Elastic Domain Research Articles

Elastic and inelastic scattering of flat-top solitons

We investigate the interaction between two flat-top solitons within the cubic-quintic nonlinear Schrödinger equation framework. Our study results point towards a significant departure of flat-top solitons' collisional characteristics from the conventional behaviors exhibited in the scattering dynamics of two bright solitons. Our investigation outlines specific regimes corresponding to the dual flat-top solitons' elastic and inelastic collisions. We determine regimes in the parameter space where exchange in the widths of the interacting flat-top solitons is possible, even within the elastic collision domain. We find a periodic occurrence of completely elastic scattering of flat-top solitons in terms of the solitons' parameters. Investigating the internal energy transfers between the solitons and the emitted radiation reveals the origin of inelasticity in flat-top soliton collisions. We perform a variational calculation that accounts for the amount of radiation produced by the collision and hence provides further insight into the physics underlying the loss of elasticity of collisions. Published by the American Physical Society 2024

Frequency-domain axisymmetric and thermomechanical viscoelastic analysis of thermoplastic composite pipe

ABSTRACT Thermoplastic composite pipe (TCP), composed of polymers and composite laminates, shows significant potential for deep-water offshore oil field development due to its lightweight and high strength. However, current mechanical studies primarily focus on the elastic domain, ignoring the critical viscoelasticity of non-metallic materials. To solve this, we introduce a comprehensive theoretical model that incorporates viscoelastic properties under both axisymmetric and thermal loads, considering radial convective thermal gradients and axial heat conduction. This model accurately predicts TCP's mechanical behavior by using stiffness coefficients, differential geometry, and radial-axial temperature transfer curves. By applying the principle of elastic-viscoelastic correspondence, we obtain viscoelastic solutions in the frequency domain, showing strong agreement with Finite Element (FE) models particularly under cyclic loading. Viscoelasticity introduces larger equivalent axial stiffness and viscoelastic damping within complex structures, which become more obvious with temperature fluctuations.

Correction to: Solution to boundary value problems on linear elastic confocal elliptic domain based on collocation technique

Correction to: Solution to boundary value problems on linear elastic confocal elliptic domain based on collocation technique

Early detection of structural damage in UHPFRC structures through the combination of acoustic emission and ultrasonic stress wave monitoring

Ultra-High-Performance Fiber-Reinforced Cementitious Composite (UHPFRC) offers several advantages compared to concrete, notably due to the strain hardening behavior under tensile actions. Structures made of this composite material are lightweight and highly durable, thanks to the UHPFRC waterproofing quality. Nonetheless, the tensile behavior leads to a different cracking pattern than conventional concrete that is not fully understood yet. This paper presents an innovative monitoring approach that combines passive acoustic emission and active ultrasonic stress wave to localize and quantify damage on a full-scale UHPFRC beam during the loading protocol. This monitoring technique involves 24 transducers that are embedded throughout a UHPFRC t-shape beam of 4.2 meters. Continuous monitoring using this unique passive and active approach enables accurate location events, such as micro-cracking within the beam. Moreover, this sensor network is able to determine the location of the macro-crack that is linked to the structural collapse just after the end of the elastic domain. This novel sensor network opens new possibilities to monitor the structural behavior and detect damage on UHPFRC structures before they affect the structural behavior in terms of deflection and strain.

Topology Design of Compliant Mechanism Design With Multiple Component Modeling Connected by Various Joints

Abstract This study presents a novel framework for the optimal design of compliant mechanisms, specifically addressing the structural drawbacks of conventional single-point or de facto hinges. The hinges often lead to structural instability and stress concentration while deriving maximum motion. To overcome these issues, we introduce a new method that can design stable and elastic domains connected by either revolute or prismatic joints. The new method, called sequential analysis based on the reaction force, can successfully eliminate weak hinge points while optimizing joint locations. The efficiency of developed methodology is validated through several numerical examples, yielding compliant mechanisms with suppressed hinges.

