Theoretical modeling of the interaction between hydrogen and the martensitic transformation in NiTi shape memory alloys (SMAs) under hydrogen-rich environments is crucial for device design and long-term service performance prediction. In this paper, a thermodynamically consistent diffusional-mechanically coupled phase field model is established to investigate the influence of hydrogen on stress-induced martensitic transformation in superelastic NiTi SMAs. Within Gurtin’s configurational force framework, the model couples the kinetic evolution equation with hydrogen diffusion, incorporating hydrogen-induced expansion strain and an asymmetric hydrogen-induced transformation resistance that acts during forward transformation. The model is applied to single-crystal and polycrystalline systems under uniform and non-uniform hydrogen concentration fields. Simulations reproduce key experimental phenomena, including a marked elevation of the forward transformation plateau and an asymmetric widening of the hysteresis loop. Under non-uniform hydrogen distributions, local hydrogen-rich regions act as strong obstacles, generating size-dependent stress concentrations that may increase local susceptibility to damage. In polycrystals, steep grain boundary hydrogen segregation gradients shift martensite nucleation sites from boundaries to grain interiors, further elevating the critical stress for forward transformation. This work provides a mesoscopic tool for assessing the long-term service performance of NiTi SMAs in hydrogen-rich environments and offers new insights into the microstructural mechanisms underlying hydrogen-induced functional degradation.
Two-dimensional (2D) materials such as graphene can deform well beyond the linear elastic regime in nanoindentation and tensile tests, requiring nonlinear constitutive models. Existing hyperelastic formulations expand the strain energy in strain and therefore yield elastic stiffnesses. A compliance formulation, by contrast, expresses strain as a function of stress and is better suited to problems in which the stress is prescribed or follows from equilibrium. This work presents a hyperelastic constitutive model for hexagonal 2D materials in which the complementary strain energy density is expanded to fifth order in the second Piola–Kirchhoff stress, with the Green–St. Venant strain recovered as its work-conjugate derivative. Hexagonal symmetry reduces the fifth-order compliance expansion to fourteen independent constants. These constants are determined from complementary-energy data formed from strain energies and stresses computed using first-principles calculations and classical interatomic potentials along deformation paths spanning combined biaxial stretch and shear. An alternative route, in which the compliances are recovered by first fitting a stiffness expansion and then inverting it, is accurate at low order but ill-conditioned at high order. The fitted compliances yield closed-form expressions for the stress-dependent Young’s modulus, Poisson’s ratio, and shear modulus. As an application, closed-form load–deflection relations are derived for the indentation of a pre-stretched membrane strip at second and third order. The compliances of graphene and molybdenum disulfide from density functional theory are compared with those from the AIREBO-M and Stillinger–Weber potentials, and the analytical predictions are validated against direct molecular-statics indentation simulations. The complementary-energy expansion gives the higher-order elastic compliances directly and provides a constitutive framework for nonlinear elastic modeling of hexagonal 2D materials.
This study presents a multiphysics damage framework that integrates the environmental degradation of multilayered protective coatings used on wind turbine blades (WTB) with mechanical fatigue induced by repetitive raindrop impacts. Rain erosion models for WTB often neglect multiple degradation mechanisms, particularly environmental ageing phenomena. Here, stiffness loss and strength degradation in each coating layer due to thermo-photo-oxidative and hydrolytic ageing are predicted to simulate service conditions. This is achieved by solving the differential equations for local heat conduction, moisture diffusion, and ultraviolet (UV) attenuation in each layer and obtaining through-thickness temperature, moisture, and UV gradients. The degraded material properties are used as inputs to a Coupled Eulerian-Lagrangian (CEL) finite element analysis and a stochastic rain scenario to calculate impact pressures due to raindrops, followed by a fatigue analysis. The raindrop erosion is predicted by the impact-fatigue model, which accounts for coating damage via continuum damage mechanics and interface debonding via a cohesive-zone formulation. The results show that ageing accelerates damage at the coating-putty (adhesive) interface, reducing impact-to-failure by ∼10–30% across impact speeds. Validation against experimental datasets of raindrop impact erosion confirms the framework’s predictive capability. The study contributes a unified methodology for evaluating the long-term performance of protective coatings, supporting design strategies for enhanced erosion resistance and durability.
