This paper presents an analytical model to predict the second stable equilibrium state of non-uniformly curved and asymmetric shells. The model is derived based on assumptions of bending-dominated deformation and linearly varying curvature. The validity of the bending-dominated hypothesis is confirmed by comparing the calculated stretching and bending energies. Model predictions are verified through nonlinear finite element simulations and experimental tests on a bistable shell with an airfoil cross-section. The resulting curvature distributions in the second stable state and the snap-through load–displacement curves show excellent agreement. A parametric study demonstrates that the model is effective for both smooth and piecewise curvature variations. However, the prediction accuracy decreases as the geometric asymmetry of the cross-section increases.
Frictional stability is as critical as strength and plasticity, and constitutes a key parameter governing the long term service performance of bulk metallic glasses (BMGs). In this study, nano scratch tests with controlled scratch rates under a constant normal load were performed on Zr50Cu40Al10 BMGs in distinct structural energy states (as-cast, relaxed, and two rejuvenated conditions) to systematically characterize nanoscale stick–slip dynamics at the nano contact interface. Time resolved friction signals were analyzed using the maximum Lyapunov exponent and detrended fluctuation analysis (DFA), together with fractal analysis, stick–slip event statistics, and a loading unloading asymmetry parameter. Across the investigated scratch speeds, the average coefficient of friction follows the order relaxed > as-cast > CR80 > CR90, indicating that structural rejuvenation improves frictional stability. At low scratch speeds, the frictional response is dominated by irregular, large amplitude stick–slip fluctuations with positive maximum Lyapunov exponents, indicating chaotic like frictional dynamics. With increasing scratch speed, the maximum Lyapunov exponent decreases toward zero or negative values, while the stick–slip asymmetry and characteristic cutoff scale of slip bursts are reduced. These trends indicate a progressive suppression of chaotic stick–slip instability and a reduction in the characteristic scale of statistically identified local intermittent events. At 20 μm/s, the smaller local event scales coexist with a pronounced periodic modulation, indicating a multiscale high speed frictional response. DFA further reveals persistent temporal correlations with hurst exponent (H>0.5) for all structural states. The coupled increase in H and decrease in fractal dimension D, together with the approximate relation (D+H=2), suggest self-affine like scaling consistency of the lateral force rate fluctuations under the present experimental conditions. Among all structural states, the rejuvenated BMGs, especially CR90, exhibit the smallest stick–slip asymmetry, the lowest characteristic slip burst scale, and the most stable sliding behavior. These results provide a statistical and mechanistic interpretation linking structural energy state, scratch speed, and nonlinear stick–slip dynamics in Zr-based BMGs, and offer guidance for rate sensitive friction and wear control under confined sliding contact
A GJK-based penetration contact model is developed within the framework of bond-based peridynamics (BBPD) for simulating complex multi-body interactions in geomaterials. Unlike conventional peridynamic contact models, the proposed approach determines the contact normal direction directly from the shortest-distance vector between interacting bodies using the Gilbert–Johnson–Keerthi (GJK) algorithm, thereby improving geometric consistency for complex contact configurations. By reconstructing object boundaries from discretized material points, the model preserves the local roughness of contacting surfaces and reduces sensitivity to discretization density and material point size. The contact interaction is further formulated in a nonlocal manner through force redistribution within the peridynamic horizon, which avoids excessive local force concentration and improves numerical stability. In addition, a two-level GJK strategy combining global body-level detection and local material-point-level evaluation is introduced to enhance computational efficiency, while a stick–slip formulation is adopted to describe tangential frictional behavior. The model is validated through benchmark examples involving slope sliding, inclined-interface stick–slip transition, and compression-induced failure of single- and double-flawed rock-like specimens. The results show that the proposed model can accurately predict contact forces, stick–slip behavior, and frictional crack evolution. It is further applied to a two-dimensional coarse-grained geomaterial assembly, where both macroscopic responses and microscopic mechanisms, including shear band formation, force-chain evolution, and local multi-particle contact behavior, are reasonably reproduced. The proposed model provides a robust, unified, and geometrically consistent computational framework for simulating contact-dominated discontinuous geotechnical problems.
