Date of Award

Fall 2013

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

First Advisor

Thomas Siegmund

Committee Chair

Thomas Siegmund

Committee Member 1

Raymond J. Cipra

Committee Member 2

J. Stuart Bolton

Committee Member 3

C. T. Sun


This thesis explores the mechanical properties of a new class of multifunctional architectured materials, Topologically Interlocking Materials (TIMs). These materials are created as an assembly of unit elements arranged in an interlocking pattern such that the load transfer between unit elements occurs by contact only. In the absence of adhesive interaction, the tensile component of the load is carried by complementary tensile elements in the form of external constraints or integrated filaments. By virtue of the bottom up design used in creating these materials, their mechanical properties are influenced by a number of controllable parameters including shape, confinement force, scale, and, composition. The overall hypothesis is that these parameters can be advantageously exploited to create a family of materials that fill empty holes in the material property space. The contributions of this research can be classified into two main tasks: (1) Experimental exploration of novel TIM designs, and, (2) The development of mechanics models that explain the deformation and failure of these materials, and hence provide rules for designing these materials for specific functional requirements.

We hypothesize that TIM assemblies made of cellular unit elements would result in a range of properties obtained from TIM assemblies, traditionally created using dense unit elements. Drop tower experiments were performed to characterize the physical properties of TIM assemblies made of different relative densities. The analysis of the experiments revealed that stiffness, strength and toughness decreased linearly with relative density. An analytical model based on the concept of thrust line analysis was developed for the prediction of the observed material behavior. Model predictions were in agreement with experimental data.

We recognize that TIM assemblies are 2D ordered granular crystals and hence provide the ability of active control of mechanical properties under the influence of varying confinement force. By varying the in-plane force, active control of TIM stiffness and energy absorption was demonstrated, with specific application towards creating an adaptive energy absorbing material. The previously developed analytical model was modified by incorporating the ability to actively control the in-plane force leading to active control of out-of-plane response. Model was able to reproduce experimentally observed results and was proposed as a means to creating an algorithm for a smart system design using TIM assemblies.

The thesis subsequently explores the scaling power laws for stiffness, strength and toughness. Even though the contact dominated mechanics of TIM assemblies is far different from the bending dominated mechanics of monolithic plates, stiffness of the 2D TIM assemblies was found to scale similar to the rectangular plates, albeit with lower magnitudes. The strength and toughness scaling laws were then predicted by using a linearized model. Toughness was seen to vary positively with both, strength and stiffness, in contrast to the inverse relationship usually obtained for the engineering materials. These scaling relationships were used to demonstrate design of materials with specific desired mechanical properties.

Finally, a novel bioinspired design was proposed by combining the concept of tensegrity, observed in biological structures, and, topological interlocking. The design proposed embedding the interlocked assembly in a woven net of fiber tows. These fiber tows now held the unit elements together replacing the previously used rigid frame. The structure showed an initial nonlinear hardening response until the first failure event followed by regaining of strength before total loss of load carrying capacity. A previously established analytical model was used to explain the experimental observations. The model was extended to propose a material with variable stiffness response, obtained by controlling the stiffness of the fibers in the fiber tow.