Elastic Model Research Articles

Γ-convergence of a discrete Kirchhoff rod energy

This work is motivated by the classical discrete elastic rod model by Audoly et al. We derive a discrete version of the Kirchhoff elastic energy for rods undergoing bending and torsion and prove Γ-convergence to the continuous model. This discrete energy is given by the bending and torsion energy of an interpolating conforming polynomial curve and provides a simple formula for the bending energy depending in each discrete segment only on angle and adjacent edge lengths. For the liminf-inequality, we need to introduce penalty terms to ensure arc-length parametrization in the limit. For the recovery sequence a discretization with equal Euclidean distance between consecutive points is constructed. Particular care is taken to treat the interaction between bending and torsion by employing a discrete version of the Bishop frame.

Effect of steel fibers and the fiber-concrete adhesion stress on the nonlinear shear behavior of beams

In this article, a theoretical model in nonlinear elasticity is presented to analyze the influence of the percentage of steel fibers and the effect of the fiber-concrete bond stress on the shear force at the rupture of beams subjected to the combined effect of bending moment, normal force, and shear force. For a given beam section, it is defined by a succession of layers of concrete and longitudinal steel elements. Each layer is defined by its height hi, width bi, and position relative to one end of the section YGi. Each longitudinal steel element is also defined by its cross-sectional area and position relative to one end of the section. The steel fibers are defined by volume percentages of 0.5%, 1%, 1.5%, and 2%, taking into account the mechanical nonlinearity of the materials. This model is based on the multilayer analysis of sections and an iterative solution procedure for each layer and each section, considering a given longitudinal deformation state and shear stress. The global equilibrium of the sections is analyzed under the assumption of flat longitudinal deformations but with, in principle, an interdependence of longitudinal normal stresses and shear stresses. In this study, using the principle of virtual work, equilibrium equations for deformations and stresses, as well as partial compatibility equations between concrete deformations and mean deformations, are derived. Comparative examples between ordinary reinforced concrete beams with variable shapes and reinforcement details, and those reinforced with steel fibers, are presented to demonstrate the accuracy of the proposed model for simulating the nonlinear shear response of beams.

An Analytic Element Model for Seepage Forces in Fractured Media

AbstractThere are many situations where groundwater flow has high flow rates, causing large seepage forces. Examples are flows around highly conductive fractures and tunnels. We present a new analytic element for a tunnel in an elastic medium. We combined the analytic element method for groundwater flow with that for linear elasticity, and include the seepage force as a body force in the linearly elastic model. We represent tunnels and fractures as analytic elements. The solution for the case considered is limited to steady state flow and fluid-to-solid coupling. We present examples of the computed seepage forces around a tunnel and a fracture as well as a comparison with another numerical model.

Physics‐constrained symbolic model discovery for polyconvex incompressible hyperelastic materials

AbstractWe present a machine learning framework capable of consistently inferring mathematical expressions of hyperelastic energy functionals for incompressible materials from sparse experimental data and physical laws. To achieve this goal, we propose a polyconvex neural additive model (PNAM) that enables us to express the hyperelastic model in a learnable feature space while enforcing polyconvexity. An upshot of this feature space obtained via the PNAM is that (1) it is spanned by a set of univariate basis functions that can be re‐parametrized with a more complex mathematical form, and (2) the resultant elasticity model is guaranteed to fulfill the polyconvexity, which ensures that the acoustic tensor remains elliptic for any deformation. To further improve the interpretability, we use genetic programming to convert each univariate basis into a compact mathematical expression. The resultant multi‐variable mathematical models obtained from this proposed framework are not only more interpretable but are also proven to fulfill physical laws. By controlling the compactness of the learned symbolic form, the machine learning‐generated mathematical model also requires fewer arithmetic operations than its deep neural network counterparts during deployment. This latter attribute is crucial for scaling large‐scale simulations where the constitutive responses of every integration point must be updated within each incremental time step. We compare our proposed model discovery framework against other state‐of‐the‐art alternatives to assess the robustness and efficiency of the training algorithms and examine the trade‐off between interpretability, accuracy, and precision of the learned symbolic hyperelastic models obtained from different approaches. Our numerical results suggest that our approach extrapolates well outside the training data regime due to the precise incorporation of physics‐based knowledge.

