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Working with Homogenized Lattices

Regular Member

Working with Homogenized Lattices

You probably know that Creo 6.0 became available recently. You can see an overview of what’s in the release here. Among the new capabilities, we’ve added homogenization for those simulating lattice structures. Arun Chavan from our development team offers this closer look at how homogenization works, why it matters, and the data behind the solution.  

 

What Is Homogenization?

Homogenization is a process of extracting effective material properties from a heterogeneous material and then viewing it as a continuum on the macroscopic level with the extracted properties ascribed to it

 

Homogenization has many important and practical applications in material sciences, particularly where repeating lattice structures (and composites) are used.  That’s because computations of models with many lattices often prove difficult, time-consuming, and error prone. With homogenization, you have an effective approach for describing the overall behaviour of large lattice structures, without the complexity.

 

Improving Performance in Creo

Say the number of cells in a structure exceeds 24,000. You may find it impractical to store or simulate full or simplified geometry models of that size in your system. These tasks simply require a too many computational resources. To facilitate the modelling of large lattice structures, Creo can now represent them as a continuous solid with material properties equivalent to those of the lattice structure.A solid with these effective material properties will have the same mass properties, stiffness, porosity, etc. as the original lattice structure.

 

process.png

Image: Creo 6.0.0.0 uses homogenization methods to facilitate the modelling of large lattice structures by computing and providing Creo Simulate the equivalent homogenized material properties. 1. Lattice structure; 2. Homogenous Continuum; 3. Process of Homogenization

 

What’s the Homogenization Procedure?

Here’s more details about how it works:

  1. For a given lattice topology, we identify a unit cell.
  2. We apply Periodic Boundary Conditions on the unit cells and calculate overall effective material property.
  3. We then use these homogenized material properties for simulation.

 

Lattice Structures Then and Now

In earlier Creo releases, to analyze lattice structures, the software would either create a full geometry lattice or simplified lattice. These both led to computationally intensive procedures, especially when the lattice region was large or included densely packed cells.

 

In Creo Parametric 6.0.0.0, the “homogenized” representation defines dense lattice structures without creating them in the model. An equivalent material property of the lattice region is extracted and used to get the equivalent mathematical model of material. In Creo Simulate, these equivalent homogenized material properties are then used to simulate the structure for linear static and modal response of a part. As a result, it takes less time to define a lattice, the model size is reduced, and simulation moves quicker.

 

The Data: How Do the Results Compare?

We compared Creo 6.0.0.0 results for three lattice structures and all of them compared very well with baseline. The homogenization results converge when compared with full lattice geometry models. As you can see in the table below, the error declines with an increase in the number of lattices in a given volume.

 

1-mm-cube.png1-5-mm-cube.png2-mm-cube.png