Functional soft materials have been a subject of great interest to researchers in engineering and material science due to the advancement of science technology and wide applications of soft materials. As a typical class of smart and soft polymeric materials, shape memory polymers (SMPs) have the capacity to return from a deformed state (impermanent shape) to their original state (permanent shape) upon the application of certain external stimuli, such as temperature, light, magnetic actuation and so on. Among them, thermo-responsive SMPs are commonly used, and they have potential applications in many fields, thus it’s very important to investigate the thermo-mechanical behaviors to extend their applications. To study the mechanical behavior of functional soft materials in relation to SMPs, this thesis concentrates on two problems: (1) buckling of film/substrate structures, and (2) buckling of periodic metamaterials.

A continuum model for large deformation buckling of film/substrate structure is developed. This model is developed based on minimizing the total energy in the film and substrate system by considering the precise curvature of the buckled film and Poisson’s ratio of the substrate. The theory is then modified to simplify the expressions of wavelength and amplitude for the buckled geometry. The predicted values obtained by using this proposed theory are validated with the previous experimental results.

Based on the assumption that the buckling occurs instantaneously, the buckling behavior of thin Si film on SMP substrate is studied in both theoretical analysis and finite element simulations. The critical buckling strain at a glassy state is found to be larger than that at the rubbery state, and a programming method is then proposed and realized according to this finding to control the buckling of thin film on the SMP substrate with the help of numerical simulation.

When compressed beyond a critical value, periodic cellular structures will display pattern transformation phenomenon accompanied by auxetic (negative Poisson’s ratio) behavior. Due to their unique properties different from common materials, auxetic materials possess many advantages which other materials cannot compare with and have broad application prospects. Therefore, in order to extend their application area, it is of great significance to study the pattern transformation behavior and lower the critical buckling conditions of periodic cellular structures.

A class of composite periodic cellular structure with interfacial layers is developed and its buckling patterns under a uniaxial compression are explored through numerical and experimental studies. It is interesting to note that by introducing very thin interfacial layers into the periodic cellular structures, the critical strain for pattern transformation of the constructed composite periodic cellular structures can be significantly influenced and is always lower than that of the single-material periodic cellular structure, regardless of the interfacial layer is harder or softer than the matrix materials, this discovery may contribute to the further application of periodic cellular structures.

A theoretical method is proposed to predict the critical strain for pattern transformation of single-material periodic cellular structures, and then, based on the simulation and experiment results of composite periodic cellular structures, the theoretical method is modified and further developed to predict the critical strain for a certain range of combinations of the materials and porosities of the periodic cellular composites with interfacial layers.

It is well known that global buckling is the prior buckling mode for conventional square lattice structures. However, during the study, we found that the prior buckling pattern can be altered to pattern transformation by modifying the sections of columns in the conventional square lattice structures, and the effective modifying region is further explored via a linear buckling analysis procedure. In addition, the critical buckling conditions for the pattern transformation of this type of modified metamaterials are theoretically analyzed. The designing method and theoretical prediction of the critical buckling conditions are verified through numerical simulations and experimental studies.