Aeroacoustic simulation of human phonation based on the flow-induced vocal fold vibrations including their contact

This paper deals with the numerical simulation of the flow induced sound as generated in the human phonation process including vocal folds (VF) contact. The hybrid approach is used allowing to separate the acoustic and the biomechanical description of the considered problem. The two-dimensional fluid–structure interaction (FSI) problem is modelled by a simplified linear elastic model coupled to the incompressible Navier–Stokes equations in the arbitrary Lagrangian–Eulerian form and special attention is paid to the treatment of the contact problem in the FSI context. Following approach of [Sváček and Horáček, 2021] the incompressible flow model is modified by an addition of fictitious porosity term and the penalization inlet boundary condition is used. Further, the Lighthill acoustic analogy is applied for calculation of sound sources and their propagation through a vocal tract model. All partial differential equations, describing the elastic body vibration, the fluid flow and the acoustics, are approximated by finite element method. Numerical results of one-sided vocal fold paralysis are presented.

Enhanced fracture risk prediction: a novel multi-trait genetic approach integrating polygenic scores of fracture-related traits.

Current polygenic scores (PGS) have limited predictive power for fracture risk. To improve genetic prediction, we developed and evaluated a novel metaPGS combining genetic information from multiple fracture-related traits. We derived individual PGS from genome-wide association studies of 16 fracture-related traits and employed an elastic-net logistic regression model to examine the association between the 16 PGSs and fractures. An optimal metaPGS was constructed by combining 11 significant individual PGSs selected by the elastic regularized regression model. We evaluated the predictive power of the metaPGS alone and in combination with clinical risk factors recommended by guidelines. The discrimination ability of metaPGS was assessed using the concordance index. Reclassification was assessed using net reclassification improvement (NRI) and integrated discrimination improvement (IDI). The metaPGS had a significant association with incident fractures (HR 1.21, 95% CI 1.18-1.25 per standard deviation of metaPGS), which was stronger than previously developed bone mineral density (BMD)-related individual PGSs. Models with PGS_FNBMD, PGS_TBBMD, and metaPGS had slightly higher but statistically non-significant c-index than the base model (0.640, 0.644, 0.644 vs. 0.638). However, the reclassification analysis showed that compared to the base model, the model with metaPGS improves the reclassification of fracture. The metaPGS is a promising approach for stratifying fracture risk in the European population, improving fracture risk prediction by combining genetic information from multiple fracture-related traits.

Impact of climate change and genetic development on Iowa corn yield

The vulnerability of corn yield to high temperature and insufficient rainfall in the US mid-west is widely acknowledged. The impact of extreme weather and genetic development on corn yield is less well known. One of the main reasons is that the multicollinearity in the variables can lead to confounding results. Here we model the impact of climate and genetic development by employing an elastic net regression model to address the multicollinearity issue. This allows us to develop a more robust multiple regression model with higher predictive accuracy. Using granular data for Iowa from 1981-2018, we find that corn yield is vulnerable to high mean summer temperatures particularly in July, a widening diurnal temperature range in June and dry summer conditions (due to extremely low rainfall) from June-August. We find that overall climate impact reduced average annual yield by 0.7%. We also find that genetic development which led to earlier planting dates, widening duration of the reproductive interval, higher growing degree day accumulation and larger net planted area had a beneficial impact on the Iowa corn yield during 1981-2018 resulting in an average annual yield improvement of 1.8% per annum. This provides a basis for optimism that these genetic developments and management practices will continue to adapt and improve in the future to counter the impact of climate change on corn yield. We have also modelled the impact of future climate change using the latest climate projections from the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR6). These climate projections show that the average temperature during the growing season (MayO-October) will increase by 2.4 -2.9 o C by mid-century while the average spring temperature (March and April) will increase by a relatively slower 1.9 -2.3 o C by mid-century. Additionally, climate projections show that both temperature and rainfall will also become more extreme in the future with the changes varying from spring to summer. Our results show that, just due to climate change alone in Iowa corn yield will decline between 1.4-1.7% per annum until mid-century (or 1.2-2.1% per annum until the late twenty first century).