Anisotropic Breakage Mechanics for cemented granular materials

The anisotropy of granular geomaterials is sensitive to their fabric, which exhibits anisotropic mechanical properties as a function of deposition history, microscopic fabric, and loading paths. Here, a new fabric-enriched continuum breakage model is proposed to examine the relation between elastic and inelastic anisotropy in granular materials and cemented granular materials. A microstructure model is first implemented in the framework of fabric-enriched continuum breakage mechanics (F-CBM), where the anisotropic behaviour prior to yielding is introduced through a symmetric second-order fabric tensor embedded in the expression of the elastic energy potential. The anisotropic strain energy storage prior to grain crushing leads to the rotation and distortion of the yield surface of cemented granular materials. Parametric analyses are performed to assess the overall capability of the model to characterize the anisotropic inelastic processes in cemented granular. It is shown that the proposed model can accurately predict the strong correlation between anisotropic elasticity and breakage-damage processes in cemented granular materials. When damage involving the skeleton is the dominant inelastic process, the size of the elastic domain contracts and the material exhibits augmented brittleness with the disintegration of cement. While breakage processes are predicted to dominate the response of lightly cemented granular materials resulting in hardening behaviour. This work can be further extended to dynamically capture the anisotropic response of cemented granular materials with water-sensitive mineral constituents by accounting for the evolution of microstructural anisotropy.

Correlations Between XRD Peak Broadening and Elastic and Plastic Deformation for Mild Steel Sheets Under Tensile Loading

The polycrystalline nature of steel sheets plays a fundamental role in their plastic behavior during forming, especially under complex stresses, such as the deep drawing process. Heterogeneous microstructures cause variable internal stress levels, which strongly impact the material’s macroscopic mechanical properties. X-ray diffraction (XRD) technique can be applied to determine microscopic internal stresses by peaks broadening analysis, which can be related to the degree of cold work at the microscopic level. As deep drawing is a complex deformation mode, an important motivating factor to perform such a study is to find the correlation between anisotropy and XRD peak broadening through tensile deformation tests. Therefore, the initial mechanical state and different deformed states were analysed by in-situ XRD peak broadening under tensile tests in various directions in the rolling plane of mild steel sheet, for both the elastic and plastic deformation domains. The results showed that the XRD peak broadening gives accurate estimations of deformation degrees. In the elastic domain, under realistic assumptions, a relation between the relative variation of peak broadening and the applied stress σ, like Hooke’s law, was obtained by exploiting the linearity between the peak broadening and the elongation measured by the strain gauge. This formula may be used to deduce The Young’s modulus. Interesting empirical relations between peak broadenings, macro deformations and hardness have been also established for the studied sheet in the plastic deformation region. Moreover, XRD peak broadenings were able to characterize the anisotropy of deformation in the rolling plane of the sheet. They are like the anisotropy coefficients in indicating the expected behavior under complex processes such as deep drawing by using ordinary tensile tests.

On the energy decomposition in variational phase-field models for brittle fracture under multi-axial stress states

Phase-field models of brittle fracture are typically endowed with a decomposition of the elastic strain energy density in order to realistically describe fracture under multi-axial stress states. In this contribution, we identify the essential requirements for this decomposition to correctly describe both nucleation and propagation of cracks. Discussing the evolution of the elastic domains in the strain and stress spaces as damage evolves, we highlight the links between the nucleation and propagation conditions and the modulation of the elastic energy with the phase-field variable. In light of the identified requirements, we review some of the existing energy decompositions, showcasing their merits and limitations, and conclude that none of them is able to fulfil all requirements. As a partial remedy to this outcome, we propose a new energy decomposition, denoted as star-convex model, which involves a minimal modification of the volumetric-deviatoric decomposition. Predictions of the star-convex model are compared with those of the existing models with different numerical tests encompassing both nucleation and propagation.

Effect of sound-induced vibrations of the pinna on head-related transfer functions: Experimental and numerical investigations.

