Abstract Nondestructive evaluation (NDE) techniques that use nonlinear wave–damage interactions have gained significant attention recently due to their improved sensitivity in detecting incipient damage. This study presents the use of finite element (FE) simulation with the experimental investigation to quantify the effects of guided waves’ propagation through multiple delaminations in unidirectional glass fiber-reinforced polymer (GFRP) composites. Further, it utilizes the outcomes of nonlinear interactions between guided waves and delaminations to locate the latter. This is achieved through probabilistic Bayesian updating with a structural reliability approach. Guided waves interacting with delaminations induce nonlinear acoustic signatures that can be quantified by the nonlinearity index (NLI). The study found that the NLI changes with the interrogation frequency, as confirmed by numerical and experimental observations. By using the numerical outcomes obtained from the nonlinear responses, a Bayesian model-based approach with subset simulation is proposed and subsequently used to locate multiple delaminations. The results indicate that both the log-likelihood and log-evidence are key factors in determining the localization phenomenon. The proposed method successfully localizes multiple delaminations and evaluates their number, interlaminar position, width, and type.

Abstract Data-driven equation identification for dynamical systems has achieved great progress, which for static systems, however, has not kept pace. Unlike dynamical systems, static systems are time invariant, so we cannot capture discrete data along the time stream, which requires identifying governing equations only from scarce data. This work is devoted to this topic, building a data-driven method for extracting the differential-variational equations that govern static behaviors only from scarce, noisy data of responses, loads, as well as the values of system attributes if available. Compared to the differential framework typically adopted in equation identification, the differential-variational framework, due to its spatial integration and variation arbitrariness, brings some advantages, such as high robustness to data noise and low requirements on data amounts. The application, efficacy, and all the aforementioned advantages of this method are demonstrated by four numerical examples, including three continuous systems and one discrete system.

Abstract 3D/4D printing offers significant flexibility in manufacturing complex structures with a diverse range of mechanical responses, while also posing critical needs in tackling challenging inverse design problems. The rapidly developing machine learning (ML) approach offers new opportunities and has attracted significant interest in the field. In this perspective paper, we highlight recent advancements of utilizing ML for designing printed structures with desired mechanical responses. First, we provide an overview of common forward and inverse problems, relevant types of structures, and design space and responses in 3D/4D printing. Second, we review recent works that have employed a variety of ML approaches for the inverse design of different mechanical responses, ranging from structural properties to active shape changes. Finally, we briefly discuss the main challenges, summarize existing and potential ML approaches, and extend the discussion to broader design problems in the field of 3D/4D printing. This paper is expected to provide foundational guides and insights into the application of ML for 3D/4D printing design.

Abstract This paper explores the decomposition of linear, multi-degree-of-freedom, conservative gyroscopic dynamical systems into uncoupled subsystems through the use of real congruences. Two conditions, both of which are necessary and sufficient, are provided for the existence of a real linear coordinate transformation that uncouples the dynamical system into independent canonical subsystems, each subsystem having no more than two-degrees-of-freedom. New insights and conceptual simplifications of the behavior of such systems are provided when these conditions are satisfied, thereby improving our understanding of their complex dynamical behavior. Several analytical results useful in science and engineering are obtained as consequences of these twin conditions. Many of the analytical results are illustrated by several numerical examples to show their immediate applicability to naturally occurring and engineered systems.

Abstract An analytical solution for the bending problem of micropolar plates is derived based on the symplectic approach. By applying Legendre's transformation, we obtain the Hamiltonian canonical equation for the bending problem of a micropolar plate. According to the method of separation of variables, the homogenous Hamiltonian canonical equation can be transformed into an eigenvalue problem of the Hamiltonian operator matrix. We derive the eigensolutions of the eigenvalue problem for the simply-supported, free and clamped boundary conditions at the two opposite sides. Based on the adjoint symplectic orthogonal relation of the eigensolutions, the solution of the bending problem of micropolar plate is expressed as a series expansion of eigensolutions. Numerical results confirm the validity of the present approach for the bending problem of micropolar plates under various boundary conditions and demonstrate the capability of the proposed approach to capture the size-dependent behavior of micropolar plates.