Two-layer elastic models for single-yeast compressibility with flat microlevers.

Unicellular organisms such as yeast can survive in very different environments, thanks to a polysaccharide wall that reinforces their extracellular membrane. This wall is not a static structure, as it is expected to be dynamically remodeled according to growth stage, division cycle, environmental osmotic pressure and ageing. It is therefore of great interest to study the mechanics of these organisms, but they are more difficult to study than other mammalian cells, in particular because of their small size (radius of a few microns) and their lack of an adhesion machinery. Using flat cantilevers, we perform compression experiments on single yeast cells (S. cerevisiae) on poly-L-lysine-coated grooved glass plates, in the limit of small deformation using an atomic force microscope (AFM). Thanks to a careful decomposition of force-displacement curves, we extract local scaling exponents that highlight the non-stationary characteristic of the yeast behavior upon compression. Our multi-scale nonlinear analysis of the AFM force-displacement curves provides evidence for non-stationary scaling laws. We propose to model these phenomena based on a two-component elastic system, where each layer follows a different scaling law..

The joint effect of long-term exposure to multiple air pollutants on non-accidental and cause-specific mortality: A longitudinal cohort study

The long-term joint impacts of fine particulate matter (PM2.5), nitrogen dioxide (NO2), and ozone (O3) on mortality are inconclusive. To bridge this research gap, we included 283,568 adults from the Taiwan MJ cohort between 2005 and 2016 and linked with the mortality data until 31 May 2019. Participants’ annual average exposures to PM2.5, NO2, and O3 were estimated using satellite-based spatial-temporal models. We applied elastic net-regularised Cox models to construct a weighted environmental risk score (WERS) for the joint effects of three pollutants on non-accidental, cardiovascular, and cancer mortality and evaluated the contribution of each pollutant. The three pollutants jointly raised non-accidental mortality risk with a WERS hazard ratio (HR) of 1.186 (95% CI: 1.118–1.259) per standard deviation increase in each pollutant and weights of 72.8%, 15.2%, and 12.0% for PM2.5, NO2, and O3, respectively. The WERS increased cardiovascular death risk [HR: 1.248 (1.042–1.496)], with PM2.5 as the first contributor and O3 as the second. The WERS also elevated the cancer death risk [HR: 1.173 (1.083–1.270)], where PM2.5 played the dominant role and NO2 ranked second. Coordinated control of these three pollutants can optimise the health benefits of air quality improvements.

Abstract PO1-15-05: Gene expression signature as a predictor of pathological complete response to neoadjuvant docetaxel, carboplatin, trastuzumab, and pertuzumab treatment in locally advanced HER2-positive breast cancer

