The main objective of this paper is to introduce complex structures with self-bending/morphing/rolling features fabricated by 4D printing technology, and replicate their thermo-mechanical behaviors using a simple computational tool. Fused deposition modeling (FDM) is implemented to fabricate adaptive composite structures with performance-driven functionality built directly into materials. Structural primitives with self-bending 1D-to-2D features are first developed by functionally graded 4D printing. They are then employed as actuation elements to design complex structures that show 2D-to-3D shape-shifting by self-bending/morphing. The effects of printing speed on the self-bending/morphing characteristics are investigated in detail. Thermo-mechanical behaviors of the 4D-printed structures are simulated by introducing a straightforward method into the commercial finite element (FE) software package of Abaqus that is much simpler than writing a user-defined material subroutine or an in-house FE code. The high accuracy of the proposed method is verified by a comparison study with experiments and numerical results obtained from an in-house FE solution. Finally, the developed digital tool is implemented to engineer several practical self-morphing/rolling structures.

This article shows how four-dimensional (4D) printing technology can engineer adaptive metastructures that exploit resonating self-bending elements to filter vibrational and acoustic noises and change filtering ranges. Fused deposition modeling (FDM) is implemented to fabricate temperature-responsive shape-memory polymer (SMP) elements with self-bending features. Experiments are conducted to reveal how the speed of the 4D printer head can affect functionally graded prestrain regime, shape recovery and self-bending characteristics of the active elements. A 3D constitutive model, along with an in-house finite element (FE) method, is developed to replicate the shape recovery and self-bending of SMP beams 4D-printed at different speeds. Furthermore, a simple approach of prestrain modeling is introduced into the commercial FE software package to simulate material tailoring and self-bending mechanism. The accuracy of the straightforward FE approach is validated against experimental observations and computational results from the in-house FE MATLAB-based code. Two periodic architected temperature-sensitive metastructures with adaptive dynamical characteristics are proposed to use bandgap engineering to forbid specific frequencies from propagating through the material. The developed computational tool is finally implemented to numerically examine how bandgap size and frequency range can be controlled and broadened. It is found out that the size and frequency range of the bandgaps are linked to changes in the geometry of self-bending elements printed at different speeds. This research is likely to advance the state-of-the-art 4D printing and unlock potentials in the design of functional metastructures for a broad range of applications in acoustic and structural engineering, including sound wave filters and waveguides.

Modeling and analyzing the sports equipment for injury prevention, reduction in cost, and performance enhancement have gained considerable attention in the sports engineering community. In this regard, the structure study of on-water sports board (surfboard, kiteboard, and skimboard) is vital due to its close relation with environmental and human health as well as performance and safety of the board. The aim of this paper is to advance the on-water sports board through various bio-inspired core structure designs such as honeycomb, spiderweb, pinecone, and carbon atom configuration fabricated by three-dimensional (3D) printing technology. Fused deposition modeling was employed to fabricate complex structures from polylactic acid (PLA) materials. A 3D-printed sample board with a uniform honeycomb structure was designed, 3D printed, and tested under three-point bending conditions. A geometrically linear analytical method was developed for the honeycomb core structure using the energy method and considering the equivalent section for honeycombs. A geometrically non-linear finite element method based on the ABAQUS software was also employed to simulate the boards with various core designs. Experiments were conducted to verify the analytical and numerical results. After validation, various patterns were simulated, and it was found that bio-inspired functionally graded honeycomb structure had the best bending performance. Due to the absence of similar designs and results in the literature, this paper is expected to advance the state of the art of on-water sports boards and provide designers with structures that could enhance the performance of sports equipment.

Dielectric actuators (DEAs), because of their exceptional properties, are well-suited for soft actuators (or robotics) applications. This article studies a multi-stimuli thermo-dielectric-based soft actuator under large bending conditions. In order to determine the stress components and induced moment (or stretches), a nominal Helmholtz free energy density function with two types of hyperelastic models are employed. Non-linear electro-elasticity theory is adopted to derive the governing equations of the actuator. Total deformation gradient tensor is multiplicatively decomposed into electro-mechanical and thermal parts. The problem is solved using the second-order Runge-Kutta method. Then, the numerical results under thermo-mechanical loadings are validated against the finite element method (FEM) outcomes by developing a user-defined subroutine, UHYPER in a commercial FEM software. The effect of electric field and thermal stimulus are investigated on the mean radius of curvature and stresses distribution of the actuator. Results reveal that in the presence of electric field, the required moment to actuate the actuator is smaller. Finally, due to simplicity and accuracy of the present boundary problem, the proposed thermally-electrically actuator is expected to be used in future studies and 4D printing of artificial thermo-dielectric-based beam muscles.