Numerical simulations of head-related transfer functions (HRTFs) conventionally assume a rigid boundary condition for the pinna. The human pinna, however, is an elastic deformable body that can vibrate due to incident acoustic waves. This work investigates how sound-induced vibrations of the pinna can affect simulated HRTF magnitudes. The work will motivate the research question by measuring the sound-induced vibrational patterns of an artificial pinna with a high-speed holographic interferometric system. Then, finite element simulations are used to determine HRTFs for a tabletop model of the B&K 5128 head and torso simulator for a number of directions. Two scenarios are explored: one where the pinna is modeled as perfectly rigid, and another where the pinna is modeled as linear elastic with material properties close to that of auricular cartilage. The findings suggest that pinna vibrations have negligible effects on HRTF magnitudes up to 5 kHz. The same conclusion, albeit with less certainty, is drawn for higher frequencies. Finally, the importance of the elastic domain's material properties is emphasized and possible implications for validation studies on dummy heads 1as well as the limitations of the present work are discussed in detail.

High mechanical strength, strong adhesion, self-healing and conductive ionic hydrogels for motion detection

The development of conductive hydrogels with outstanding mechanical properties, robust adhesion, and high sensitivity is still a major challenge. This study successfully addresses this issue by a multi-functional ionic conductive hydrogel based on a highly entangled double network (DN) structure with excellent mechanical properties, strong adhesion, high sensitivity and self-healing ability. Polyacrylic acid (PAAc)/chitosan (CS) constructed the Double Network with physical entanglement as the main effective crosslinking. The sliding entanglement points made the hydrogel show a more uniform directional network structure during stretching, and the energy dissipation was greatly reduced. Active chemically reactive polydopamine (PDA), CS, and PAAc are complexed with aluminum ions (Al3+) respectively (building appropriate chemical crosslinking networks), and Al3+ acts as a “bridge” to build a hierarchical porous networks through multiple reversible coordination bond mediated interactions, alternating rigid and elastic domains, thereby improving the comprehensive performance of hydrogels. The tensile strength of PAAc/PDA/CS (ADC) was 173.4 kPa and the elongation at break was 921.9%, both of which were improved simultaneously. Moreover, ADC composite hydrogels exhibit excellent self-healing and adhesion properties, which can be attributed to the rich reversible/irreversible interactions brought about by PDA, with an impressive adhesion strength of 85.2 kPa on pig skin, further enhancing its practicality. Additionally, the ionic hydrogel demonstrates high strain sensitivity to tension, making it an ideal material for stable sensor signal output. The sensitivity coefficient (GF) reaches an impressive 11.24, highlighting the importance of this hydrogel in ensuring consistent and precise data collection. This innovative approach expands the idea and provides data support for the molecular structure design of high-performance wearable hydrogel sensors.

Melt flow characterization of highly loaded cooper filled poly(acrylonitrile-co-butadiene-co-styrene)

The knowledge of the rheological behavior of hybrid polymer melts is essential to develop fused deposition modeling (FDM) filaments to print metal and ceramic goods. In this contribution, we performed an in-depth analysis of the morphology and the rheological behavior in the linear elastic domain of poly(acrylonitrile-co-butadiene-co-styrene) (ABS) highly filled with copper microparticles functionalized by bioinspired polydopamine, containing polyethylene waxes (PEW) as lubricant agent. The composite systems have potential applicability in manufacturing FDM filaments for the 3D printing of metallic parts. Small amplitude oscillatory shear (SAOS) tests, scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy (FTIR) demonstrate complex relationships among polydopamine coating, filler content, morphology, and rheological properties of the ABS/PEW/Cu system. Furthermore, PEW affects the interface adhesion and shear transmission between the ABS copolymer and the copper filler coated with polydopamine. Also, the polydopamine influences the rheological parameters of the polymer composites, namely retardation and relaxation times, melt flow, and cohesive energy density (Ec).

Robust contact-constrained topology optimization considering uncertainty at the contact support

In this paper, the general framework for contact-constrained topology optimization of Strömberg and Klarbring (2010) is extended to robust topology optimization. In doing so, a linear elastic design domain is considered and the augmented Lagrangian approach is used to model the unilateral contact. For topology optimization, the design space is parametrized with the SIMP-approach and the Sigmund’s filter is applied. Additionally, the robust framework considers uncertainties at the contact support such as deviations of the geometry of the contact surface and the friction coefficient. Both uncertainties are described by the first-order second-moment method which leads to minimal additional costs. In fact, only two additional linear equations must be solved to obtain the robust objective and its gradient with respect to the design variables. Having both the objective and the gradient, the design update is computed with the method of moving asymptotes. The robust framework is applied to 2D and 3D examples to prove its scalability for real-world applications.