Abstract Background: Neoadjuvant pertuzumab and trastuzumab in combination with chemotherapy can achieve pathological complete response (pCR, defined as ypT0/is ypN0) in approximately 40–60% of patients with human epidermal growth factor receptor 2-positive (HER2+) breast cancer (BC). Patients who achieve pCR have significantly improved survival. Therefore, the prediction of pCR is crucial for optimizing neoadjuvant therapy. Methods: To identify a gene expression signature that could predict pCR in patients with HER2+ BC, we used the nCounter Breast Cancer 360TM V2 panel to quantify the expression of 758 genes in 104 HER2+ BC samples from patients who received neoadjuvant docetaxel, carboplatin, trastuzumab, and pertuzumab (TCHP) chemotherapy and subsequent curative breast surgery. Data normalization, differentially expressed gene (DEG) analysis, and gene set enrichment analysis (GSEA) were performed using the NanoTube Bioconductor package. Using the elastic net logistic regression model with optimal hyperparameters determined by 5-fold cross-validation (5-CV), we developed a chemosensitivity score based on the expression of significant DEGs (genes with absolute log2-fold-change ≥0.5 and q-value < 0.1). We tested its predictive value for pCR using multivariable logistic regression analysis. Results: The median age at diagnosis was 49.5 years. The clinical stage was II in 53 (51%) patients and III in 51 (49%) patients at diagnosis. Ninety (86.5%) patients had a HER2 immunohistochemistry (IHC) score of 3+, while the remaining 14 (13.5%) patients had HER2 IHC 2+ but HER2 amplification detected by in situ hybridization. Pathological evaluation of surgical specimens revealed that 55 (52.9%) patients achieved pCR. Menopausal status (p = 0.01), PAM50 intrinsic subtype (p = 0.002), hormone receptor (HR) status (p < 0.001), and HER2 IHC score (p = 0.019) were significantly correlated with the pCR rate. DEG analysis using the PAM50 intrinsic subtype, HR status, and HER2 IHC score as covariates revealed 6 downregulated DEGs and 33 upregulated DEGs in patients who achieved pCR compared to patients who did not (Table 1). The 39 DEGs were significantly enriched in nine preselected MSigDB hallmark gene sets representing immunological processes (p < 0.001). The optimal elastic net logistic regression model containing 39 DEGs achieved the mean 5-CV area under the receiver operating characteristic curve of 0.81. The chemosensitivity score calculated using the optimal model parameters was significantly correlated with pCR after adjustment for the PAM50 intrinsic subtype, HR status, and HER2 IHC score (p < 0.001). GSEA revealed eight hallmark gene sets that were significantly up- or downregulated in samples with pCR, including epithelial-mesenchymal transition (normalized enrichment score [NES] = -2.16; q < 0.001), late estrogen response (NES = -2.01; q = 0.004), early estrogen response (NES = -1.972; q = 0.005), and inflammatory response (NES = 1.53; q = 0.06). Conclusion: Our findings demonstrate that gene expression patterns can predict the response to neoadjuvant TCHP chemotherapy in HER2+ BC. The functional characterization of 39 DEGs suggests that the tumor microenvironment, including adjacent immune cells, plays a significant role in modulating the response to neoadjuvant chemotherapy in HER2+ BC. Table 1. Significant DEGs Citation Format: Junghoon Shin, Ji-Yeon Kim, Eun Yoon Cho, Seok Won Kim, Jeong Eon Lee, Hyunwoo Lee, Yeon Hee Park, Jin Seok Ahn, Young-Hyuck Im. Gene expression signature as a predictor of pathological complete response to neoadjuvant docetaxel, carboplatin, trastuzumab, and pertuzumab treatment in locally advanced HER2-positive breast cancer [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr PO1-15-05.

Research on the widths of protective coal pillars in main roadway based on the damaged foundation beam model

Long-term stability of the protective coal pillars in coal mines can ensure normal and safe use of roadways; in turn, the integrity of the roadway plays an important role in safe and efficient mining in coal mines. The initial damage and rheological damage caused by coal-seam excavation disturbance have important influences on the selection of reasonable widths of the protective coal pillars. Based on damage mechanics and the theory of elastic foundation beams, a coupled damage constitutive relationship of rock-like materials is proposed in this work by considering the influence of threshold and residual strength to establish the mechanical model of the elastic damage foundation beam. By theoretical analysis and numerical calculation, the differential equation of the deflection curve of the beam is solved, the influence range of the advance abutment pressure under the condition of coupling damage is obtained, and the width of the protective coal pillar is determined. The results show that compared with the elastic foundation beam model, after considering the coupling damage of coal, the influence range of the advance abutment pressure increases with time over a certain duration. At the end of this duration, the influence range of the advance abutment pressure remains almost unchanged. For the case considered in this paper, the long-term stability of the roadway is guaranteed when the width of the coal pillar is 120 m. The potential interference or change related to the specific situation of the site can be studied by changing the relevant parameters in the model to study different working conditions, or the damage of the roof rock beam during the mining process of the working face can be considered, which will be the subject of further research in the future.

