Deformation Model Research Articles

Thermomechanical modeling in elastic body with corotated total Lagrangian SPH

In this paper, we propose a novel thermal deformation formulation for elastic bodies' thermomechanical simulation with total Lagrangian smoothed particle hydrodynamics (TLSPH), which employing fixed reference configuration. We utilize implicit corotated TLSPH as a base methodology to address tensile instability and enhance the robustness of simulation. The reference configuration of heat transfer model is updated, but the reference configuration of thermal deformation model is fixed like TLSPH. As particle's temperature is changed, the inter-particle distance in reference configuration is updated by using linear thermal expansion theory. Validation involved two basic cantilever beam loading cases and a thermomechanical analysis with heat-induced thermal deformation on a cantilever beam. The TLSPH simulation results were compared against Finite Element Method simulations and analytical solutions, demonstrating equivalent accuracy across all tests. This study indicates the potential for conducting a wide array of simulations involving thermal deformation using the TLSPH method, which efficiently supports parallel computing on an individual particle basis.

Deformation of solid earth by surface pressure: equivalence between Ben-Menahem and Singh’s formula and Sorrells’ formula

SUMMARY Atmospheric pressure changes on Earth’s surface can deform the solid Earth. Sorrells derived analytical formulae for displacement in a homogeneous, elastic half-space, generated by a moving surface pressure source with speed $c$. Ben-Menahem and Singh derived formulae when an atmospheric P wave impinges on Earth’s surface. For a P wave with an incident angle close to the grazing angle, which essentially meant a slow apparent velocity $c_a$ in comparison to P- ($\alpha ^{\prime }$) and S-wave velocities ($\beta ^{\prime }$) in the Earth ($c_a \ll \beta ^{\prime } \lt \alpha ^{\prime }$), they showed that their formulae for solid-Earth deformations become identical with Sorrells’ formulae if $c_a$ is replaced by $c$. But this agreement was only for the asymptotic cases ($c_a \ll \beta ^{\prime }$). The first point of this paper is that the agreement of the two solutions extends to non-asymptotic cases, or when $c_a /\beta ^{\prime }$ is not small. The second point is that the angle of incidence in Ben-Menahem and Singh’s problem does not have to be the grazing angle. As long as the incident angle exceeds the critical angle of refraction from the P wave in the atmosphere to the S wave in the solid Earth, the formulae for Ben-Menahem and Singh’s solution become identical to Sorrell’s formulae. The third point is that this solution has two different domains depending on the speed $c$ (or $c_a$) on the surface. When $c/\beta ^{\prime }$ is small, deformations consist of the evanescent waves. When $c$ approaches Rayleigh-wave phase velocity, the driven oscillation in the solid Earth turns into a free oscillation due to resonance and dominates the wavefield. The non-asymptotic analytical solutions may be useful for the initial modelling of seismic deformations by fast-moving sources, such as those generated by shock waves from meteoroids and volcanic eruptions because the condition $c / \beta ^{\prime } \ll 1$ may be violated for such fast-moving sources.

Numerical modelling of large elasto-plastic multi-material deformations on Eulerian grids

Abstract The paper deals with an Eulerian model for heterogeneous multiphase (multi-material) elasto-plastic media based on the diffuse interface method in the one-dimensional uniaxial strain approximation. In this approximation, an equilibrium hypoelastic Wilkins bi-material model is derived. This is carried out on the basis of an analogy between the elasto-plastic Wilkins and hydrodynamic Euler models. For the obtained model, a Godunov-type numerical method is developed based on the approximate Riemann solver HLLC. The results of the proposed Eulerian diffuse interface model are compared with reference solutions on moving grids with explicit tracking interfaces. It is shown that the present diffuse interface numerical model describes with good accuracy strong shock-wave processes in heterogeneous multiphase elasto-plastic media.

