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Simulation of the Deformation Mechanisms of Bulk Metallic Glass (BMG) Foam using the Material Point Method

Jin Ma1, Jay C. Hanan1, Ranga Komanduri1, Hongbing Lu2

School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, Oklahoma 74078-5016, USA
Department of Mechanical Engineering, The University of Texas at Dallas, Richardson, Texas 75080-3021, USA. phone: 972-658-5459, fax: 972-883-4659, e-mail:,(H. Lu)

Computer Modeling in Engineering & Sciences 2012, 86(4), 349-384.


Amorphous metallic foams are an exciting class of materials for an array of high impact absorption applications, the mechanical behavior of which is only beginning to be characterized. To determine mechanical properties, guide processing, and engineer the microstructure for impact absorption, simulation of the mechanical properties is necessary as experimental determination alone can be expensive and time consuming. In this investigation, the material point method (MPM) with C1 continuous shape function is used to simulate the response of a bulk metallic glass (BMG) closed-cell foam (Pd42.5Cu30Ni7.5P20) under compression. The BMG foam was also tested experimentally under compression for validation of the simulation results. To build the model for simulation, the complex internal microstructure of the 70% porosity foam was characterized using micro-computed tomography (m-CT). Material points for the simulation, with location and mass density determined from m-CT, were assigned to the cell-walls. The mechanical properties of the cell-walls were determined from nanoindentation and used as inputs for the MPM model. Minimum size of the representative volume element (RVE) used for the simulation of the mechanical response prior to failure was shown to depend on local density. In order to accurately characterize yield of the bulk sample, an RVE must be selected with a dimension of at least 6 average cell diameters. Such an RVE also exhibits bulk sample density. A material point deletion method, using a critical equivalent plastic strain as the failure criterion, was used for simulation of failure in the walls that leads to the collapse of the foam. Simulation of the full densification of an RVE was made to a compressive strain of 80%. Results indicate that prior to full consolidation, ~ 50% of cells carry a majority of the load. The load applied on the foam transfers from one region of a cell to another, as compression increases. Significant cell-wall bending followed by local buckling is observed, contributing to the collapse of the cell-walls in the foam. While compression induces primarily bending and compressive stresses, the loading path forms diagonally to the loading axis, exhibiting an apparent shear band as the global failure mode.


Cite This Article

Ma, J., Hanan, J. C., Komanduri, R., Lu, H. (2012). Simulation of the Deformation Mechanisms of Bulk Metallic Glass (BMG) Foam using the Material Point Method. CMES-Computer Modeling in Engineering & Sciences, 86(4), 349–384.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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