We present the Direct Insertion Method (DIM), a constitutive time-integration framework for linear viscoelasticity derived directly from the discrete strain-increment form of the Boltzmann superposition principle. In DIM, stress evolves through explicit causal accumulation of decaying contributions generated by successive strain increments, providing a compact and transparent discrete realization of hereditary constitutive behavior. For relaxation kernels represented as sums of exponentials, the formulation yields a stable recursive update that efficiently evaluates the Boltzmann convolution in time.The constitutive behavior of DIM is first validated using classical rheological tests in simple shear for Burgers media, including stress relaxation (strain-controlled) and creep (stress-controlled). In these tests, DIM reproduces reference responses with small relative L2 errors (e.g., below 0.5% for relaxation and below 0.02% for creep at Δt=0.01 s), confirming the correctness of the incremental stress-accumulation framework for multi-mechanism viscoelasticity.As a representative large-scale application, DIM is embedded in a staggered-grid finite-difference time-domain solver for viscoelastic wave propagation. Two-layer Maxwell and heterogeneous Burgers (anticline) simulations show high waveform similarity with a reference implementation across multiple attenuation levels. Additional time-step refinement tests in the Maxwell benchmark show systematic reduction of the global relative L2 error, indicating that the remaining discrepancies are primarily associated with temporal discretization rather than with the DIM formulation itself. These results position DIM as a general constitutive time-integration framework, particularly suited for modular implementation in large-scale computational mechanics applications.
The thickness-dependent Mode Ⅱ interlaminar fracture behaviour of z-pinned CFRP laminates was investigated using End Notched Flexure (ENF) tests. Both non-precracked (NPC) specimens and precracked (PC) ENF specimens were investigated to evaluate the influence of crack propagation on z-pin toughening. The results show that z-pinning leads to only marginal improvements in fracture toughness for NPC tests, whereas significant enhancements of approximately 29.4%, 16.9%, and 17.5% are obtained in PC tests for 3 mm, 5.4 mm, and 10.2 mm laminates, respectively. Crack growth measurements show that z-pinning suppresses delamination propagation, reducing crack extension in PC tests from 16 to 22 mm to 6∼10 mm for 3 mm specimens and from 12 to 22 mm to 5∼8 mm for 5.4 mm specimens, while the reduction becomes less pronounced for 10.2 mm specimens. These results demonstrate that specimen thickness governs the relative contributions of fracture process zone (FPZ) development and z-pin bridging through its influence on crack propagation behaviour, thereby explaining the transition from FPZ-dominated fracture behaviour in NPC tests to bridging-dominated fracture behaviour in PC tests.
A topology-controlled microstructural motif is developed to investigate structure-resolved damage localization and connectivity in a cavity-bearing intergranular film (IGF) network embedded in a load-bearing solid skeleton under prescribed segregation-induced weakening and compression. The framework combines a quadruple-junction-centered irregular cavity, a prescribed segregation-index field, crystal-plasticity-governed solid skeleton domains, and a segregation-sensitive viscoplastic-damage description of the IGF. A 27-case design matrix within one fixed topology and crystallographic orientation realization independently varies segregation localization, segregation severity, and degradation sensitivity. The results show that cavity compaction, confinement build-up, IGF strain localization, and IGF damage development evolve concurrently under the imposed weakening map. Within this controlled design space, degradation sensitivity produces the largest variation in global weakening, while segregation localization and segregation severity primarily shape the spatial concentration and pathway organization of damage. IGF damage progresses from accumulation to activation of high-damage regions and then to connected-path formation. A strong monotonic association is identified between cavity confinement and the IGF damage/connectivity response, with cavity pressurization co-varying with end-state damage intensity and path connectivity. An operational mechanism-regime map organizes safe, localization-dominant, connectivity-prone, and strongly associated localization-connectivity responses across the 27-case matrix. The results demonstrate the feasibility of the structure-resolved fixed-motif framework for isolating and comparing defect-relevant weakening mechanisms and provide quantitative comparative trends for the investigated configuration.
