Research Papers

A Coarse Model for the Multiaxial Elastic-Plastic Response of Ductile Porous Materials

[+] Author and Article Information
Andreas Schiffer

Department of Mechanical Engineering,
Khalifa University of Science and Technology,
Abu Dhabi 127788, UAE
e-mail: andreas.schiffer@ku.ac.ae

Panagiotis Zacharopoulos

Department of Aeronautical Engineering,
Imperial College London,
London SW7 2AZ, UK
e-mail: panagiotis.zacharopoulos08@imperial.ac.uk

Dennis Foo

Department of Aeronautical Engineering,
Imperial College London,
London SW7 2AZ, UK
e-mail: dennis.foo15@imperial.ac.uk

Vito L. Tagarielli

Department of Aeronautical Engineering,
Imperial College London,
London SW7 2AZ, UK
e-mail: v.tagarielli@imperial.ac.uk

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received November 10, 2018; final manuscript received April 4, 2019; published online May 13, 2019. Assoc. Editor: A. Amine Benzerga.

J. Appl. Mech 86(8), 081002 (May 13, 2019) (8 pages) Paper No: JAM-18-1638; doi: 10.1115/1.4043439 History: Received November 10, 2018; Accepted April 04, 2019

We propose a modeling strategy to predict the mechanical response of porous solids to imposed multiaxial strain histories. A coarse representation of the microstructure of a porous material is obtained by subdividing a volume element into cubic cells by a regular tessellation; some of these cells are modeled as a plastically incompressible elastic-plastic solid, representing the parent material, while the remaining cells, representing the pores, are treated as a weak and soft compressible solid displaying densification behavior at large compressive strains. The evolution of homogenized deviatoric and hydrostatic stress is explored for different porosities by finite element simulations. The predictions are found in good agreement with previously published numerical studies in which the microstructural geometry was explicitly modeled.

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Fig. 1

Nonperiodic microstructures of different porosities (1%, 5%, and 20% from left to right)

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Fig. 2

Plastic constitutive response of the fictitious pore material; prescribed history of the equivalent Deshpande–Fleck stress as a function of the corresponding equivalent plastic strain

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Fig. 3

(a) Example of SVEs at increasing NCELL, for the choice NCELL = NFE, (b) sensitivity of compressive and tensile flow stress at a strain of 0.01 to the parameter NCELL, and (c) sensitivity of the macroscopic compressive or tensile stress at the first yield to NCELL. All error bars indicate the range of the outputs.

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Fig. 4

(a) Examples of SVEs at increasing NFE, for the choice NCELL = 125, (b) sensitivity of compressive and tensile flow stress at a strain of 0.01 to the parameter NFE, (c) sensitivity of macroscopic compressive or tensile stress at the first yield to NFE, and (d) sensitivity of the compressive strength to NFE/NCELL

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Fig. 5

(a) Time histories of von Mises stress for loading cases 1–9 and (b) time histories of von Mises stress for loading cases 10–18

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Fig. 6

(a) Time histories of hydrostatic stress for loading cases 1–9 and (b) time histories of hydrostatic stress for loading cases 10–18

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Fig. 7

Yield surface and its evolution for a 30% porous solid. Squares correspond to an equivalent von Mises strain of 0.01 and circles correspond to an equivalent von Mises strain of 0.04.

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Fig. 8

Predicted initial yield surfaces at different porosity. Results by Fritzen et al. [28] are fitted by the modified GTN model [28] and compared with the predictions from the current study. Here, σF denotes the yield stress of the parent material.

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Fig. 9

Compressive Young’s modulus and flow stress at 0.01 strain as a function of relative density



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