Velocity Measurements of Powdered Rock at Low Confining Pressures and Comparison to Lunar Shallow Seismic Velocity

AbstractSeismic methods will be useful for future lunar near‐surface characterization, and high‐fidelity elastic models will be required to aid interpretation of seismic observations. To develop an elastic lunar near‐surface model, we performed ultrasonic velocity measurements of lunar regolith simulant at low confining pressure and developed a rock physics model calibrated to these measurements. Grain contact models based on Hertz‐Mindlin theory produce accurate results at high confining pressure (i.e., several hundred meters or more burial depth) but historically fail to predict observed velocities in unconsolidated media at low pressure. Therefore, we heuristically modified existing models to fit our measured data over a range of porosities and confining pressures. To compare with Apollo 14 and 16 active seismic experiments, we used our new heuristic rock physics model to produce lunar subsurface velocity profiles. We performed ray tracing through our velocity profiles to calculate seismic traveltime, which results in good agreement with first arrivals interpreted from the Apollo experiments. Our model suggests a slightly higher velocity‐pressure dependence than inferred from in situ measurements, which may be due to porosity reduction in the lunar regolith from impact‐induced and natural vibrations.

A Macro-Micro Approach for Identifying Crystal Plasticity Parameters for Necking and Failure in Nickel-Based Alloy Haynes 282

This work develops a two-scales macro-micro approach to address the challenge in calibrating crystal plasticity microstructural models when samples undergo necking prior to fracture. The crystal plasticity models are crucial for predicting the materials’ plastic deformation and failure at the microstructure level, identifying the materials’ intrinsic properties as well as investigating the microstructure-properties relationships. However, after necking occurs, the experimentally measured stress-strain curves fail to reflect the materials ‘true’ stress-strain behavior and cannot be directly fitted into crystal plasticity models. The proposed macro-micro approach employs a top-down strategy to address this challenge, which has been studied with experimental tests on precipitation-strengthened Ni-based superalloy Haynes® 282®. In this approach, a macro rate-dependent anisotropic plasticity model with Voce-type hardening and Rice-Tracey damage law is first utilized to model the deformation and failure of the tensile bar, and calibrated by matching the stress-strain curves, necking strain, and reduction of area. Especially, to match the testing results under different applied strain rates, the rate-sensitivity parameter m and saturation stress in the elasticity model are modified to incorporate dependence on the local strain rate. Then, the ‘true’ stress-strain behaviors are extracted from the necking zone of the macro-model, which are used to calibrate a micro-model with explicit microstructures and governed by an extended crystal plasticity law. The consistency between the micro-model and macro-model are enforced during calibration. The calibration outcomes from the crystal plasticity model elucidate the materials intrinsic properties for slip, hardening, and failure, which is vital for further investigations into the microstructure-properties relationship and for accurate prediction of the material behavior under various test and service conditions.

The Response of Taupō Volcano to the M7.8 Kaikōura Earthquake

AbstractSeveral studies suggest that large earthquakes (M > 7.0) can act as external triggers of volcanic unrest, and even eruption. This triggering is attributed to either ground shaking (dynamic stresses) or to permanent ground deformation (associated with static stress changes). However, large earthquakes are rare and testing triggering hypotheses has proven difficult. We use geodetic data to show that the 13 November 2016 Kaikōura earthquake (Mw 7.8) triggered local deformation of up to 11 mm at Taupō volcano, 500 km away, which lasted for approximately twelve days. Using elastic geodetic models, we infer that the observed deformation was caused by either aseismic fault slip or a dike intrusion. We then use strong motion data from the surrounding area to show that the Kaikōura earthquake caused maximum dynamic stress changes in the range of 0.15–0.9 MPa in the vicinity of Taupō volcano and conclude that these dynamic stress changes triggered local faulting or dike activity and the associated deformation at Taupō volcano.