Gold exhibits excellent chemical stability in bulk form and unique physicochemical properties at the nanoscale, enabling broad applications in nanotechnology and biomedical fields. Although bulk gold generally adopts a face-centered cubic (FCC) structure, experimental studies have revealed the formation of hexagonal close-packed (HCP) structures in ultrathin gold nanostructures, together with unusual mechanical properties associated with phase-dependent deformation mechanisms. However, most existing Au interatomic potentials are developed for the FCC phase and cannot accurately describe the energetic competition, phase coexistence, and deformation behavior between FCC and HCP structures.In this work, an FCC/HCP-compatible embedded-atom method (EAM) potential is developed for Au by modifying the electron-density function and optimizing potential parameters against structural, energetic, and mechanical properties of both FCC and HCP phases. The developed potential provides an atomistic framework for investigating FCC/HCP phase stability, interface behavior, and deformation mechanisms in nanoscale Au systems. Molecular dynamics simulations reveal the thickness-dependent stability of FCC and HCP Au structures and demonstrate that reduced thickness promotes HCP phase stabilization through nanoscale surface effects. The FCC/HCP interfaces remain structurally stable during tensile deformation, while defect nucleation and propagation are mainly confined within individual phases. Furthermore, nanocrystalline simulations show that the developed potential captures dislocation-mediated plastic deformation and the transition of grain boundaries between dislocation sources and obstacles. This work establishes a theoretical framework for understanding phase-dependent mechanical behavior in nanoscale Au systems and provides a reliable atomistic tool for studying phase-engineered metallic nanostructures.
This work presents a theoretical framework for investigating plane wave propagation in a homogeneous, isotropic, and unbounded thermoelastic medium by incorporating the Klein–Gordon type nonlocal elasticity formulation together with some recently proposed non-Fourier heat conduction based generalized thermoelastic theories. The proposed formulation enables a unified investigation of nonlocal elastic interactions and finite-speed thermal effects on thermoelastic wave behavior. The governing equations are derived and expressed in terms of scalar and vector potentials using the Helmholtz decomposition, which leads to the identification of three fundamental wave modes: two coupled longitudinal waves exhibiting dispersion and attenuation, and one uncoupled transverse shear wave. Analytical dispersion relations are obtained and solved to determine the phase velocity, attenuation coefficient, and specific loss for each mode. The analysis is carried out in a unified framework for six advanced thermoelastic models, namely the Lord–Shulman (LS), Green–Naghdi-II (GN-II), Green–Naghdi-III (GN-III), Dual-Phase-Lag-1 (DPL-1), Hyperbolic Dual-Phase-Lag (HDPL), and Moore–Gibson–Thompson (MGT) models. The results demonstrate that the Klein–Gordon nonlocal elasticity parameter and angular frequency significantly modify the dispersion, attenuation, and energy dissipation characteristics of thermoelastic waves. A comparative analysis among the considered models reveals notable differences in wave propagation behavior arising from different non-Fourier heat conduction mechanisms. The present study provides deeper insight into the combined influence of nonlocal elasticity and generalized thermoelastic heat conduction on wave propagation in the contexts of some advanced thermoelastic models.
