure. The 3 instances display undeformed spheres simply touching, deformed spheres driven closer to each other with contact strictly enforced, and rigid spheres penetrating each other. The distance among the facilities of the spheres is the identical for the middle and right instance as shown in figure above. The middle instance of deformed spheres with no penetration is of physical behaviour. The right instance of rigid spheres penetrating each other is a typical DEM approximation.

If the variable δ is defined as:

δ=r1+r2−d,

where r1 and r2 are the radii of the two spheres and d is the distance between the sphere centres,  when the undeformed spheres are just touching then δ=0  and  if the distance between the sphere centres is less than the combined radii the δ>0 . For the DEM approximation, δ corresponds to the maximum penetration distance between the particles. If the contact stiffness is tuned i.e., contact force v/s penetration, then the accuracy of some DEM applications can be improved. Also, tuning helps to replicate the Hertz contact solution for DEM particles.

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Why Use DEM?

• Each DEM particle has individual rotational, positional, radial and momentum vectors that can be easily calculated.
• Simulating DEM method is quite simpler than SPH method and consists of initialisation, time stepping and post processing.
• DEM can be ideally used for modelling granular matter, powders, rock masses, particle packing, particle flow, particle fluid interaction, colloids etc.

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Applications of DEM

• Mixing of Chemicals
• Pharmaceuticals
• Powder Metallurgy
• Ceramics
• Food industry
• Agriculture
• Geophysics/Seismology
• Rock fracture
• Soil Mechanics
• Ice blocks floating into bridge supports
• Mining
• Mineral Processing
• Oil and Gas

 

 

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Advantages of DEM  

• DEM is used to study micromechanical level of analysis describing every single position, rotation and velocity for every single particle.
• Accurately model granular and discontinuous materials using DEM to validate models virtually thereby saving a lot of costs that would other incur for the physical testing.
• DEM can be coupled with CFD and FEM to model progressive fracture.

A job can be run from the command prompt without opening Abaqus CAE as long as the job is set up and already saved. Command prompt is used to submit the analysis. This will be helpful if the pre-processing stage of the model is completed. Pre-processing can be done in any of the pre-processors including ABAQUS, but to run the analysis using ABAQUS, the file format must be converted to input file (.inp). The main reason behind this is to run several jobs simultaneously based on availability of CPU storage and tokens. Submitting the job through CAE is also available to run the analysis but this method will be helpful for user when he can access the job submission by using the command window.

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Following are the steps to be followed to run the analysis using command prompt:

• Go to the folder in which input file (.inp) is located. Input file is the one which contains all the pre-processed data of the model.
• Select the path of the folder, type cmd in the place of path and click Enter. With this, Command prompt will be opened and will step in to the folder where input file is located.
  
  

• Now type the command to run the job abaqus j=<type input file name> cpus=<no. of CPU> and click Enter. The analysis will begin and different files are generated in the folder during the analysis.
  
  
• The results can be visualized with output database file (.odb) once the analysis is completed.
• If the job already exists in the selected folder while executing the job in command prompt, the job can be overwritten. This can be done by giving the input as “y” and click Enter.
  
• If the job needs to be terminated, the command abaqus terminate job=<type input file name> can be given as input. With this above command, the analysis can be terminated.
  

 

This is the step-by-step process to execute analysis by using the command prompt. This method is helpful for running multiple jobs of pre-processed model.