Acid-assisted subcritical blunt-tip crack propagation in carbonate rocks

AbstractSubcritical crack propagation in stressed carbonate rocks in a chemically reactive environment is a fundamental mechanism underlying many geomechanical processes frequently encountered in the engineering of geo-energy, including unconventional shale gas, geothermal energy, carbon sequestration and utilization. How a macroscopic Mode I crack propagates driven by a reactive fluid pressurizing on the crack surfaces with acidic agents diffusing into the rock matrix remains an open question. Here, the carbonate rock is modeled as an elasto-viscoplastic material with the mineral mass removal process affecting the rock properties in both elastic and plastic domains. A blunt-tip crack is considered to avoid any geometrically induced singularity problem and to allow a numerical analysis on the evolution of the chemical field being linked to the micro-cracking activities in front of the crack tip, affecting the delivery of acid. The model is capable of reproducing an archetypal three-region behavior of subcritical crack growth in a reactive environment. The crack propagation exhibits a prominent acceleration in Region III due to a two-way mutually enhancing feedback between mineral dissolution and the degradation process, which is most pronounced in front of the crack tip. With the consideration of initial imperfections in the rock, the macroscopic crack propagation is further accelerated with a secondary acceleration arising due to self-organization of micro-bands inside the chemically enabled plasticity zone.

Influence of fiber orientation on the high cycle tensile fatigue resistance of ultra-high performance fiber reinforced cementitious composites (UHPFRC)

This paper quantitatively studies the influence of fiber orientation on the high cycle tensile fatigue resistance of ultra-high performance fiber reinforced cementitious composites (UHPFRC) within and beyond elastic domain. Eight tensile fatigue tests and re-analysis of sixteen fatigue tests from a previous study are conducted, which have specimens statically preloaded to the strain from 0.19‰ to 0.5‰ and from 1.1‰ to 2‰, considered to be in the elastic and post-elastic domains in tension, respectively. For the eight fatigue tests, the local fiber orientation and dosage of each specimen are determined before testing using a magnetic probe. During testing, specimen behavior is characterized by displacement transducers, digital image correlation and acoustic emission. Based on the above, the fatigue endurance limit at 10 million cycles is determined to be about SUte,10%= 0.9 of the elastic limit tensile stress for UHPFRC within elastic domain. For UHPFRC preloaded beyond the elastic domain, the fatigue resistance decreases with increasing pre-applied strain and decreasing average fiber orientation (increasing average angle between fibers and principle tensile direction). With pre-applied strain from 1.1‰ to 2.0‰, the endurance limit may be taken as SUte,10%=0.60 to 0.65 for typical UHPFRC structures. Two original fatigue resistance models are proposed, which describe the relationship between average fiber orientation, number of cycles and maximum fatigue stress for UHPFRC within and beyond the elastic domain.

The experimental and numerical analysis of elastic rock mechanical properties in tight conglomerate rock samples: a case study in Junggar Basin

Tight conglomerate rocks consist of gravels and rock matrices. The existence of these stiff gravels leads to heterogeneity in conglomerates and makes it difficult to characterize rock mechanical properties, which then affects drilling and hydraulic fracturing operations in tight conglomerate hydrocarbon-bearing reservoirs. This case study introduces a series of experimental and numerical analyses for the better understanding of rock deformation and elastic wave propagation patterns in a tight conglomerate reservoir in Junggar Basin, China. Tri-axial compression tests, acoustic test, and finite element modeling of rock deformation and elastic wave propagation in conglomerate rocks are presented. Experimentally tested samples exhibit good brittleness and shearing failure patterns, while well correlated static-dynamic elastic moduli and P-S wave velocities are captured. Numerical results show that the existence of stiff gravels leads to strong direction-dependent stress and strain anisotropies. Stress concentrations are also induced by gravels radially and axially. In the elastic wave domain, stiff gravels facilitate the propagation of elastic waves. The gravel close to the wave source also induces stronger compressive/tensile states in the wave domain, indicating that the existence of gravels in conglomerates can alter waveforms. This integrated approach improves the quantitative understanding of stress, strain, and elastic wave responses in heterogeneous tight conglomerates. This case study also serves as a reference for the brittleness evaluation and geomechanical evaluation in the study area. The contribution of this work is primarily about the integrated experimental study, solid deformation modeling, and elastic wave modeling of tight conglomerate rocks.