A fluid–solid coupling model for hydraulic fracture of deep coal seam based on finite element method

The fluid–solid coupling effect is more pronounced in the process of deep coal seam development compared to shallow coalbed methane, exerting a greater influence on production, and cannot be disregarded. Throughout the extraction process, the interaction between effective stress and gas desorption triggers deformation within the coal seam, leading to dynamic changes in both porosity and permeability. This paper has developed a fully coupled gas flow and deformation model that contains the coal matrix and discrete fractures to describe the dynamic gas seepage behavior and deformation of deep coal seams within a coupled wellbore–hydraulic fractures–matrix system. The model's validity is corroborated through the examination of fracture aperture, employing the finite element numerical simulation capabilities of COMSOL Multiphysics. Subsequent to the model's validation, an in-depth investigation into the permeability and production variations under diverse parametric conditions is conducted. This analysis also encompasses the assessment of hydraulic fracture geometry's impact. The simulation outcomes reveal that the permeability alterations during coal seam development are subject to the counteracting influences of gas desorption and effective stress. Moreover, it is observed that an increase in the Langmuir volume strain constant and initial porosity correlates with enhanced production, whereas a diminution in the hydraulic fracture compression coefficient leads to increased cumulative production. Notably, the optimal production is attained when hydraulic fractures are oriented vertically yet asymmetrically relative to the horizontal well.

Comparison study of the in-plane crushing failure behavior of traditional and arc-curved hexagonal honeycomb

The honeycomb structures have been widely adopted as the aerospace engineering for the impact dynamic performance. To reveal the in-plane crushing behavior and improve the energy absorption ability, the influence of typical honeycomb structure is studied under different impact velocity and wall thickness. The deformation behavior of arc-curved hexagonal honeycomb with in-plane impact is researched. Results show that three typical deformation model including I, V and X shape are exhibited for traditional and arc-curved types. The deformation model would transfer from X to I shape with the increasing of impact velocity, and the impact load would be more unstable. With the increasing of central angle of arc-curved hexagonal honeycomb, the global deformation occurs instead of local deformation including X and V model, and stronger energy absorption ability is exhibited for the larger angle.

Multi-phase deformation and analogue modelling of the Junggar Basin, NW China

Multi-phase deformation and analogue modelling of the Junggar Basin, NW China

MODELING THE DYNAMICS OF DEFORMABLE OBJECTS BASED ON VOLUMETRIC PATCHES OF FREE FORMS

A method for solving nonlinear implicit numerical integration problems based on volumetric patches of free forms for modeling deformable objects with high-speed dynamics is proposed. This method improves the accuracy, consistency and controllability of deformation modeling and animation. The method is characterized by speed, accuracy, stability and uses optimization with region decomposition. The method is well suited for modeling deformable bodies with a large time step, in a wide range of deformation dynamics. We propose decomposed optimization, an optimization method based on free-form patches with region decomposition to minimize incremental potentials at each time step. The method uses quadratic matrix decomposition to combine non-overlapping subregions. The Hessian is evaluated once at the beginning of the time step. The advantages of the method are as follows. Geometric primitives and their mathematical models are proposed, which allow the reasonable application of these primitives to solve problems of volume-oriented modeling. Such requirements are met by volumetric patches of free forms based on analytical perturbation functions relative to the base triangles. The decomposed Hessian is constructed for each subregion and calculated using a set of vertices taken from a complete non-decomposed grid. The weights add the missing second-order Hessian data to the vertices of the subregions from the neighbors along the decomposition boundaries. Thanks to this, the descent is performed along the grid coordinates. There is no need to add gradients. During the descent, the gradient is determined. The Hessians under the region are calculated and factorized in parallel once per time step. They are used as an initializer at each iteration. Then the results are mixed together. This ensures stable and continuous high-quality modeling. An automated and reliable optimization method adapted for modeling nonlinear materials, high-speed dynamics and large deformations is proposed.

A DTSD model based on PS-InSAR surface multi-type deformation monitoring of villages in the mining area

Evaluating building damage in mining areas using Interferometric Synthetic Aperture Radar (InSAR) has inherent challenges. This work presents a Delaunay Triangulation of Surface Deformation (DTSD) model that utilizes Permanent Scatter InSAR to analyze various types of deformations in villages. This model created a network of irregular triangles using Delaunay triangulation and PS points as the input. The calculation involved determining the inclination of triangular edges and the torsion of spatial Bezier curves fitted by these edges. The PS points' maximum inclination and curvature values were identified by solving over-determined equations. Results from a slurry injection mine in Huaibei, China, indicate that the various types of deformations in the neighboring communities were below 8 %, and the buildings experienced minimal damage. The DTSD model offers a theoretical framework for monitoring and assessing various types of surface deformation and designing essential zones for building protection.

