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We present a general formulation of a class of uniaxial phenomenological models, able to accurately simulate hysteretic phenomena in rate-independent mechanical systems and materials, which requires only one history variable and leads to the solution of a scalar equation for the evaluation of the generalized force. Two specific instances of the class, denominated Bilinear and Exponential Models, are developed as an example to illustrate the peculiar features of the formulation. The Bilinear Model, that is one of the simplest hysteretic models which can be emanated from the proposed class, is first described to clarify the physical meaning of the quantities adopted in the formulation. Specifically, the potentiality of the proposed class is witnessed by the Exponential Model, able to simulate more complex hysteretic behaviors of rate-independent mechanical systems and materials exhibiting either kinematic hardening or softening. The accuracy and the computational efficiency of this last model are assessed by carrying out nonlinear time history analyses, for a single degree of freedom mechanical system having a rate-independent kinematic hardening behavior, subjected either to a harmonic or to a random force. The relevant results are compared with those obtained by exploiting the widely used Bouc–Wen Model.

The fatigue properties of neat polyimide and the “polyimide + 10 wt.% milled carbon fibers + 10 wt.% polytetrafluoroethylene” composite were investigated under various cyclic loading conditions. In contrast to most of the reported studies, constructing of hysteresis loops was performed through the strain assessment using the non-contact 2D Digital Image Correlation method. The accumulation of cyclic damage was analyzed by calculating parameters of mechanical hysteresis loops. They were: (i) the energy losses (hysteresis loop area), (ii) the dynamic modulus (proportional to the compliance/stiffness of the material) and (iii) the damping capacity (calculated through the dissipated and total mechanical energies). On average, the reduction in energy losses reached 10–18% at the onset of fracture, whereas the modulus variation did not exceed 2.5% of the nominal value. The energy losses decreased from 20 down to 18 J/m3 (10%) for the composite, whereas they reduced from 30 down to 25 J/m3 (17%) for neat PI in the low-cycle fatigue mode. For high-cycle fatigue, energy losses decreased from 10 to 9 J/m3 (10%) and from 17 to 14 J/m3 (18%) for neat PI and composite, respectively. For this reason, the changes of the energy losses due to hysteresis are of prospects for the characterization of both neat PI and the reinforced PI-based composites.

Nematic liquid crystal elastomers (N-LCE) exhibit intriguing mechanical properties, such as reversible actuation and soft elasticity, which manifests as a wide plateau of low nearly-constant stress upon stretching. N-LCE also have a characteristically slow stress relaxation, which sometimes prevents their shape recovery. To understand how the inherent nematic order retards and arrests the equilibration, here we examine hysteretic stress-strain characteristics in a series of specifically designed main-chain N-LCE, investigating both macroscopic mechanical properties and the microscopic nematic director distribution under applied strains. The hysteretic features are attributed to the dynamics of thermodynamically unfavoured hairpins, the sharp folds on anisotropic polymer strands, the creation and transition of which are restricted by the nematic order. These findings provide a new avenue for tuning the hysteretic nature of N-LCE at both macro- and microscopic levels via different designs of polymer networks, toward materials with highly nonlinear mechanical properties and shape-memory applications. Nematic liquid crystal elastomers (N-LCE) have a slow relaxation, which can prevent their shape recovery. Here, the authors examine mechanical hysteresis in a series of main-chain N-LCE to understand how the inherent nematic order retards and arrests the equilibration.

This paper addresses the mechanical characteristics of a passive earth pressure problem taking into account water retention curve (SWRC) hysteresis. Both hydraulic (drying and wetting cycles) and mechanical hysteresis were considered. Parametric studies were carried out at various air entry values ( AEV = 5–30 kPa), different wall frictions (δ = 0, 0.33 ϕ , 0.5 ϕ , 0.67 ϕ and δ = ϕ ), and unsaturated conditions (covering the zone from the fully saturated to the transition suction, 0 - ~40 kPa) using an upper bound theorem. The numerical results were compared with a passive earth pressure equation based on the limit equilibrium method. The results indicated significant influences of SWRC hysteresis and wall frictions on the passive thrust ( P p ) for the modeled suction profiles. An increase of 1.31-fold in P p was obtained when the AEV changed from 10 to 20 kPa at the water table (H w ) = -2 m. Additionally, the combined effects of AEV and δ were found to be significant. An increase of 4.14-fold in P p at H w = -3 m was obtained when comparing the case of AEV = 30 kPa and δ = ϕ with AEV = 5 kPa and δ = 0. Based on the parametric studies, a series of design charts of the exerted passive thrust were proposed.

The results of investigations into the influence of disperse particles on the temperatures of martensitic transformations as well as values of thermal and mechanical hysteresis in the FeNiCoAlTa, CoNiGa, NiFeGa, TiNi single crystals are reported. It is shown that the disperse particles are responsible for refining martensitic crystals and changing their fine twin structure as compared with the monophase state. This, in turn, affects the values of thermal and mechanical hysteresis and the temperature range of superelasticity.

