International Journal of Material Forming

, Volume 12, Issue 1, pp 123–134 | Cite as

A simple and systematic scheme implemented in explicit FEM solver for surface tension effects in powder injection moulding process

  • Jianjun ShiEmail author
  • Thierry BarriereEmail author
  • Baosheng Liu
  • Zhiqiang Cheng
Original Research


In order to simulate more accurately the powder injection moulding process, the explicit finite element method solver is extended with the surface tension effect. The evaluation of surface tension takes the notion of pressure boundary method, while a simple and systematic scheme is proposed to fit the finite element method solver for the Laplacian operator. Because of the difference in dimension for filling function and velocity function, the integration of filling function in second derivative is not suitable to be transformed into the boundary integration and the integration of function in lower order derivative. To evaluate conveniently the curvature of filling front, hence the force of surface tension, a simple and systematic scheme is suggested and implemented into the finite element method solver. This specific scheme includes only the vectorial operations in low cost, and is completely systematic without piecemeal operations. Fitness of the proposed method is proved by the numerical examples of filling flow in a small-scaled channel. It shows the considerable effect of surface tension for the problems in micro-scale of sub-millimeter sizes, in which the boundary conditions at front surface are not negligible in powder injection moulding process. The surface tension effect becomes the dominating role for governing the trace and shape of filling front, which can no longer be neglected.


Surface tension Injection moulding Solution scheme Explicit solver 



This work is financially supported by the National Natural Science Foundation of China (Grant No. 11502219) and Doctoral Research Foundation of Southwest University of Science and Technology (Grant No. 14zx7139).

Compliance with ethical standards

Conflict of interest

We confirm that this work is original and has not been published elsewhere nor is it currently under consideration for publication elsewhere.

We confirm with have no conflict of interest and their research proposal to publication in line with best practices and codes of conduct of relevant.


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Copyright information

© Springer-Verlag France SAS, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Shock and Vibration of Engineering Materials and Structures Key Laboratory of Sichuan ProvinceSouthwest University of Science and TechnologyMianyangChina
  2. 2.Department of Applied Mechanics, Femto-ST InstituteUniversity Bourgogne-Franche-Comté, COMUE UBFCBesançonFrance
  3. 3.Department of Mechanics and EngineeringSouthwest Jiaotong UniversityChengduChina

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