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One of the intriguing features exhibited by the layered MAX phase compounds, is the nonlinear elastic behaviour. Since the experimental observation of this curious behaviour, the underlying micro-mechanism has been discussed to interpret experimental observations. However, the theoretical investigation remained a challenge due to the associated length and time scales of the phenomena. In the present work, we adopt a data driven approach to develop a machine learned interatomic potential for the MAX compound Ti _2 AlC following the moment tensor potential protocol. The constructed potential is validated in lattice constant, formation energy, elastic constant, and stacking fault energies. Finally, applying machine learned potential in classical molecular dynamics provides a faithful representation of the experimentally observed nonlinear elasticity for Ti _2 AlC. The generated atomic configurations confirm the proposal of formation of ripplocations which allow atomic layers to glide relative to each other without breaking the in-plane bonds. We find common defects, like Al vacancy, strongly influence the hysteresis properties of the stress–strain curve, paving the route to defect-engineered nonlinear elasticity.

The finite element method is widely used for studying the intervertebral disc at the organ level due to its ability to model complex geometries. An indispensable requirement for proper modelling of the intervertebral disc is a reliable porohyperelastic framework that captures the elaborate underlying mechanics. The increased complexity of such models requires significant computational power that is available within high-performance computing systems. The objective of this study is to present such a framework, validated both against literature and experiments, aiming to enable intervertebral disc research to benefit from state-of-the-art computational resources. In the context of this work, we implement a biphasic model that captures the mechanical response of the intricate, tissue-dependent models of the solid phase along with the hydrostatic pressure effects of the fluid phase. The tissue-dependent models involve the hyperelastic ground substance, fibrillar reinforcement, and osmotic swelling. The derived porohyperelastic, staggered scheme is implemented in Alya, a finite element code targeted at high-performance computing applications. The formulation is subsequently verified and validated by comparing the results of consolidation simulations with literature data for simulations and experiments using either generic or patient-specific geometries. Additionally, in-house experiments are replicated, evaluating the model's ability to simulate alternating loading. Finally, the implementation's circadian response is compared to previous implementation of similar material models in commercial software. Results align well with experimental and literature findings in terms of disc height reduction (4% error), intradiscal pressure (14% error) and disc bulging. Validating the patient-specific geometry results in 4% and 7% deviation in measuring height loss. Simulations show excellent agreement with in-house experimental results, with less than 1% error regarding height reduction. Finally, the comparison to similar, published, earlier implementation in commercial software unveils excellent agreement of less than 1% error for the water content during circadian simulations. Simulation times are reported at 4 min per circadian cycle in the supercomputer Marenostrum V. This work presents a clear and validated formulation for simulating porohyperelastic materials based on assumptions that comply with the non-linear elasticity theory. The implementation in Alya enables intervertebral disc research to benefit from high-performance computing systems. • Multiphysics intervertebral disc model for high-performance computing frameworks. • Staggered coupling scheme to resolve porohyperelasticity. • Extensive validation against literature findings and in-house experiments. • Comparison to results of existing simulation packages. [ABSTRACT FROM AUTHOR]

We analytically study finite torsional and extensional deformations of rubberlike material circular cylinders with the two material moduli in the Mooney–Rivlin relation assumed to be continuous functions of the undeformed radius. It is shown that under null resultant axial load on the end faces the cylinder length increases upon twisting. Furthermore, when the two moduli are affine functions of the radius the inhomogeneity parameters can be found to have the maximum shear stress occur at a pre-determined interior point. Whereas the radial stress is finite at the center of a cross-section of a homogeneous material cylinder, it may have large values for an inhomogeneous material cylinder. The closed-form solutions provided herein for the two moduli having affine, power-law and exponential functions of the radius should benefit numerical analysts verify their algorithms and engineers design soft material robots for improving their performance under torsional loads. [ABSTRACT FROM AUTHOR]