Crystal plasticity based constitutive model for deformation in metastable β titanium alloys

Due to attractive mechanical properties, metastable β titanium alloys have become very popular in many industries including aerospace, marine, biomedical, and many more. It is often the complex interplay among the different deformation mechanisms that produces many of the sought-after properties, such as enhanced ductility, super-elasticity, and shape memory effects. Stress induced martensitic transformation is an important deformation mechanism for these alloys. Understanding of it and the influence it has on the microstructural evolution of materials is of great importance. To this end we have developed a crystal plasticity based constitutive model which accounts for both martensitic phase transformation and slip based plasticity simultaneously in metastable β titanium alloys. We present a new formulation for the evolution of martensite transformation, based on physical principles and crystal plasticity theory. To understand and demonstrate this feature of the model, a parametric assessment of the newly developed constitutive model is conducted. This is followed by first of its kind analyses of stress induced martensitic transformation in metastable β titanium alloys. We firstly present validations against uniaxial loading experiments for different metastable β titanium alloys exhibiting stress induced martensite transformation. As part of this, single crystal simulations in metastable β titanium alloys are used for the first time to investigate the interaction of individual transformation systems during unconstrained transformation. This study shows good agreement between the experimental and simulated responses during all stages of deformation in which elastic, transformation and finally the slip stage are exhibited. Relatively ‘strong’ and ‘weak’ orientations for transformation are observed, consistent with experimental studies. The work done here demonstrates the ability of this crystal plasticity finite element method to capture physical mechanisms while bringing new insight about the interaction of different deformation mechanisms in metastable β titanium alloys.

BEARING CAPACITY OF BEAMS UNDER SHORT-TERM LOADS USING THE DIAGRAM OF CONCRETE DEFORMATION IN THE APPEARANCE OF THE FIFTH DEGREE POLYNOM

The theoretical determination of the load-bearing capacity of reinforced concrete beams under short-term loads using the concrete deformation diagram in the form of a fifth degree polynomial and its comparison with the results of experimental studies is considered. In the calculations of reinforced concrete structures using the deformation model of sections, the bending moments are calculated relative to the neutral line, which is located at a distance from the extreme fiber of the compressed concrete and limits its height. In the DBN of Ukraine, it is proposed to describe the concrete deformation diagram by a polynomial of the fifth degree or by a fractional-rational dependence, which was proposed and substantiated by the State Research Institute of Building Structures. Under these conditions, the theoretical bearing capacity of the reinforced concrete beam was obtained, which was also found experimentally. The authors conducted experimental studies of the load-bearing capacity of three series of beams of different types (three identical samples in each series): Series I - beams made of ordinary concrete; II series - steel-reinforced concrete beams; III series - beams of combined section, in which the lower (stretched) height zone is made of steel fiber concrete, and the upper (compressed) zone is made of ordinary concrete. Fiber, the total volume of which was 1%, was uniformly added to the composition of the concrete mass for the II and III series of samples during mixing. A comparison of the theoretical bearing capacity of a reinforced concrete beam with its value obtained experimentally shows that the theoretical value is quite significantly (1.36 times) higher than the experimental value.

A modified viscous flow law for natural glacier ice: Scaling from laboratories to ice sheets

Glacier flow modulates sea level and is governed largely by the viscous deformation of ice. Multiple molecular-scale mechanisms facilitate viscous deformation, but it remains unclear how each contributes to glacier-scale deformation. Here, we present a model of ice deformation that bridges laboratory and glacier scales, unifies existing estimates of the viscous parameters, and provides a framework for estimating the parameters from observations and incorporating flow laws derived from laboratory observations into glacier-flow models. Our results yield a map of the dominant deformation mechanisms in the Antarctic Ice Sheet, showing that, contrary to long-standing assumptions, dislocation creep, characterized by a value of the stress exponent [Formula: see text], likely dominates in all fast-flowing areas. This increase from the canonical value of [Formula: see text] dramatically alters the climate conditions under which marine ice sheets may become unstable and drive rapid rates of sea-level rise.