Compared with isotropic elastic materials, the magneto-electro-mechanical multi-field coupling effect in multiferroic composites renders their microscale adhesion behavior far more complex. Existing works only focus on the dry adhesive contact behaviors of multiferroic composites, where the adhesion effect arises from van der Waals interaction. However, capillary force induced by liquid bridge replaces the van der Waals force and dominate the mechanical behaviors of adhesion system as contact occurs in a humid environment. In this paper, the axisymmetric frictionless capillary adhesive contact problem between a rigid spherical indenter with different electro-magnetic properties and a multiferroic composite half-space is investigated, where the capillary adhesion is governed by the Laplace pressure generated by the liquid bridge. The coupling effect between capillary force and magneto-electro-elastic deformation is taken into account. The stated problem is reduced to dual integral equations by virtue of Hankel integral transform, which are then solved analytically. The analytical solutions of the physical quantities within the contact region and the relationships among the indentation load, indentation depth and contact radius are obtained. Combined with the thermodynamics equilibrium of capillary condensation, two competitive factors closely relevant to the relative humidity are found to affect the capillary force. The effects of the relative humidity (RH), the volume of liquid bridge, the electro-magnetic loadings and electro-magnetic properties of the spherical indenter on capillary adhesion behaviors are discussed in details. It is found that the capillary force increases with increasing the volume of liquid bridge or decreasing the magnitude of the RH. Exerting the electro-magnetic loadings can enhance the capillary adhesion effect between the spherical indenter and the multiferroic composite half-space. The results obtained from this work are helpful to understand the capillary adhesive contact behaviors of multiferroic composites.
This study presents a vibrational physics-guided neural network (VPGNN) framework for the dynamic characterization of 3D-printed soft auxetic metastructures. The central contribution is a physics-guided self-supervised framework that integrates structural and experimental metadata with analytical impulse-response modeling for estimating the natural frequency and damping ratio. Instead of relying on explicit differential equations, the network incorporates an analytical impulse response function derived from a simplified model into the loss formulation, guiding training toward physically consistent outcomes. The proposed framework identifies the dynamic properties by reconstructing measured impulse responses using the estimated parameters, without requiring labeled modal properties. To improve the stability of self-supervised identification under different structural and experimental conditions, the model also integrates physical metadata such as unit cell length, re-entrant angle, strut thickness, sampling frequency, and signal duration. These metadata are combined with features extracted from the impulse response to enable the network to associate temporal patterns with relevant physical and experimental parameters. This hybrid strategy effectively bridges experimental measurements and physical modeling, enabling accurate estimation of equivalent dynamic properties of deformation-sensitive soft auxetic metastructures from impulse responses under the present experimental conditions. The proposed framework was evaluated under noisy conditions against a purely data-driven baseline and conventional identification methods, including analytical, time-domain, and time-frequency approaches. The results demonstrate that VPGNN provides a robust and interpretable approach to vibration-based analysis of architected soft materials. The proposed framework serves as a complementary tool to conventional analytical and simulation methods that often struggle with the complexity and variability inherent in soft mechanical systems.
The failure mechanism and energy absorption characteristics of plain-woven carbon fiber-reinforced silicon carbide (C/SiC) composites were investigated under high-speed impact. A testing method that subjects C/SiC composite specimens to high-speed impacts using flat-nose square bullets was proposed. A mesoscopic model of C/SiC was developed for a numerical simulation. The results of the numerical simulations were integrated with microcharacteristics of fracture surfaces to analyze the effect of interlayer voids on the failure behavior of the specimens. The identified failure modes and mechanisms were used to decompose the total absorbed energy into compression- and shear-related components. Corresponding models were established to calculate energy absorption rates under shear and compression conditions. Further, a homogeneous C/SiC model was developed and penetration simulations were conducted. The results were compared and analyzed in relation to total absorbed energy. The results indicate that preexisting internal voids influenced crack evolution: cracks tended to initiate at the void edges, which locally inhibited further crack propagation, and some propagating cracks coalesced with neighboring voids. The failure modes can be categorized into compressive, shear, and tensile-shear coupled failures. Further, with increasing impact velocity (200 to 500 m s−1), the energy absorption rate associated with the compression-dominated region increased from 0.291 to 1.499 J/mm3, while that associated with the shear-dominated region increased from 0.563 to 1.792 J/mm3. When the impact velocity ranges between 300 and 500 m s−1, the proposed model demonstrated high predictive accuracy for the total energy absorption of homogeneous C/SiC materials with a deviation of less than 8.2%.
