*Article* **Two-Scale Tomography Based Finite Element Modeling of Plasticity and Damage in Aluminum Foams**

#### **Yasin Amani, Sylvain Dancette \*, Eric Maire, Jérôme Adrien and Joël Lachambre**

University of Lyon, INSA Lyon, CNRS UMR5510, Laboratoire MATEIS, F-69621 Villeurbanne CEDEX, France; yasin.amani@univ-pau.fr (Y.A.); eric.maire@insa-lyon.fr (E.M.); jerome.adrien@insa-lyon.fr (J.A.); joel.lachambre@insa-lyon.fr (J.L.)

**\*** Correspondence: sylvain.dancette@insa-lyon.fr; Tel.: +33-472-43-85-41

Received: 11 September 2018; Accepted: 6 October 2018; Published: 15 October 2018

**Abstract:** In this study, finite element (FE) modeling of open-cell aluminum foams in tension was performed based on laboratory X-ray tomography scans of the materials at two different scales. High-resolution stitching tomography of the initial state allowed local intermetallic particles to be distinguished from internal defects in the solid phase of the foam. Lower-resolution scans were used to monitor the deformation and fracture in situ during loading. 3D image-based FE models of the foams were built to simulate the tensile behavior using a new microstructure-informed Gurson–Tvergaard–Needleman model. The new model allows quantitative consideration of the local presence of brittle intermetallic particles in the prediction of damage. It performs well in the discrimination of potential fracture zones in the foam, and can be easily adapted to any type of architectured material where both the global architecture and local microstructural details should be taken into account in the prediction of damage behavior.

**Keywords:** aluminum foams; intermetallics; X-ray tomography; finite element analysis; damage