Universal displacements are those displacements that can be maintained for any member of a specific class of linear elastic materials in the absence of body forces, solely by applying boundary tractions. For linear hyperelastic (Green elastic) solids, it is known that the space of universal displacements explicitly depends on the symmetry group of the material, and moreover, the larger the symmetry group the larger the set of universal displacements. Linear Cauchy elastic solids, which include linear hyperelastic solids as a special case, do not necessarily have an underlying energy function. Consequently, their elastic constants do not possess the major symmetries. In this paper, we characterize the universal displacements of anisotropic linear Cauchy elasticity. We prove the result that for each symmetry class, the set of universal displacements of linear Cauchy elasticity is identical to that of linear hyperelasticity. [ABSTRACT FROM AUTHOR]

Since the initial observation of carbon nanotubes (CNTs) and graphene platelets (GPLs) in the 1990 and 2000s, the demand for high-performance structural applications and multifunctional materials has driven significant interest in composite structures reinforced with GPLs and CNTs. Incorporating these nanofillers into matrix materials markedly enhances the mechanical properties of the structures. To further improve efficiency and functionality, functionally graded (FG) distributions of CNTs and GPLs have been proposed. This study presents an extensive review of computational approaches developed to predict the global behavior of composite structural components enhanced with CNT and GPL nanofillers. The analysis focuses on key structural elements, such as plate-type configurations, cylindrical and curved shells, and beams, emphasizing the computational techniques utilized to simulate their mechanical behavior. The utilization of three-dimensional elasticity theories and equivalent single-layer (ESL) frameworks, which are widely employed in the modeling and analysis of these composites, is comprehensively discussed. Additionally, the paper examines various mechanical performance aspects, including static, buckling, post-buckling, vibrational, and dynamic responses for the mentioned structures. The unique features of hybrid nanocomposites, combining CNTs and GPLs, are also analyzed. Furthermore, the study delves into the fabrication and processing techniques of these materials, with a particular focus on strategies to mitigate nanofiller agglomeration. The review extends to cover thermal and electrical properties, durability under environmental exposure, fatigue resistance, and vibration-damping characteristics. In conclusion, the paper underscores the necessity for ongoing advancements in computational modeling to facilitate improved design, analysis, and optimization of nanocomposite structures. Future research opportunities in this rapidly advancing domain are also outlined. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose and analyze a stabilization-free virtual element method for the non-selfadjoint convection–diffusion eigenvalue problem. The method is based on high order harmonic polynomial projections which are used to approximate the continuous sesquilinear forms. In order to analyze the continuous and discrete eigenvalue problems, we introduce solution operators and we prove convergence in norm. Then, by using the approximation spectral theory for compact non-selfadjoint operators, we show that the scheme provides a correct approximation of the spectrum and prove optimal error estimates for the eigenfunctions and a double order for the eigenvalues. The theoretical analysis considers only the case of quadrilateral meshes. Our study is supported by a series of numerical experiments, that assess the robustness of the method. [ABSTRACT FROM AUTHOR]

In maximally Ca2+-activated demembranated fibres from the mammalian skeletal muscle, the depression of the force by lowering the temperature below the physiological level (~35 °C) is explained by the reduction of force in the myosin motor. Instead, cooling is reported to not affect the force per motor in Ca2+-activated cardiac trabeculae from the rat ventricle. Here, the mechanism of the cardiac performance depression by cooling is reinvestigated with fast sarcomere-level mechanics. We determine the changes in the half-sarcomere compliance of maximally Ca2+-activated demembranated rat trabeculae in the range of temperatures of 10–30 °C and analyse the data in terms of a simplified mechanical model of the half-sarcomere to extract the contribution of myofilaments and myosin motors. We find that the changes in the ensemble force are due to changes in the force per motor, while the fraction of actin-attached motors remains constant independent of temperature. The results demonstrate that in the cardiac myosin, as in the skeletal muscle myosin, the force-generating transition is endothermic. The underlying large heat absorption indicates the interaction of extended hydrophobic surfaces within the myosin motor, like those suggested by the crystallographic model of the working stroke. [ABSTRACT FROM AUTHOR]