Shape Memory Alloy (SMA) spring actuators are extensively employed in various fields such as aerospace, medicine, and robotics thanks to their functional properties induced by martensitic transformation. In fact, the latter leads to large displacements, high output forces, and competitive power-to-weight ratios. Several research works have focused on predicting the thermomechanical response of SMA springs through finite element computation with significant computational time consuming. To address this issue, this paper deals with the development of a one-dimensional computational design tool for SMA spring actuators and its experimental validation. It combines the formulation of the spring’s response, and a one-dimensional (1D) SMA thermomechanical constitutive law based on the Chemisky et al’s model. This tool predicts accurately the thermomechanical response of SMA springs with lower computational time. It matches closely the three-dimensional finite element and experimental results, particularly for large range values of geometrical parameters. For experimental validation, SMA springs are manufactured from superelastic NiTi wires. Tensile tests are carried out on these springs for the validation process. The validated numerical tool enabled the design of SMA springs using advanced genetic algorithms. This development significantly reduces the computational time and leads to an accurate design of SMA springs considering superelasticity or shape memory effect.
The instability-induced wrinkling impedes the engineering applications of polygonal membranes, while existing wrinkle-suppression solutions suffer from the interfacial delamination-related premature structural failure, undesirable weight increase and irregular pattern-induced integrity loss. Here we propose a wrinkle-free design strategy through optimizing morphologies of free edges to modulate stress distribution and achieve wrinkle-free polygonal membranes under arbitrary displacement loadings. A physics-informed neural network (PINN) model with the small-deformation assumption is employed to predict the stress distribution of polygonal membranes even with a small ratio of clamped edge to circumradius where the Marguerre function-based theoretical solution becomes invalid. The related wrinkling capability is sequentially evaluated through considering the stress-based wrinkling criterion. The non-gradient Bayesian optimization algorithm is performed to obtain the optimized free edges for polygonal membranes, and the related wrinkle-free performance is verified through both finite-deformation post-buckling analyses and physical experiments. An empirical wrinkle-free solution is also proposed for polygonal membranes with different geometries.
The unique deformation compatibility and strengthening mechanism inherent to gradient-distributed microstructures endow gradient-structured (GS) materials with a superior synergy of strength and toughness compared to their homogeneous counterparts. Nevertheless, a reliable experimental method for determining the local macroscopic stress–strain response of GS materials is currently lacking; consequently, the development of constitutive models remains constrained by the scarcity of directly measured data. To overcome this obstacle, the present study develops a general methodology for constructing the depth-dependent elastoplastic constitutive relationship of strain-hardening GS metallic materials. Through quasi-static axial tensile tests, a series of depth-hardness measurements are first obtained for materials with varying degrees of strain hardening. Subsequently, using experimentally accessible hardness as an intermediate variable, a variable separation method based on a laminated plate model is proposed and then employed to inversely derive the linear mapping relationship between flow stress and hardness. Based on the depth-strain-hardness experimental data, the depth-dependent elastoplastic constitutive relationship is thereby established. Finally, the close correspondence between the experimental results and finite-element simulations for both axial tension and three-point flexure of the sandwich specimen validates the proposed methodology and the elastoplastic constitutive relationships, and deepens our understanding of the formation and evolution of the multiaxial stress–strain state during axial tension
Atomic Force Microscopy (AFM) is a key tool for characterizing the mechanical properties of biological tissues via force-indentation (F-I) curves. However, analyzing AFM curves with contact mechanics models to extract Young’s modulus is complex and time-consuming. This study presents a novel two-stage machine learning (ML) approach to streamline this process by first identifying the appropriate contact theory (Hertz, JKR, or BCP) for F-I curves (1–50 kPa) and then predicting Young’s modulus. The ML models were trained exclusively on synthetic datasets generated from these established contact models. Results demonstrate that the choice of contact model critically impacts prediction accuracy. While mismatched models produce significant errors despite visual curve alignment, appropriate models yield negligible errors, demonstrating that graphical fitting alone is inadequate for modulus determination and highlighting the ML model’s ability to discern underlying physical algorithms. This underscores the necessity of selecting the appropriate contact model before estimating Young’s modulus. The approach was validated against theoretical and experimental F-I curves from MCF7, H460 and A549 cancer cells. By delivering precise predictions with high computational efficiency, this ML-based framework not only enhances AFM nanoindentation analysis by addressing existing limitations, but also provides an automated solution for appropriate contact model selection, thereby enabling more reliable mechanical characterization of soft tissues.