Highlights A dual-network hydrogel (PGEH) cross-linked via liquid metal induction was developed exhibiting remarkable mechanical properties and skin-temperature-triggered on-demand adhesion capabilities. The PGEH capacitive sensor demonstrates exceptional sensitivity (1.25 kPa), rapid dynamic response (30 ms), and long-term cycling stability (20,000 cycles), enabling precise monitoring of human motion and reliable signal transmission. Low-impedance electrophysiological sensor (310 ohms) maintains 14-day signal fidelity (25.2 dB), paired with machine learning-based attention monitoring (91.38% of accuracy) for real-time cognitive feedback in focus-demanding scenarios. Due to their high mechanical compliance and excellent biocompatibility, conductive hydrogels exhibit significant potential for applications in flexible electronics. However, as the demand for high sensitivity, superior mechanical properties, and strong adhesion performance continues to grow, many conventional fabrication methods remain complex and costly. Herein, we propose a simple and efficient strategy to construct an entangled network hydrogel through a liquid–metal-induced cross-linking reaction, hydrogel demonstrates outstanding properties, including exceptional stretchability (1643%), high tensile strength (366.54 kPa), toughness (350.2 kJ m −3 ), and relatively low mechanical hysteresis. The hydrogel exhibits long-term stable reusable adhesion (104 kPa), enabling conformal and stable adhesion to human skin. This capability allows it to effectively capture high-quality epidermal electrophysiological signals with high signal-to-noise ratio (25.2 dB) and low impedance (310 ohms). Furthermore, by integrating advanced machine learning algorithms, achieving an attention classification accuracy of 91.38%, which will significantly impact fields like education, healthcare, and artificial intelligence.

By assimilating shape memory alloys with mathematical multifractal-type objects, a theoretical model based on Scale Relativity Theory in the form of The Multifractal Theory of Motion, in order to explain the mechanical behavior of such material, is proposed. The model is validated by analyzing the mechanical behavior of Cu–Al–Zn shape memory alloy with various chemical compositions. More precisely, the multifractal tunnel effect can “mime” the mechanical hysteresis of such a material, a situation in which a direct correspondence for several mechanical properties of Cu–Al–Zn is highlighted (the chemical composition can be correlated with the shapes of the curves controlled through the multifractality degree, while the areas delimited by the same curves can be correlated with the multifractal specific potential, as a measure of the mechanical memory degree).

In this paper, we report on mechanical properties observed during bending experiments conducted on quinary Ni–Mn–Ga–Co–Cu melt-spun ribbons. Depending on the ribbon’s side to which force is applied, different mechanical response is noted. Substantially larger mechanical instabilities are observed when force is applied to the “free side” than to the “wheel side” of ribbons. When force is applied to the latter, much lower force fluctuations are recorded and the amplitude of the force–displacement response remains within the experimental resolution limit. It is also shown that the character of the force–displacement curve changes upon cycling; mainly by decreasing the maximum force and mechanical hysteresis. These results are important for materials design and optimization of the magnetic field-induced bending effect recently shown in Ni–Mn–Ga-based melt-spun ribbons.

The influence of carbon black (CB) structure and surface area on key rubber properties such as monotonic stress-strain, cyclic stress–strain, and dynamic mechanical behaviors are investigated in this paper. Natural rubber compounds containing eight different CBs were examined at equivalent particulate volume fractions. The CBs varied in their surface area and structure properties according to a wide experimental design space, allowing robust correlations to the experimental data sets to be extracted. Carbon black structure plays a dominant role in defining the monotonic stress–strain properties (e.g., secant moduli) of the compounds. In line with the previous literature, this is primarily due to strain amplification and occluded rubber mechanisms. For cyclic stress–strain properties, which include the Mullins effect and cyclic softening, the observed mechanical hysteresis is strongly correlated with carbon black structure, which implies that hysteretic energy dissipation at medium to large strain values is isolated in the rubber matrix and arises due to matrix overstrain effects. Under small to medium dynamic strain conditions, classical strain dependence of viscoelastic moduli is observed (the Payne effect), the magnitude of which varies dramatically and systematically depending on the colloidal properties of the CB. At low strain amplitudes, both CB structure and surface area are positively correlated to the complex moduli. Beyond ~2% strain amplitude the effect of surface area vanishes, while structure plays an increasing and eventually dominant role in defining the complex modulus. This transition in colloidal correlations reflects the transition in stiffening mechanisms from flexing of rigid percolated particle networks at low strains to strain amplification at medium to high strains. By rescaling the dynamic mechanical data sets to peak dynamic stress and peak strain energy density, the influence of CB colloidal properties on compound hysteresis under strain, stress, and strain energy density control can be estimated. This has considerable significance for materials selection in rubber product development.

Basalt/glass fiber polypropylene hybrid composites were developed as subjects of investigation, with the aim to characterize their properties. An injection molding machine was used to produce the test samples. The following three different tests, at various specimen temperatures, were conducted: tensile test, three-point flexural test, and Charpy impact test. To determine fatigue behavior, the samples were uniaxially loaded and unloaded. Mechanical hysteresis loops were recorded and the dissipation energy of each loop was calculated. To determine the adhesion and dispersion between the fibers and the matrix, the fractured surfaces of the various specimens, after the tensile test, were investigated using a scanning electron microscope. The results show that the production of a composite with both basalt and glass fibers, in a polypropylene matrix with maleic anhydride-grafted polypropylene, can be successfully achieved. The addition of the two types of fibers increased the tensile strength by 306% and the tensile modulus by 333% for a composition, with 20% by weight, of fibers. The material properties were estimated with the help of a simulation software, and validated with a FEA. A satisfactory correlation between the simulation and measurement data was achieved. The error lays in a range of 2% between the maximum stress values. At a lower strain (up to 0.02), the stress values are very well matched.