To predict the mid-span deflection and crack width of reinforced ultra-high-performance concrete (R-UHPC) shallow T-shaped beams, a simplified analysis model comprising a bilinear curve with several characterization points is proposed in this paper. The proposed model is distinguished from existing deflection and crack width prediction methods by its consideration of several significant factors, including the tensile stiffening effect, tension contribution of UHPC post-cracking, nonconstant bond behavior of the interface, and shrinkage and creep effect. To obtain closed-form solutions, the proposed simplified analysis model directly incorporates the bond properties from bond tests, thereby eliminating the reliance on constant bond stress simplification and the subsequent necessity for member calibration, which is commonly required in existing design codes for UHPC-based structures. To validate the proposed model, six reinforced UHPC shallow T-shaped specimens with dimensions of 3.7 m × 0.7 m × 0.22 m, varying reinforcement ratios and fiber types within UHPC, are utilized and tested statically under four-point bending conditions. The experimental values obtained from these tests are then compared with the theoretical calculations derived from the simplified analysis model. The ratios of mid-span deflections and crack widths at reinforcement yielding, calculated using the simplified analysis model, to the counterparts from experimental values are found to be within a range of 0.9 and 0.95, respectively. The average percentage of differences between experimental and predicted values for the deflections and crack widths at reinforcement yielding are 4.2% and 5.8%, respectively. These findings demonstrate that the simplified analysis model proposed is accessible and accurate for predicting the deflection and crack width of reinforced UHPC shallow T-shaped beams, which has the potential to be a valuable reference for the design and calculation of such beams. [ABSTRACT FROM AUTHOR]

We investigate the data-driven holographic transport models without translation symmetry, focusing on the real part of frequency-dependent shear viscosity, η re (ω) . We develop a radial flow equation of the shear response and establish its relation to η re (ω) for a wide class of holographic models. This allows us to determine η re (ω) of a strongly coupled field theory by the black hole metric and the graviton mass. The latter serves as the bulk dual to the translation symmetry breaking on the boundary. We convert the flow equation to a Neural Ordinary Differential Equation (Neural ODE), which is a neural network with continuous depth and produces output through a black-box ODE solver. Testing the Neural ODE on three well-known holographic models without translation symmetry, we demonstrate its ability to accurately learn either the metric or mass when given the other. By specifying the metric to be asymptotically AdS, we also train the Neural ODE to learn the metric and mass simultaneously. Furthermore, we apply the Neural ODE to the experimental data from a two-dimensional liquid strongly coupled dusty plasma. Interestingly, the emergent metric exhibits non-monotonic behavior, and the mass squared is negative. [ABSTRACT FROM AUTHOR]

The solution of the non-linear Föppl–von Kármán equations for square plates in the form of expansion over a system of eigenfunctions, generated by a linear self-adjoint operator, is obtained. The coefficients of the expansion are determined via the reduction method from the infinite-dimensional system of cubic equations. This allows the proposed solution to be considered as a non-linear generalization of the classical Galerkin approach. The novelty of the study is in the strict formulation of the auxiliary boundary problem, which makes it possible to take into account a rigid fixation against any displacements along the boundary. To verify the proposed solution, it is compared with experimental data. The latter is obtained by the holographic interferometry of small deflection increments superimposed on the large deflection caused by initial pressure. Experiment and theory show a good agreement. [ABSTRACT FROM AUTHOR]

