The size effect in the thermo-mechanical behavior of polymeric materials is a critically important phenomenon and has been the subject of many researches in past decades. For example, polystyrene (PS), a widely used polymeric material, is brittle at the bulk state. When the dimensions decreases to the nanoscale, such as PS in nanofibers, their ductility becomes orders higher than their bulk state. In recent years a number of diverse applications, such as scaffolds in tissue engineering, drug delivery devices, as well as soft robotics, are designed by utilizing the unique properties of polymers at nanoscale. However, the inside mechanism of the size dependency in polymeric materials are still not clear yet. In this dissertation, systematic computational and experimental studies are made in order to understand the origins of the size effect for one- and two-dimensional polymeric materials. This framework is also expanded to investigate the size-dependent multi-physics response of functional polymeric materials (shape memory polymers) which are actuated by high-intensity focused ultrasound (HIFU). Our computational studies are based on molecular dynamic (MD) simulations at the atomistic scale, and experimentally-validated finite element models at the bulk level. From bottom-up direction, molecular dynamics can reveal the mechanisms of the size effect in polymers at molecular level, and help predict properties of the bulk materials. In this research, MD simulations are performed to track the origins of the size-effect in the mechanical properties of PE and PS nanofibers. In addition, the size-dependent thermal response of functional polymeric films is also studied at the atomistic scale by utilizing molecular dynamics simulations to predict the thermal properties and actuation mechanisms in these materials when subjected to HIFU fields. From top-down direction, experiments and finite element analysis, are also conducted in this research. An experimentally-validated finite element framework is built to study the mechanical response of shape memory polymers (SMPs) triggered by HIFU. As an external trail towards application fields, a SMP composite with enhanced shape memory ability and also a two-way SMP are synthesized. A smart gripper and also a self-rolling structure are designed by using these SMPs, which approves that these SMPs are good components in designing soft robotics. Finally, The influence of evaporation during fiber forming process is investigated by molecular dynamics simulation. It is found that the formation of the microstructure of polymeric fibers at nanoscale depends on the balance of stretching force and evaporation rate when the fiber is forming. / Doctor of Philosophy / Thermomechanical properties of a thin fiber, a thin film and a cube made of a polymer are significantly different. Although, based on the extensive research that has been performed in recent years our understanding of this size-dependency is advanced to a great degree in the past decades, there are still many unanswered basic questions that can only be addressed by performing computational and experimental investigation at different length scales, from atomistic up to bulk level in polymers. In this research we target exploring some unknown aspects of the size dependency in the thermomechanical properties of polymers by investigating their deformation mechanisms at different length scales. As the first step, we will investigate the mechanical properties of polymeric fibers. For these fibers, the mechanical properties are strongly connected to the fiber's diameter. The prevailing hypothesis is that this size dependency is closely related to the thickness of the surface layer of the nanofibers. Our results show some unknown origins behind the size dependency of the mechanical properties in polyethylene (PE) and polystyrene (PS) nanofibers, which originate from the deformation mechanisms at the atomistic scale. In addition, not just the mechanical properties, the thermal properties and response of functional polymers subjected to an external stimulation are also related to their size. For example, the thermal conductivity of a fiber, a sheet and a cube may be significantly different. Our study shows the thermal responses of different polymers triggered by ultrasound are also different. The size and the type of the polymers will both have influence on the final temperature in the polymeric materials, when the polymeric materials are heated by same ultrasound source. We also have applied our computational and experimental frameworks to investigate this phenomenon. In addition, we also used a new shape memory polymer composite and a two-way shape memory polymer on designing soft robotics-like structures. Overall this research indicates that both mechanical response and thermal responses of polymers are highly related to their dimension. Taking advantage of these unique size effects, and by tailoring this property, diverse devices can be made for being used in a broad range of applications.