Bin Li

High-Q chiral responses can be achieved in symmetry-breaking metasurfaces based on quasi-bound states in the continuum (q-BICs). However, deep-subwavelength single-layer metallic metasurfaces in the microwave regime face inherent limitations in breaking out-of-plane symmetry to achieve chiral response. To overcome this challenge, we theoretically propose and experimentally implement a bilayer helical chiral metasurface in microwave frequencies, which is systematically verified to exhibit a high-Q chiral response with large circular dichroism (CD). The structure supports two bound states in the continuum (BIC) modes exhibiting distinct chiral characteristics, with one achieving strong extrinsic chirality under oblique incidence, while the other attaining strong intrinsic chirality with a CD value exceeding 0.9 over a wide range of asymmetry parameters through out-of-plane symmetry breaking. The evolution of the far-field polarization states of the two BIC modes reveals the generation mechanism of the strong chirality. At last, we perform microwave experiments to validate the intrinsic chiral response of the designed metasurface with out-of-plane symmetry breaking, and the microwave experimental measurements agree well with the simulation results. This work opens new avenues for high-performance microwave chiral metasurfaces, with promising applications in polarization control, chiral sensing, and next-generation wireless communication systems.

Incompressibility is commonly observed in the majority of hyperelastic materials, which are fundamental to a wide range of technical applications owing to their distinctive properties, particularly their flexibility, stretchability, and resilience. However, the incompressibility constraint poses a significant challenge in modeling such materials, further complicating efforts to accurately describe or reproduce crack propagation through numerical simulations. Mixed element formulations, for example, the so‐called Q1P0 approach, are extensively employed to mitigate locking issues associated with incompressibility at finite deformations. In this study, the Q1P0 approach is formulated via the Simo–Taylor–Pister (STP) three‐field formulation, which emanates from the Hu‐Washizu variational principle, resulting in an equivalent single‐field displacement formulation. This framework is subsequently coupled with the phase‐field method to predict finite strain fracture of nearly incompressible hyperelastic materials. To the best of the authors' knowledge, this represents the first successful coupling of the phase‐field approach with the STP‐based Q1P0 formulation. Through a consistent derivation and condensation of the pressure field, the novel four‐field formulation is reduced to a pure displacement‐phase‐field approach. This reduction constitutes a major advantage of the proposed formulation, as it preserves the size of the global system without introducing additional degrees of freedom. To alleviate the innate conflict between the incompressibility constraint and diffuse crack opening, a tailored phase‐field degradation function is integrated into the volumetric contribution, accelerating pressure release and thereby facilitating crack opening. Accordingly, the incompressibility constraint is relaxed in damaged material while remaining strictly enforced in intact material. The proposed formulation offers two more benefits: (i) it provides enhanced generality and applicability with respect to the choice of the volumetric strain‐energy function, and (ii) it results in a physically consistent material response in both the nearly incompressible and the compressible regimes. Subsequently, several numerical examples are presented to illustrate the characteristics of the proposed formulation.

Double network (DN) materials exhibit extraordinary strength and toughness that far exceed the linear combination of their constituents. Although these systems have been widely explored across length scales, a unifying physical principle bridging local microscopic processes to the macroscopic nonlinear response remains elusive. Here, we demonstrate that a minimal three-dimensional model consisting of two coupled, disordered linear-elastic networks is sufficient to capture the essential physics of DN nonlinear mechanics. Without invoking intrinsic material plasticity, this minimalist model reproduces the full suite of emergent mechanical behaviors, including yielding, stable necking, strain hardening, and the global brittle-to-ductile transition. We find that the stark mechanical contrast between the hard and soft networks drives inter-network load transfer, which screens defects and suppresses stress concentrations within the hard network. By defining a localized stress-concentration factor, K_sc, we establish a universal scaling law in which the hard-network failure strain varies linearly with 1/K_sc, directly linking microscopic defect shielding to macroscopic yielding. We further show that the spatial localized-to-delocalized damage crossover is regulated by the efficiency of this inter-network load transfer, whereas the brittle-to-ductile boundary is dictated by the failure-stress balance between the constituent networks. Finally, the stable necking plateau is identified as an energetic selection governed by a dissipation-regulated Maxwell construction, balancing potential energy release against irreversible rupture dissipation. Together, these findings demonstrate that a simple linearly elastic, network architecture can account for the rich nonlinear landscape of DN materials, providing a physical framework and a general design principle for next-generation tough solids.