Changes in pore pressure within geological reservoirs, due to, for example hydrocarbon production, CO2 and energy storage or wastewater disposal, may cause substantial stress changes in the overburden, altering propagation velocities of elastic waves. The corresponding time-shifts are detected and quantified using time-lapse (4-D) seismic analysis. To invert seismic time-shifts for changes in stress and strains, stress sensitivity of rocks is studied in laboratory experiments on core plugs. Such measurements are typically conducted at ultrasonic frequencies. However, previous studies indicate that the stress sensitivity of velocities at seismic frequencies could be higher than that at ultrasonic frequencies. Therefore, calibration based on laboratory ultrasonic data may lead to inaccurate prediction of stresses and strains when applied to 4-D seismic data. To study the influence of frequency on stress sensitivity of acoustic wave velocities, a series of laboratory experiments was performed on two overburden shales with different petrophysical properties. In a low-frequency apparatus—a triaxial pressure cell that combines measurements at low (seismic) and high (ultrasonic) frequencies—the shale samples underwent stress changes with different ratios of horizontal to vertical stress amplitudes to mimic stress variations across the overburden. High-frequency velocity changes were directly recorded, while low-frequency velocity changes were obtained indirectly from the elastic parameters measured at seismic frequency by applying a rock physics inversion using third-order elasticity model. The experiments were conducted at undrained conditions, a representative state for reservoir overburden composed of shales. The results suggest that the stress sensitivities and strain sensitivities (R-factor) of P -wave velocities could be two to four times greater at seismic frequencies than at ultrasonic frequencies. Furthermore, it was found that the previously reported linear relation between the stress sensitivity and stress-path parameter (horizontal/vertical stress change) at ultrasonic frequencies also holds for seismic frequencies. We discuss the theoretical background for frequency-dependent stress sensitivity of wave velocities that supports the experimental findings. The effect of frequency when using laboratory-based calibrations should be taken into account when inverting time-lapse seismic data for changes in stresses and strains. [ABSTRACT FROM AUTHOR]

Terahertz (THz) waves reside in the electromagnetic spectrum between the microwave and infrared bands. In recent decades, THz technology has demonstrated its potential for biomedical applications. With the highly unique characteristics of THz waves, such as the high sensitivity to water and optimal spatial resolution coupled with the characteristics of the human cornea, such as its high water content, THz technology has been explored as a potential modality to assess corneas and corneal diseases. This systematic review provides an overview of the characteristics of THz waves, the safety profile of THz technology in the field of ophthalmology, and its clinical applications, including the objective evaluation of the corneal hydration, tear film, dry eye disease, corneal endothelium, corneal elasticity, and scarring. The paper also presents our viewpoint on the present challenges and future directions of THz technology prior to its broader integration into clinical practice. [ABSTRACT FROM AUTHOR]

This study explores in situ small-strain shear modulus in low-density structured chalk, a key input parameter in empirical and numerical models. A range of in situ testing procedures, supported by detailed core logging, have highlighted the difficulties and opportunities in characterizing the in situ shear modulus of the stiff fractured chalk mass. Over 1,000 seismic traces obtained from tightly controlled PS logging, borehole geophysical, and seismic cone penetration testing were assessed for data quality. Interpretation using the automated cross-correlation technique demonstrated robustness while more time consuming and subjective approaches were essential for lower-quality data. Where comparable measurements were taken, the results tended to be relatively consistent between measurement techniques. The spacing and nature of fractures in the mass were shown to influence the results. The in situ shear modulus from seismic and pressuremeter tests tended to increase steadily from relatively low values at ground level. Sharp increases were seen at the water table, where the fractures became partly closed and water-filled, with a weak tendency to increase with depth or burial stress thereafter. While laboratory shear modulus significantly exceeded the in situ values in the shallower layers, the results are shown to converge with depth as the fracture frequency reduces. The new in situ shear modulus profile offers important insights and input parameters for chalk structure interaction models. Based on the results, guidance is offered for obtaining high-quality measurements in structured chalk masses for engineering applications. [ABSTRACT FROM AUTHOR]

The finite-element method (FEM) is a well-established procedure for computing approximate solutions to deterministic engineering problems described by partial differential equations. FEM produces discrete approximations of the solution with a discretisation error that can be quantified with a posteriori error estimates. The practical relevance of error estimates for biomechanics problems, especially for soft tissue where the response is governed by large strains, is rarely addressed. In this contribution, we propose an implementation of a posteriori error estimates targeting a user-defined quantity of interest, using the dual-weighted residual (DWR) technique tailored to biomechanics. The proposed method considers a general setting that encompasses three-dimensional geometries and model nonlinearities, which appear in hyperelastic soft tissues. We take advantage of the automatic differentiation capabilities embedded in modern finite-element software, which allows the error estimates to be computed generically for a large class of models and constitutive laws. First, we validate our methodology using experimental measurements from silicone samples and then illustrate its applicability for patient-specific computations of pressure ulcers on a human heel., (© 2025 John Wiley & Sons Ltd.)