arXiv subjects

Shiheng Zhao

Publications and source records attributed to Shiheng Zhao.

9 recordsLinked to original sources

arXiv2026

Stretching and bending of (really) thick elastic plates

The mechanical energy of an elastic plate separates into stretching and bending energies. This is a result for asymptotically thin plates, but it is often a surprisingly accurate approximation for thick plates, too. Here, we address this conundrum: We compute the deformations of a thick elastic plate resulting from imposed, asymptotically small deformations of its midline to discover effective stretching and bending moduli. They soften with increasing plate thickness, but, strikingly, their ratio remains approximately constant. In this way, our calculations provide a justification for applying the thin-plate picture of stretching and bending to thick plates such as biological cell sheets.

cond-mat.soft↗

arXiv2026

Nonlinear isotropic odd elasticity

The nonconservative elastic responses of active solids have driven a recent explosion of interest in two-dimensional "odd" elasticity: small, linear deformations of these Cauchy elastic solids enable new behaviour absent from classical, passive elasticity. Here, we establish the description of large, nonlinear deformations of isotropic two-dimensional Cauchy elastic solids. We apply our framework to the Rivlin problem, perhaps the simplest problem of elasticity lacking a linear analogue: a square deforms under dead load tractions. Surprisingly, we find that oddness suppresses the bifurcations of a passive Rivlin square. By contrast, we discover that the bifurcations of a three-dimensional Rivlin cube survive oddness even though there is no isotropic, odd linear elasticity in three dimensions. Our results thus form the basis for describing large deformations of active, biological solids while revealing their unexpected nonlinear behaviour that arises even in minimal problems.

cond-mat.soft↗

arXiv2025

Euler buckling on curved surfaces

Euler buckling epitomises mechanical instabilities: An inextensible straight elastic line buckles under compression when the compressive force reaches a critical value $F_\ast>0$. Here, we extend this classical, planar instability to the buckling under compression of an inextensible relaxed elastic line on a curved surface. By weakly nonlinear analysis of an asymptotically short elastic line, we reveal that the buckling bifurcation changes fundamentally: The critical force for the lowest buckling mode is $F_\ast=0$ and higher buckling modes disconnect from the undeformed branch to connect in pairs. Solving the buckling problem numerically, we additionally find a new post-buckling instability: A long elastic line on a curved surface snaps through under sufficient compression. Our results thus set the foundations for understanding the buckling instabilities on curved surfaces that pervade the emergence of shape in biology.

cond-mat.soft↗

arXiv2025

A model for boundary-driven tissue morphogenesis

Tissue deformations during morphogenesis can be active, driven by internal processes, or passive, resulting from stresses applied at their boundaries. Here, we introduce the Drosophila hindgut primordium as a model for studying boundary-driven tissue morphogenesis. We characterize its deformations and show that its complex shape changes can be a passive consequence of the deformations of the active regions of the embryo that surround it. First, we find an intermediate characteristic triangular shape in the 3D deformations of the hindgut. We construct a minimal model of the hindgut primordium as an elastic ring deformed by active midgut invagination and germ band extension on an ellipsoidal surface, which robustly captures the symmetry-breaking into this triangular shape. We then quantify the 3D kinematics of the tissue by a set of contours and discover that the hindgut deforms in two stages: an initial translation on the curved embryo surface followed by a rapid breaking of shape symmetry. We extend our model to show that the contour kinematics in both stages are consistent with our passive picture. Our results suggest that the role of in-plane deformations during hindgut morphogenesis is to translate the tissue to a region with anisotropic embryonic curvature and show that uniform boundary conditions are sufficient to generate the observed nonuniform shape change. Our work thus provides a possible explanation for the various characteristic shapes of blastopore-equivalents in different organisms and a framework for the mechanical emergence of global morphologies in complex developmental systems.

physics.bio-ph↗

arXiv2024

A Constrained Mechanical Metamaterial Towards Wave Polarization and Steering Control

Precise control of the polarization and propagation direction of elastic waves is a fundamental challenge in elastodynamics. Achieving efficient mode conversion along arbitrary paths with conventional techniques has proven difficult. In this letter, we propose an innovative harmonimode mechanical metamaterial by integrating classical lattice architecture with a constrained mechanism. The constrained discrete mass-spring model is formulated and homogenized to reveal the unique harmonimode behavior, which supports single-mode polarized propagation and perfect impedance matching with the reference medium. Leveraging multi-scale simulations and the discrete transformation method, the metamaterial is designed to exhibit degenerated wave polarization and broadband mode conversion along various paths by simply adjusting constraint orientations. Finally, hinge joints are proposed for the physical realization of the metamaterial with sub-wavelength microstructures. Numerical simulations confirm its exceptional wave control performance over a broad frequency range. This work presents a comprehensive framework for designing harmonimode metamaterials capable of arbitrary polarization control.