Existing variational phase-field models for brittle fracture under multi-axial stress states face a critical limitation: they typically address either crack nucleation or unilateral contact behavior, but not both in a unified manner. Non-variational approaches, while capable of capturing these behaviors, often compromise the theoretical rigor inherent to the variational framework. To overcome this limitation, we propose a novel elastic strain energy decomposition scheme rooted in structured deformation theory. This decomposition enables the recovery of multi-axial failure surfaces corresponding to a wide range of phenomenological failure criteria, including the Rankine, Tresca, Mohr-Coulomb, von Mises, and Drucker-Prager types. Furthermore, it provides an accurate and consistent representation of complex crack kinematics-such as crack face contact and friction-within a smeared continuum framework. A key contribution of our work is the derivation of a regularized residual strain energy formulation that replicates the mechanical behavior of sharp cracks while preserving thermodynamic consistency through the generalized standard materials framework. By explicitly incorporating the crack normal-prescribed a priori via material-specific failure criteria-our approach defines the residual strain energy of fully disaggregated material at the representative volume element scale. This naturally integrates crack orientation into the macroscopic strain kinematics, ensuring both physical fidelity and computational efficiency. By reconciling variational principles with material-specific strength criteria, our framework offers a unified, theoretically sound, and versatile tool for modeling fracture in brittle and cohesive-frictional materials. We demonstrate the model's capabilities through numerical simulations that validate predicted crack nucleation stresses and orientations. Furthermore, the model accurately reproduces post-fracture contact and sliding behavior, consistent with classical crack-face tractions observed during crack closure.

Freestanding ferroelectric thin films have been studied recently due to their enhanced properties over traditional thin films. After removing the substrate, the freestanding ferroelectric thin films tend to become folded below the ferroelectric transition temperature, and they may become unfolded under the electron beam from a transmission electron microscope (TEM). It was proposed that this folding behavior is caused by the electrostatic force produced by the bound charges on the thin film surface. In this work, a comprehensive model for explaining the folding behavior in freestanding ferroelectric thin films is presented as a synergy of mechanical bending theory and phase-field model of ferroelectrics. The model provides a validation for the proposed folding mechanism by demonstrating a semi-quantitative agreement with the observed film folding behavior. It is found for the first time that there exists a critical ratio between the length and thickness of the film beyond which the folding may happen. The model also shows that the unfolding transition under the TEM electron beam may be the result of electron beam-induced surface charge compensation.

Despite intensive investigations on the droplet receding contact angle on superhydrophobic surfaces, i.e., a key parameter characterizing surface wettability and adhesion, the quantitative correlation between the surface structure mechanical properties (softness) and the droplet receding contact angles remains vague. By systematically varying the geometric dimensions and mechanical properties of soft pillar arrays, we find that the droplet receding contact angles decrease with the decrease in the pillar spring constant. Most surprisingly, the densely packed pillar arrays may result in larger receding contact angles than those on sparsely packed pillars, opposing the understanding of rigid pillar arrays, where the receding contact angles increase with a decrease in the packing density of pillars. This is attributed to the collective effects of capillarity and elasticity, where the energy consumed by the sliding contact line, the energy stored in the distorted liquid-vapor interface, and the energy stored in the deflected pillar contribute to the droplet depinning characteristics. We develop an analytical model to predict the droplet receding contact angles on soft superhydrophobic pillar arrays with knowledge of the material intrinsic receding contact angle, the pillar geometry, and the pillar mechanical properties. The predictions are corroborated by the experimental data measured in this and prior studies.