Phospholipase-catalyzed degradation drives domain morphology and rheology transitions in model lung surfactant monolayers.

Lung surfactant is inactivated in acute respiratory distress syndrome (ARDS) by a mechanism that remains unclear. Phospholipase (PLA2) plays an essential role in the normal lipid recycling processes, but is present in elevated levels in ARDS, suggesting it plays a role in ARDS pathophysiology. PLA2 hydrolyzes lipids such as DPPC-the primary component of lung surfactant-into palmitic acid (PA) and lyso-PC (LPC). Because PA co-crystallizes with DPPC to form rigid, elastic domains, we hypothesize that PLA2-catalyzed degradation establishes a stiff, heterogeneous rheology in the monolayer, and suggests a potential mechanical role in disrupting lung surfactant function during ARDS. Here we study the morphological and rheological changes of DPPC monolayers as they are degraded by PLA2 using interfacial microbutton microrheometry coupled with fluorescence microscopy. While degrading, domain morphology passes through qualitatively distinct transitions: compactification, coarsening, solidification, aggregation, network percolation, network erosion, and nucleation of PLA2-rich domains. Initially, condensed domains relax to more compact shapes, and coarsen via Ostwald ripening and coalescence up until the domains solidify, marked by a distinct roughening of domain boundaries that does not relax. Domains aggregate and eventually form a percolated network, whose elements then erode and whose connections are broken as degradation continues. The relative enzymatic activity of PLA2, set by the age of the sample, impacts the order and the duration of morphology transitions. The fresher the PLA2, the faster the overall degradation, and the earlier the onset of domain solidification: domains solidify before aggregating with fresh PLA2 samples, but aggregate and percolate before solidification with aged PLA2. Irrespective of the activity of the PLA2, all measured linear viscoelastic surface shear moduli obey the same dependence on condensed phase area fraction (log|G*| ∝ ϕ) throughout monolayer degradation. Moreover, the onset of domain solidification coincides with the time when the relative surface elasticity begins to increase.

Computing leaky Lamb waves for waveguides between elastic half-spaces using spectral collocation.

In non-destructive evaluation guided wave inspections, the elastic structure to be inspected is often embedded within other elastic media and the ensuing leaky waves are complex and non-trivial to compute; we consider the canonical example of an elastic waveguide surrounded by other elastic materials that demonstrates the fundamental issues with calculating the leaky waves in such systems. Due to the complex wavenumber solutions required to represent them, leaky waves pose significant challenges to existing numerical methods, with methods that spatially discretise the field to retrieve them suffering from the exponential growth of their amplitude far into the surrounding media. We present a spectral collocation method yielding an accurate and efficient identification of these modes, leaking into elastic half-spaces. We discretise the elastic domains and, depending on the exterior bulk wavespeeds, select appropriate mappings of the discretised domain to complex paths, in which the numerical solution decays and the physics of the problem are preserved. By iterating through all possible radiation cases, the full set of dispersion and attenuation curves are successfully retrieved and validated, where possible, against the commercially available software disperse. As an independent validation, dispersion curves are obtained from finite element simulations of time-dependent waves using Fourier analysis.

