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Bin Wang's picture

Simultaneous improvements of strength and toughness in topologically interlocked ceramics, Mirkhalaf, Zhou, Barthelat, PNAS, 2018


Develop a topologically interlocked material (TIM) design that is tougher (25-50X) and stronger (1.2X) than the monolithic plates with the same material (increasing impact resistance without sacrificing strength/toughness).

A nondimensional “interlocking parameter” is proposed to account for the mechanisms and guide the exploration and optimization of TIMs for future architecture systems.

Scientific question:

To develop a high performance TIM and also relevant design guidelines/criteria (structure-mechanics-performance) to select optimum architectures for given applications and requirements.

Key of how:

Through a systematic exploration (fabrication, mechanical testing, mechanism and theoretical analyzing) of 15 different designs of TIMs, one architecture based on octahedral blocks stands out with best overall performance (tougher and stronger), due to the disrupted stresses by interfaces and the balance between interlocking strength and surface damage from frictional contact stresses.

A nondimensional interlocking parameter, derived by considering important deformation mechanisms, can be applied to any geometries/structures, thus allowing to explore a larger design space.   

Major points:

1. Specially architecture materials show interesting properties (e.g., negative Poisson’s ratio). One full-solid type are TIMs, in which the constituent blocks generate an interlocking effect via the geometry and arrangement rather than adhesives.

The interlocked, polyhedral platonic/truncated blocks can slide, rotate, or separate to provide a wealth of deformation mechanisms and properties, while usually an increase of impact resistance/energy absorption sacrifices the overall strength. Thus, comprehensive guidelines of structural design for specific property/application are needed.

2. Using calcium sulfate through a replica method to fabricate 15 designs of TIMs (6 are platonic/truncated tetrahedral blocks, 8 are octahedral, 1 is dodecahedron); each contains 7X7 interlocking blocks, is further placed in an Al frame and fixed with CaS paste to form a panel.

The medial sections of the blocks form a surface-filling tessellation made of regular polygons. Interlocking geometries are introduced by tilting the sidefaces appropriately; the size effects are removed by fixing the size and number of all geometries.

3. Static and impact tests (point force loading) show that: monolithic panels exhibit brittle failure (catastrophic fragmentation) at small deflections, while the TIMs generally show significantly larger deflection and energy absorption, and localized failure with integrity/shape retained.

Blocks rotation and slide on one another, and two regimes are identified, rapid increase in average rotation and sliding area with panel deflection and much slow increase in sliding area (increased geometrical locking, surface cracking of blocks).

4. The deformation mechanisms are similar for all the 15 TIMs, while all properties, stiffness, maximum force (strength) and energy absorption improve significantly with increasing interlocking angle, up to 20o (due to increased interlocking effect restricting relative motion), and then decrease (because of excessive contact stresses at interface damage individual blocks, then decrease interlocking strength).

The panels show rate behavior (similar stiffness and higher maximum force and energy absorption from static to impact loading), attributed to features of ceramic materials, reduced friction and delayed surface damage with improved strength and sliding spreading, and attenuation of elastic waves.

5. Panels of octahedral blocks show the best overall performance in both quasi-static and impact conditions: energy absorption 20X and 25X (actual energy dissipation by cracking is 35-50X) and maximum force ~1.2X higher than those of monolith panels.

The remarkable increase in strength can be understood by the failure mode (distributed and thus smaller stresses in individual blocks provides strengthening (PS: not clear how)) and increased stability.

6. By capturing the geometrical effects for collective sliding (considering both geometric and frictions contact for sliding is too costly/complex) based on an elastic block interlocked by rigid stationary neighbors, deriving the elastic energy U w.r.t. the pushout distance leads to a nondimensional locking parameter.

Strength and energy absorption initially increase rapidly with the locking parameter, then the slope decreases progressively because of surface damage of the blocks due to contact stresses, indicating the appropriateness of this parameter to predict the performance for a wider range of architectured materials.

Here is the link of the fulltext:


Zhigang Suo's picture

Thank you for pointing to this paper. It looks fascinating, and I will study it.

In preparing for my graduate course on fracture, I have tweeted several threads: Hope they are useful to you.

Also, you will reach many readers on Twitter.

Zhigang Suo's picture

I have just tweeted your reading notes:

Bin Wang's picture

Thank you so much, Prof. Suo.  Following your "To Read Is Human, to Watch Divine", I am trying to get into the first stage, and further for the second one.  Such a foresight with pioneering endeavors is impressive, enlightening, and exciting. I wish and pursue to contribute to this.

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