Abstract Liquid crystal elastomers (LCEs) are made of liquid crystal molecules integrated with rubber-like polymer networks. An LCE exhibits both the thermotropic property of liquid crystals and the large deformation of elastomers. It can be monodomain or polydomain in the nematic phase and transforms to an isotropic phase at elevated temperature. These features have enabled various new applications of LCEs in robotics and other fields. However, despite substantial research and development in recent years, thermomechanical coupling in polydomain LCEs remains poorly studied, such as their temperature-dependent mechanical response and stretch-influenced isotropic-nematic phase transition. This knowledge gap severely limits the fundamental understanding of the structure-property relationship, as well as future developments of LCEs with precisely controlled material behaviors. Here, we construct a theoretical model to investigate the thermomechanical coupling in polydomain LCEs. The model includes a quasi-convex elastic energy of the polymer network and a free energy of mesogens. We study the working conditions where a polydomain LCE is subjected to various prescribed planar stretches and temperatures. The quasi-convex elastic energy enables a “mechanical phase diagram” that describes the macroscopic effective mechanical response of the material, and the free energy of mesogens governs their first-order nematic-isotropic phase transition. The evolution of the mechanical phase diagram and the order parameter with temperature is predicted and discussed. Unique temperature-dependent mechanical behaviors of the polydomain LCE that have never been reported before are shown in their stress-stretch curves. These results are hoped to motivate future fundamental studies and new applications of thermomechanical LCEs.

Abstract This paper presents a refined model for a mechanical diode based on a mass-spring system. The proposed model utilizes a bilinear spring to construct a frequency converter, which effectively disrupts the reciprocal transmission of acoustic waves. By employing a mass-spring-mass system as a filter, a nonlocal connection is introduced to generate an extremely low-frequency band gap (2–4 Hz), thereby achieving a mechanical diode with a lower operating frequency. The feasibility of these low-frequency mechanical diodes is demonstrated through comprehensive numerical simulations and experimental analyses. In addition, we evaluated the effect of bilinear springs and nonlocal connection parameters on the diode performance.

Abstract This paper studies the dynamic deployment of cylindrical thin-shell structures with open cross section, attached to a rigid base. The structures are elastically folded and then released. Previous experiments have shown that the total energy decreases while a fold moves back and forth along the structure, which was explained in terms of energy losses related to the fold “bouncing” against the boundary. This paper uses a rigorous numerical simulation, based on an in-house isogeometric shell finite element code that simultaneously eliminates shear locking and hourglassing without any intrinsic energy dissipation, to show that the total energy of the system is conserved during deployment. The discrepancy with the previous results is explained by showing that energy transfers from low-frequency, “rigid body” modes, to higher frequency modes.

Abstract The spatial variation of the coefficient of restitution for frictionless impacts along the length of a circular beam is investigated using a continuous impact model. The equations of motion are obtained using the finite element method, and direct time integration is used to simulate the collision on a fast time scale. For collision of a pinned beam with a fixed cylinder, the spatial variation of the coefficient of restitution, impulse magnitude, duration of collision, energetics, and the role of damping are investigated. In the absence of significant external damping, the kinematic and kinetic definitions of the coefficient of restitution provide identical results. Experiments validate the results from simulation which indicate that the coefficient of restitution is sensitive to the location of impact.

Abstract Thermomechanical buckling of slender and thin-walled structural components happens without warning and can lead to catastrophic failure. Similar phenomena are observed during plasmolysis (contraction of a plant cell’s protoplast) and rupture of viral capsids. Analytical formulas derived from stability analyses of elastic plates and shells that do not account for the effects of random geometric imperfections introduced during the manufacturing process or biological growth may vastly over-estimate buckling capacity. To ensure structural safety, the formulas must therefore be combined with empirical data to define “knockdown factors” which are in turn used to establish safety factors. Towards improved understanding of the role of imperfections on mechanical response, ingenious methods have been used to fabricate and test near-perfectly hemispherical shells and those containing dimple-like defects. However, a method of inducing imperfections in the form of randomly shaped surfaces remains elusive. We introduce a protocol for realizing such imperfect shells and measuring the pressure required to buckle them. Silicone is poured onto an elastomeric mold under an acoustic excitation, which can be either random sound, or if desired the same as the modal frequency of the mold. Illustrative micro-computed-tomography images and buckling pressure experiments of a nearly perfect shell and an imperfect one show that the method is effective in introducing randomly shaped imperfections of significant magnitudes. This proof-of-concept study demonstrates that the experimental results when combined with computational simulations can lead to improved understanding of stochastic buckling phenomena.