Geometry simplification of open-cell porous materials for elastic deformation FEA


Estimation of mechanical properties of porous materials is central for their medical and industrial application. However, the massive size of accurate boundary representations (B-Rep) of the foams makes the numerical estimations intractable. Even for small domain sizes, the mesh generation for finite element analysis (FEA) may not terminate. Current efforts for simulating porous materials use statistical predictions of the material structure. The simulated and actual materials present different geometry and topology, with consequences on the simulation results. To overcome these limitations, this manuscript presents a method, which (1) synthesizes an accurate truss abstraction from the raw geometry data, (2) executes efficient FEA simulations, and (3) processes nodal displacements to estimate apparent mechanical moduli of the porous material. The method addresses materials whose ligaments have circular cross-sections. The iso-surface present in the Computer Tomography (CT) scan of the porous material is used to synthesize a truss graph whose edges are truncated cones. Then, optimization and simplification methods are applied to produce a topologically and geometrically correct truss representation for the foam domain. Comparative FEA load simulations are conducted between the full B-Rep and truss representations of the material. The truss model proves to be significantly more efficient for FEA, departing from the Full B-Rep FEA by a maximum of 16% in the estimation of equivalent mechanical moduli. Geometric assessments such as porosity and Hausdorff distance confirm that the truss abstraction is a cost-effective one. Ongoing efforts concentrate on point set geometric algorithms for enforcement of standardized material testing.

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Bounding box


Boundary representation of a solid in \(R^3\). The usual topological hierarchy: BODY (3D), LUMP (3D), SHELL (2D), FACE (2D), LOOP (1D), EDGE (1D), VERTEX (0D). FACEs (i.e. ’trimmed surfaces’) may be mounted on either smooth surfaces or planes (triangles)


Computer tomography


Finite element


Finite element analysis


Finite element method


Mean curvature flow

Reference model:

Model to measure the simplification against. In this manuscript the Reference model is the Full B-Rep of the foam

\(\epsilon _{k}\) :

Strain in k direction

\(E(\epsilon )_k\) :

Apparent Young Modulus at strain \(\epsilon\) caused by loads in k direction

\(G(\epsilon )_k\) :

Apparent Shear Modulus at strain \(\epsilon\) caused by loads in k direction

\(V(\epsilon )_{ij}\) :

Apparent Poisson ratio computed from a contraction in j direction given an extension in i direction

\(\phi\) :

Porosity of a porous material sample


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Correspondence to Camilo Cortés.

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Cortés, C., Osorno, M., Uribe, D. et al. Geometry simplification of open-cell porous materials for elastic deformation FEA. Engineering with Computers 35, 257–276 (2019).

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  • Geometry simplification
  • Open-cell foams
  • Elastic properties
  • FEA