Modern outlook on the source of the 551 AD tsunamigenic earthquake that struck the Phoenician (Lebanon) coast

On July 9th, 551 AD, a strong earthquake followed by a noticeable tsunami and another destructive shock hit the littoral zone of Phoenicia, currently Lebanon. The sequence of events was associated with active faults in the region, but the source able to explain both seismic and tsunami effects is still a matter of open debate. This article contributes to unlocking this enigma by providing a modern analysis of the historical accounts of macroseismic effects, earthquake environmental and tsunami effects, and archaeoseismic findings. Here, we conduct seismotectonic research, evaluate the intensities of all the associated effects, and perform coseismic deformation and numerical tsunami modeling to infer the most likely source. Our results suggest that either the thrust system noted as Mount Lebanon Thrust underlying Lebanon and crops out at the seabed offshore of the coast or the intermittent transpressive Tripoli-Batroun-Jounieh-Damour fault zone along the Lebanese coast are the best candidate sources for the 551 AD earthquakes and tsunami. Both of these sources allow us to better explain the macroseismic, morphological and tsunamigenic effects. Remarkably, the notable uplift of the coastal, marine-cut terraces along the Lebanese littoral zone is well reproduced by the coseismic uplift associated with these sources, thus also clarifying the considerable drawback of the sea and limited inundation reported by the historical accounts.

DMGM: deformable-mechanism based cervical cancer staging via MRI multi-sequence * *This work was financially aided by the Natural Science Foundation of China (U1934221, 61773323), and Sichuan Science and Technology Program (2019YFG0345, 2019YJ0210).

Objective. This study aims to leverage a deep learning approach, specifically a deformable convolutional layer, for staging cervical cancer using multi-sequence MRI images. This is in response to the challenges doctors face in simultaneously identifying multiple sequences, a task that computer-aided diagnosis systems can potentially improve due to their vast information storage capabilities. Approach. To address the challenge of limited sample sizes, we introduce a sequence enhancement strategy to diversify samples and mitigate overfitting. We propose a novel deformable ConvLSTM module that integrates a deformable mechanism with ConvLSTM, enabling the model to adapt to data with varying structures. Furthermore, we introduce the deformable multi-sequence guidance model (DMGM) as an auxiliary diagnostic tool for cervical cancer staging. Main results. Through extensive testing, including comparative and ablation studies, we validate the effectiveness of the deformable ConvLSTM module and the DMGM. Our findings highlight the model’s ability to adapt to the deformation mechanism and address the challenges in cervical cancer tumor staging, thereby overcoming the overfitting issue and ensuring the synchronization of asynchronous scan sequences. The research also utilized the multi-modal data from BraTS 2019 as an external test dataset to validate the effectiveness of the proposed methodology presented in this study. Significance. The DMGM represents the first deep learning model to analyze multiple MRI sequences for cervical cancer, demonstrating strong generalization capabilities and effective staging in small dataset scenarios. This has significant implications for both deep learning applications and medical diagnostics. The source code will be made available subsequently.

Deformation of rectangular orthotropic laminate resting on thin elastic foundation with nonlinear change of displacements over thickness under edge loading

Deformation of rectangular orthotropic laminate resting on a thin elastic orthotropic foundation with fully fixed bottom plane is studied in this paper. The laminate is subjected to an in-plane uniaxial load uniformly distributed over one of its edges. Models of joint deformation of the laminate and foundation are created based on the equations of plane elasticity for an orthotropic body. The applicability of such equations is justified by the uniformity of edge loading. A laminate model allows for the transverse shear strain, whereas a model created for the foundation considers a nonlinear character of variation of the transverse and axial displacements. A governing system of differential equationsmodelling the joined deformation of the laminate and foundation is derived using static and kinematic contact conditions. The corresponding boundary value problem is solved using the sweep method. Based on this solution, effects of laminate and foundation thicknesses, and elasticity characteristics on the stress–strain state of the jointed structure are investigated. The model created and the method of its analysis enable the strong oscillating behaviour of stresses and strains to be studied. The results obtained can be utilized for verification of solutions of similar problems found by other numerical methods, including finite-element analyses.