physics.app-ph↗

arXiv2024

Mechanics of poking a cyst

Indentation tests are classical tools to determine material properties. For biological samples such as cysts of cells, however, the observed force-displacement relation cannot be expected to follow predictions for simple materials. Here, by solving the Pogorelov problem of a point force indenting an elastic shell for a purely nonlinear material, we discover that complex material behaviour can even give rise to new scaling exponents in this force-displacement relation. In finite-element simulations, we show that these exponents are surprisingly robust, persisting even for thick shells indented with a sphere. By scaling arguments, we generalise our results to pressurised and pre-stressed shells, uncovering additional new scaling exponents. We find these predicted scaling exponents in the force-displacement relation observed in cyst indentation experiments. Our results thus form the basis for inferring the mechanisms that set the mechanical properties of these biological materials.

cond-mat.soft↗

arXiv2023

Tunable topological phase transition in soft Rayleigh beam system with imperfect interfaces

Acoustic metamaterials, particularly the topological insulators, exhibit exceptional wave characteristics that have sparked considerable research interest. The study of imperfect interfaces affect is of significant importance for the modeling of wave propagation behavior in topological insulators. This paper models a soft Rayleigh beam system with imperfect interfaces, and investigates its topological phase transition process tuned by mechanical loadings. The model reveals that the topological phase transition process can be observed by modifying the distance between imperfect interfaces in the system. When a uniaxial stretch is applied, the topological phase transition points for longitudinal waves decrease within a limited frequency range, while they increase within a larger frequency scope for transverse waves. Enhancing the rigidity of the imperfect interfaces also enables shifting of the topological phase transition point within a broader frequency range for longitudinal waves and a confined range for transverse waves. The transition of topologically protected interface modes in the transmission performance of a twenty-cell system is verified, which include altering frequencies, switching from interface mode to edge mode. Overall, this study provides a new approach and guideline for controlling topological phase transition in composite and soft phononic crystal systems.

cond-mat.soft↗

arXiv2021

Elastic Wave Propagation and Bandgaps in Finitely Stretched Soft Lattice Material

In this study, the in-plane Bloch wave propagation and bandgaps in a finitely stretched square lattice were investigated numerically and theoretically. To be specific, the elastic band diagram was calculated for an infinite periodic structure with a cruciform hyperelastic unit cell under uniaxial or biaxial tension. In addition, an elastodynamic "tight binding" model was proposed to investigate the formation and evolution of the band structure. The elastic waves were found to propagate largely under "easy" modes in the pre-stretched soft lattice, and finite stretch tuned the symmetry of the band structure, but also "purify" the propagation modes. Moreover, the uniaxial stretch exhibits the opposite impacts on the two "easy" modes. The effect of the biaxial stretch was equated with the superposition of the uniaxial stretches in the tessellation directions. The mentioned effects on the band structure could be attributed to the competition between the effective shear moduli and lengths for different beam components. Next, the finite stretch could tune the directional bandgap of the soft lattice, and the broadest elastic wave bandgaps could be anticipated in an equi-biaxial stretch. In this study, an avenue was opened to design and implement elastic wave control devices with weight efficiency and tunability. Furthermore, the differences between the physical system and the corresponding simplified theoretical model (e.g., the theoretically predicted flat bands) did not exist in the numerical calculations.

cond-mat.soft↗

arXiv2021

Elastic wave velocities in finitely pre-stretched soft fibers

Elastic wave velocity in a soft fiber that varies depending on material constitution and axial stress level is an essential measure of mechanical signals in many technical applications. In this work, based on the small-on-large theory, we establish a model of linear elastic wave propagation in a finitely pre-stretched soft fiber. The formulas of longitudinal (Primary, P-) and transverse (Secondary, S-) wave velocities are provided and validated by numerical simulations as well as by experimental data on spider silk. The influences of material constitution, compressibility, and pre-stress on the wave propagation are investigated. We found that with increasing pre-stress, the variation of P-wave velocity highly relies on the concavity of the stress-strain curve. In contrast, an increase of S-wave velocity exhibits regardless of any constitutive model. For both P- and S-waves, the variation of the velocities is more significant in a compressible fiber than that in a nearly-incompressible one. Moreover, for minuscule pre-stress, we propose a modified formula for S-wave velocity based on the Rayleigh beam theory, which reveals the competition mechanism between "string vibration" and "beam vibration." This may provide a reliable theoretical basis for precise mechanical characterization of soft fibers and open a route for lightweight, tunable wave manipulation devices.

cond-mat.soft↗