The present-day kinematics of the Tianshan orogenic belt constrained by GPS velocities

Since the late Cenozoic, the reactivated Tianshan orogenic belt has accommodated crustal shortening exceeding 200 km, primarily due to the far-field effects of the India-Eurasia plate collision. However, the details of the strain partitioning in the Tianshan Mountain range remain elusive. We interpret a new compilation of GPS velocities covering the whole Tianshan range with a classic elastic block model. Compared to previous studies with a block modeling approach, the Tianshan orogenic belt is further subdivided into several blocks based on geological fault traces and a clustering analysis approach. In addition to obvious crustal shortening on the bounding thrust faults of the Tianshan, our inverted fault slip rates also reveal that faults within the Tianshan orogenic belt, such as the Nalati Fault and the southern margin of the Issyk-Kul Lake Fault, which plays a crucial role in accommodating the tectonic crustal shortening. In the 72°E−78°E region, the internal shortening rate within the mountain is approximately 5–7 mm/yr. Besides crustal shortening, strike-slip motion occurs on faults in the interior of the mountain range as well as in the foreland fold-and-thrust belts, especially in the southern margin of the Tianshan. These findings suggest that the crustal deformation in the Tianshan Mountain range is more complex than previously thought, and the oblique convergence between the Tarim Basin and the Tianshan probably results in both strike-slip and thrust motion.

Viscoelastic earthquake cycle model for the Caribbean subduction zone in northwestern Colombia: implications of coastal subsidence for seismic/tsunami hazards

Recent interplate coupling results from the inversion of GPS data in northwestern Colombia have shed light on the seismogenic and tsunami potential along the Caribbean coast. The identified locked region on the subduction interface could generate an Mw8.0 earthquake every 600 years, followed by a subsequent tsunami. While observed horizontal velocities have been reproduced successfully by the elastic coupling model, vertical velocities remain unexplained and differ, both in their signs and magnitudes, from the model prediction. To explain 3-dimensional velocities, particularly rapid coastal subsidence, we evaluate the viscoelastic response of the lithosphere-asthenosphere system to an earthquake cycle at the Caribbean subduction zone. We confirm that the role of viscous relaxation on interseismic deformation is critical when the recurrence interval is longer than the asthenosphere relaxation time. Moreover, fitting observed crustal motions requires a thick "strong" lithosphere (60-100 km) consistent with the depth of the lithosphere-asthenosphere boundary. Our results support the hypothesis of the Caribbean as a locus of seismic and tsunami hazards but do not resolve the vertical motion paradox at different time scales since the interseismic crustal motions recover completely the coseismic and postseismic displacements caused by the potential mainshock. Supplementary geological investigation is essential to validate our current interpretation and resolve the remaining gaps.

Measuring the viscoelastic relaxation function of cells with a time-dependent interpretation of the Hertz-Sneddon indentation model

The Hertz-Sneddon elastic indentation model is widely adopted in the biomechanical investigation of living cells and other soft materials using atomic force microscopy despite the explicit viscoelastic nature of these materials. In this work, we demonstrate that an exact analytical viscoelastic force model for power-law materials, can be interpreted as a time-dependent Hertz-Sneddon-like model. Characterizing fibroblasts (L929) and osteoblasts (OFCOLII) demonstrates the model's accuracy. Our results show that the difference between Young's modulus EY obtained by fitting force curves with the Hertz-Sneddon model and the effective Young's modulus derived from the viscoelastic force model is less than 3%, even when cells are probed at large forces where nonlinear deformation effects become significant. We also propose a measurement protocol that involves probing samples at different indentation speeds and forces, enabling the construction of the average viscoelastic relaxation function of samples by conveniently fitting the force curves with the Hertz-Sneddon model.