A comparative approach for estimating microstructural characteristics of BaTi1−xZrxO3 (0.0 ≤ x ≤ 0.3) nanoparticles via X-ray diffraction patterns

Barium titanate materials are currently a special topic for scientific research due to their effective technological applications. The tetragonal BaTi1-xZrxO3 (0.0 ≤ x ≤ 0.3) nanoparticles (NPs) were synthesized using a modified citrate technique. The current work provides a comparative approach for the calculation of crystallite size, stress, strain, and elastic characteristics based on X-ray diffraction (XRD) patterns. Various models have been developed to analyze XRD data; these models differ in their assumptions, mathematical approaches, and the type of information they provide. The Scherrer model ignores lattice micro-structures that develop in nanostructures, such as intrinsic strain. To overcome such drawbacks, three Williamson-Hall models, (the uniform deformation model (UDM)), the uniform stress deformation model (USDM), and the uniform deformation energy density model (UDEDM) have been discussed. According to the USDM model, with increasing Zr ion concentrations, interplanar space increases, causing a drop in Young’s modulus. All the previous approaches take into account the diffraction angle (2θ)-dependent peak broadening, which is thought to represent a combination of size and strain-driven induced broadening.Graphical

Electrical detachment of triboelectrically charged bumpy particles from rough surfaces

The detachment of bumpy particles from smooth and rough surfaces through electrostatic fields was studied. The Johnson–Kendall–Roberts (JKR) adhesion model for elastic interface deformations was used to account for the individual bump adhesion, including the electrostatic forces. It was assumed that the elastic deformation of asperities determines the real contact area, and the effect of topographic properties of substrates was included in the analysis. For a fixed charge per unit mass, the Coulomb, the image, the dielectrophoretic, and the polarization forces acting on the particle in the presence of an imposed electric field were evaluated. The electrostatic detachment of bumpy toner particles for various applied electrostatic fields was studied. The triboelectric charges were concentrated on the hemispherical bumps, and the critical electric field strength needed to detach charged particles from surfaces with varying roughness levels was evaluated. It was shown that the particle charge, surface roughness, and the number of bumps significantly affect the removal of particles from surfaces. For higher charges (∼5 × 10−15 C ), decreasing the number of bumps from 22 to 14 and the roughness parameter from 0.83 to 0.77 approximately doubled the detachment field needed to remove 8.3 μ m polystyrene (PSL) particles from the aluminum oxide substrate. The model predictions are compared with the available experimental data, and good agreement was observed. The study’s findings predicting the electric field needed for charged particle removal could lead to more efficient copiers and electrostatic cleaning devices.

FE-analytical slice model and verification test for load distribution analysis and optimization of planetary gear train in wind turbine

Load distribution behavior of planetary gear train (PGT) is crucial for the contact and bending fatigue failure of wind turbine transmission system. With the increasing power of wind turbines, the load and failure rate of wind turbine become larger, which leads to the demand of accurate and efficient modeling, analysis and optimization for load distribution of PGT. In this paper, a new efficient and accurate FE-analytical slice model for load distribution analysis and optimization of PGT in wind turbine is proposed, which is explicitly formulated by the geometry slice model of external/internal gear contact, original FE-analytical slice model for local contact deformation, and efficient finite element (FE) model for global structural deformation. In the FE-analytical slice model, geometry errors are effectively descripted by discretizing gears into a series of slices, while gear tooth contact elasticity and structural elasticity are addressed by the FE-analytical method accurately and efficiently. Upon the proposed model, the load distribution behaviors of PGT with coupling effects of elasticity and errors are revealed and optimized by tooth modification and in-phase eccentricity arrangement strategy. The load distribution tests of PGT in wind turbine are conducted, verifying the proposed FE-analytical slice model which is significant to improve the load-bearing capacity and avoid the fatigue failure of wind turbine transmission system.

Editing mesh sequences with varying connectivity

Time-varying connectivity of triangle mesh sequences leads to substantial difficulties in their processing. Unlike editing sequences with constant connectivity, editing sequences with varying connectivity requires addressing the problem of temporal correspondence between the frames of the sequence. We present a method for time-consistent editing of triangle mesh sequences with varying connectivity using sparse temporal correspondence, which can be obtained using existing methods. Our method includes a deformation model based on the usage of the sparse temporal correspondence, which is suitable for the temporal propagation of user-specified deformations of the edited surface with respect to the shape and true topology of the surface while preserving the individual connectivity of each frame. Since there is no other method capable of comparable types of editing on time-varying meshes, we compare our method and the proposed deformation model with a baseline approach and demonstrate the benefits of our framework.

