Design methodology for porous composites with tunable thermal expansion produced by multi-material topology optimization and additive manufacturing


Positive thermal expansion is an important physical phenomenon that is critical in medical vessel dilators as well as thermal actuators. A negative thermal expansion is equally important for implementation in high precision and high temperature devices as it cancels thermal expansion of conventional materials. Negative thermal expansion is naturally rare. Therefore, materials that exhibit negative thermal expansion have become attractive. Nevertheless, negative thermal expansion is limited to particular perovskite ceramics and tuning negative thermal expansion is still a challenge.

Constructing a porous composite of two materials with varying thermal expansion coefficients is a powerful way of realizing negative thermal expansion. This approach can result in an effective negative thermal expansion owing to the composite internal geometry. The design of the internal structure of the porous composites must take into account thermal deformation of the materials, which is based on their thermal expansion coefficients and stiffness. Numerical structural optimization is an effective method of designing complicated structures as it allows for automatic structural optimization via optimization methods and numerical structural analysis.

Topology optimization can be adopted to optimize the target structure and the number of void spaces. On the experimental space, rapid prototyping as well as additive manufacturing has been adopted to generate 3D structures. Recent advancements in the technology have enhanced the manufacturing precision as well as the level of detail possible in 3D composites and porous components to a scale of approximately 10 µm. This small fabrication can be implemented to come up with novel composite materials. Additive manufacturing is another method that could be used to easily produce multi-material composites by tuning the location of the supplied components.

Makoto Kobashi at Nagoya University and Akihiro Takezawa at Hiroshima University in Japan developed a design methodology for porous composites with arbitrary thermal-expansion attributes derived from their internal geometry. They also examined, for the first time, negative thermal expansion together with anisotropic and isotropic, extra-large effective positive thermal expansion behavior in the structures. Their research work is published in research journal, Composites Part B.

The authors adopted a numerical topology optimization based on the finite element method to design the internal geometry while maximizing the macroscopic outward or inward deformation and maintain a selected level of stiffness. They then fabricated test specimens with the designed internal structure from a photopolymer through additive manufacturing. By measuring the thermal deformation of the test specimens, the authors were able to verify the internal thermal expansion.

Kobashi and Takezawa observed that the measured effective thermal expansion coefficient values varied in the order anisotropic extra-large positive thermal expansion> isotropic extra-large positive thermal expansion>bulk materials>0> isotropic negative thermal expansion> anisotropic negative thermal expansion. They found that anisotropic materials had higher positive thermal expansion and negative thermal expansion because they made use of a bigger space as opposed to isotropic material. Maximum and minimum effective thermal expansion coefficients were 1X10-3 K-1 and -3X10-4 K-1 respectively. For this reason, the authors designed materials exhibiting coefficients of thermal expansion with a wide range of values.

Design methodology for porous composites with tunable thermal expansion produced by multi-material topology optimization and additive manufacturing. Advances in Engineering

About the author

Dr. Makoto Kobashi received his Ph.D. degree from the School of Engineering at Nagoya University, Japan in 1995. Since then he has been a faculty member of Nagoya University, and now he is served as a Professor in the Department of Materials Process Engineering. He was also a visiting researcher at the Department of Materials in Oxford University, U.K. from 1996 to 1997. He studied state-of-the-art thermal barrier coating technique and simulation skills in Oxford University. In April 2016, he was assigned as the Director of the Materials Backcasting Technology (MBT) Research Center in Nagoya University.

His research field involves porous materials, composite materials, meta/ceramic bonding and additive manufacturing. His research focuses on exothermic reactions and the reaction enthalpy. He has been trying to use the heat of reaction for the processing of porous and composite materials. It is notable that he developed a reactive processing technique of the highly-porous intermetallics. He also indicated the principal of the morphological control of the cell structure in porous materials.

Another his outstanding achievement is the development of the spontaneous infiltration technique of ceramics preforms with molten metals. This technique made it possible to produce metal/ceramics and metal/metal composite materials by a simple processing. By these achievements, he received the NAGAI Science Award from “The NAGAI Foundation for Science & Technology”, and holds more than 20 domestic and international patents.

Recently he started to develop some functional materials using additive manufacturing technique. Materials with negative coefficient of thermal expansion is one of them. Ultra-hard dies, molds equipped with inner cooling system, heat exchanger are other examples.


Akihiro Takezawa and Makoto Kobashi. Design methodology for porous composites with tunable thermal expansion produced by multi-material topology optimization and additive manufacturing. Composites Part B, volume 131 (2017), pages 21-29.


Go To Composites Part B: Engineering

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