An unsplit-field viscoelastic complex-frequency-shifted perfectly matched layer for analysis of transient waves in heterogeneous media based on an efficient voxel element method

Wave propagation analysis of heterogeneous unbounded media employing domain discretization methods necessitates truncation of the finite computational domain at its truncation boundaries. The Perfectly Matched Layer (PML) is a robust absorbing boundary condition, which is extensively employed to favorably absorb outgoing scattered waves from the interior computational domain, regardless of frequencies and directions of outgoing waves. Nonetheless, most available PMLs are developed for elastic domains, while their developments in domain discretization methods, which consider damping using the Rayleigh damping formulation, are insufficient. In this study, a viscoelastic PML formulation is developed that accommodates the Rayleigh-type damping. The PMLs are basically developed from a coordinate transformation concept using a complex stretching function. Suitable stretching functions can efficiently control the absorptive properties and the spectral character of the PML. Besides, the stretching functions play a crucial role in the long-time stability of transient wave simulations. The standard stretching function usually results in spurious reflections, especially when propagating waves incident to the truncation boundary at near-grazing incidence. On the other hand, the complex-frequency-shifted (CFS) stretching function has been shown to mitigate long-time instability. Therefore, the proposed viscoelastic PML in the time-domain and frequency-domain are derived using the CFS stretching function for the first time. Comprehensive formulations of the proposed viscoelastic CFS-PML are given, where the displacement field is represented as the sole unknown variable of the problem. Hence, the proposed CFS-PML can be incorporated into any domain discretization method. However, the proposed CFS-PML is further developed in the context of the voxel element method, where element-by-element iterative strategies are implemented to solve the governing equations without storing global matrices in the computer memory. Comprehensive numerical experiments are conducted to demonstrate the validity and efficiency of the proposed viscoelastic CFS-PML formulation in analyzing soil profiles with various damping ratios and properties. Moreover, long-time stability for problems involving waveguides and near-grazing wave incidence is studied, where no instabilities are detected.

High pressure-driven effects on the structural and spectroscopic attributes of Eu3+-doped amorphous silicates

The present study focuses on synthesizing and investigating the structure of Eu3+-doped sodium calcium silicate and calcium alumino silicate glasses under extreme high-pressure conditions. For a thorough understanding of glassy systems in extreme conditions, we conducted in-situ micro-luminescence experiments using a diamond anvil cell, reaching pressures up to 16 GPa. Hydrostatic pressure demonstrated a notable impact on luminescence, attributed to the nephelauxetic effect causing the contraction of central-ion-ligand distances. The band transitions of Eu3+ from the 5D0 to 7F1,2 states revealed pronounced pressure-induced splitting, highlighting the pressure influence on crystal-field properties. The energy shifts for the 5D0 → 7F1 transitions were determined to be 0.14 nmGPa−1 and 0.20 nmGPa−1 for sodium calcium silicate and calcium alumino silicate, respectively. These distinct slope differences indicated a lower structural adaptability of the former glass, resulting in reduced deformability under high-pressure conditions. Furthermore, as pressure increased, the asymmetry ratio of the 5D0 → 7F2/1 transitions decreased, though it consistently maintains levels higher than unity, reflecting the highly asymmetric environment surrounding Eu3+ ions. The estimated elastic limit for both samples was approximately 7 GPa. To assess pressure-induced changes in the local environment, Judd-Ofelt intensity parameters were employed for the calcium alumino silicate glass. The trends observed throughout compression revealed that Ω2 > Ω4 up to 6.8 GPa, while Ω2 < Ω4 for higher pressures, indicating higher covalency between Eu3+ ions and ligands in the elastic domain compared to the plastic domain. The observed increase in Si and Al coordination in the plastic domain was found to play a role in these parameters.

A damped elastodynamics system under the global injectivity condition: local wellposedness in L^p-spaces

The purpose of this paper is to model mathematically mechanical aspects of cardiac tissues. The latter constitute an elastic domain whose total volume remains constant. The time deformation of the heart tissue is modeled with the elastodynamics equations dealing with the displacement field as main unknown. These equations are coupled with a pressure whose variations characterize the heart beat. This pressure variable corresponds to a Lagrange multiplier associated with the so-called global injectivity condition. We derive the corresponding coupled system with nonhomogeneous boundary conditions where the pressure variable appears. For mathematical convenience a damping term is added, and for a given class of strain energies we prove the existence of local-in-time solutions in the context of the L^p-parabolic maximal regularity.