Creep Characteristics of Reconstituted Silty Clay under Different Pre-Loading Path Histories

Due to the long-term deformation settlement of foundations, issues such as damage and functional failure of buildings and structures have long been a concern in the engineering field. The creep of soil is one of the primary causes leading to long-term deformation of foundations. In this paper, the consolidation deformation, creep characteristics, and creep model of reconstituted saturated silty clay were studied using the isotropic consolidation creep test and triaxial compression creep test. The results show that for the isotropic consolidation creep test, although the applied load adopted different stages of loading, as long as the final applied confining pressure was the same, the number of stages applied by the confining pressure had little effect on the final isotropic consolidation deformation of the sample and the triaxial undrained shear strength after creep. However, for the triaxial shear creep test, it was found that under the same final deviatoric stress, the final deviatoric strain of the sample was closely related to the number of loading stages of deviatoric stress. The test showed that the more loading stages with the same deviatoric stress, the smaller the final deviatoric strain, and the triaxial undrained shear strength of the sample after creep increased. In addition, it was reasonable to set the pore pressure dissipation of the sample at 95% ((u0 − u)/u0 = 95%) as the time (t100) at which the primary consolidation of the soil sample was completed. The isotropic consolidation creep curves and the triaxial compression creep curves showed certain non-linearity. Then, the logarithmic model and the hyperbolic model were used to fit the creep curves of the samples. It was found that the hyperbolic model had a better fitting effect than the logarithmic model, but for the triaxial compression creep test, the creep parameters of the sample changed greatly. Therefore, studying the creep characteristics of soil under different pre-loading steps is of significant engineering importance for evaluating the long-term deformation of underground structures.

Geodetic innovation in Chilean mining: The evolution from static to kinematic reference frame in seismic zones

Abstract The use of regional kinematic reference frames (mRFs) in seismic zones is uncommon worldwide. This article proposes a solution implemented for Chilean mining, whose current projects are based on the classic reference frames (PSAD56 and SAD69). The approach is to move from a classic reference frame to an mRF in seismic countries where earthquakes constantly alter the frame. Our research group calculated an mRF (REDGEOMIN) that includes interseismic, coseismic, and postseismic deformation using CORS with open data from 2009 to 2022 and processed with scientific standards global navigation satellite system. REDGEOMIN consists of a deformation model (ADELA) with an interpolation approach through thin plate spline, allowing the greatest deformation to be modelled at campaign points. The relationship between classical and modern systems was explored with conformal transformations and NTv2 grids to include deformations, especially coming from PSAD56 and SAD69. The results demonstrate that REDGEOMIN aligns with the IGb14 reference frame (<1.0 mm), SIRGAS (ENU = 1.0, 1, 0, 2.0 mm), and the Chilean national reference frame SIRGASChile@2021.00 (ENU = 1, 2, 1, 6, 4.3 mm) aligns with millimetric precision. ADELA deformation model accurately models period locations to within 5 mm. Densification of REDGEOMIN@2022.00 at passive points PSAD56/SAD69 shows centimetric precision. PSAD56/SAD69, adjusted in the 1970s, are outdated due to crustal movement and seismic events and have metric errors. Therefore, different types of transformations were evaluated between PSAD56/SAD69 and REDGEOMIN@2022, whose RMS is between 1.57 and 1.69 m, and national grid transformations (NTv2) with an RMS of 0.23 and 0.16 m for PSAD56 and SAD69, respectively. The relationship between the classic systems and REDGEOMIN allows the transformation of the entire Chilean mining cadastre to epoch 2022.00. Starting in 2022.00, REDGEOMIN/ADELA offers millimetre precision, which is crucial in seismic zones. Furthermore, it paves the way to implement an updated national-level mRF in case of seismic events. Currently, Chilean mining laws are rigid, geodesically speaking. Therefore, legal-technical suggestions for implementing REDGEOMIN are also included in this article.