DCES-PA: Deformation-controllable elastic shape model for 3D bone proliferation analysis using hand HR-pQCT images

Bone proliferation is an important pathological feature of inflammatory rheumatic diseases. Although recent advance in high-resolution peripheral quantitative computed tomography (HR-pQCT) enables physicians to study microarchitectures, physicians’ annotation of proliferation suffers from slice inconsistency and subjective variations. Also, there are only few effective automatic or semi-automatic tools for proliferation detection. In this study, by integrating pathological knowledge of proliferation formation with the advancement of statistical shape analysis theory, we present an unsupervised method, named Deformation-Controllable Elastic Shape model, for 3D bone Proliferation Analysis (DCES-PA). Unlike previous shape analysis methods that directly regularize the smoothness of the displacement field, DCES-PA regularizes the first and second-order derivative of the displacement field and decomposes these vector fields according to different deformations. For the first-order elastic metric, DCES-PA orthogonally decomposes the first-order derivative of the displacement field by shearing, scaling and bending deformation, and then penalize deformations triggering proliferation formation. For the second-order elastic metric, DCES-PA encodes both intrinsic and extrinsic surface curvatures into the second-order derivative of the displacement field to control the generation of high-curvature regions. By integrating the elastic shape metric with the varifold distances, DCES-PA achieves correspondence-free shape analysis. Extensive experiments on both simulated and real clinical datasets demonstrate that DCES-PA not only shows an improved accuracy than other state-of-the-art shape-based methods applied to proliferation analysis but also produces highly sensitive proliferation annotations to assist physicians in proliferation analysis.

Thermal fatigue life prediction of Ag-2.5Sn solder joint in flip chip

The heat dissipation needs of high-power devices cannot now be met by traditional packing solders due to the fast development of microelectronics interconnect technology. In addition to having outstanding thermal and electrical conductivity, nano-silver-tin paste better satisfies the needs of electronic devices. Studying the thermal reliability of solder joints is extremely important, this article investigates the fatigue life of the nano-silver-tin solder joints in temperature cycling experiments. Based on the life test results, the thermal cycling fatigue life of the nano-silver-tin solder joint is determined to be 2880 cycles. Finite element software was used to replicate the chip’s bonding process and assess the solder joint stress and strain distribution. The stress and strain of nano-silver-tin solder connections under thermal cycling load are accurately modeled using the Anand viscoplastic model and elastic model. The findings indicate that the contact region between the solder connections and copper columns is where the chip generates the most stress and strain. The fatigue life of the solder joint is estimated by using the Coffin–Manson modified equation, and this prediction aligns closely with the experimental results.

Altered asymmetry of functional connectome gradients in major depressive disorder.

Major depressive disorder (MDD) is a debilitating disease involving sensory and higher-order cognitive dysfunction. Previous work has shown altered asymmetry in MDD, including abnormal lateralized activation and disrupted hemispheric connectivity. However, it remains unclear whether and how MDD affects functional asymmetries in the context of intrinsic hierarchical organization. Here, we evaluate intra- and inter-hemispheric asymmetries of the first three functional gradients, characterizing unimodal-transmodal, visual-somatosensory, and somatomotor/default mode-multiple demand hierarchies, to study MDD-related alterations in overarching system-level architecture. We find that, relative to the healthy controls, MDD patients exhibit alterations in both primary sensory regions (e.g., visual areas) and transmodal association regions (e.g., default mode areas). We further find these abnormalities are woven in heterogeneous alterations along multiple functional gradients, associated with cognitive terms involving mind, memory, and visual processing. Moreover, through an elastic net model, we observe that both intra- and inter-asymmetric features are predictive of depressive traits measured by BDI-II scores. Altogether, these findings highlight a broad and mixed effect of MDD on functional gradient asymmetry, contributing to a richer understanding of the neurobiological underpinnings in MDD.