Dynamic Deformation Research Articles

Stretchable and High‐Performance Fibrous Sensors Based on Ionic Capacitive Sensing for Wearable Healthcare Monitoring

AbstractElectronic textiles with remarkable breathability, lightweight, and comfort hold great potential in wearable technologies and smart human‐machine interfaces. Ionic capacitive sensors, leveraging the advantages of the electric double layer, offer higher sensitivity compared to traditional capacitive sensors. Current research on wearable ion‐capacitive sensors has focused mainly on two‐dimensional (2D) or three‐dimensional (3D) device architectures, which show substantial challenges for direct integration with textiles and compromise their wearing experience on conformability and permeability. One‐dimensional (1D) stretchable fiber materials serve as vital components in constructing electronic textiles, allowing for rich structural design, patterning, and device integration through mature textile techniques. Here, a stretchable functional fiber with robust mechanical and electrical performances is fabricated based on semi‐solid metal and ionic polymer, which provided a high stretchability and good electrical conductivity, enabling seamless integration with textiles. Consequently, high‐performance stretchable fiber sensors are developed through different device architecture designs, including pressure sensors with high sensitivity (7.21 kPa−1), fast response (60 ms/30 ms), and excellent stability, as well as strain sensors with high sensitivity (GF = 1.05), wide detection range (0–300% strain), and excellent sensing stability under dynamic deformations.

Highly Elastic Full Hydrocarbon Ultralong RTP Polymers with Visible Light Excitable S0→T1 Population

AbstractHighly elastic ultralong organic room temperature phosphorescence (RTP) polymers are highly desired in wearable optoelectronic fields, but they are hardly realized in rubbers since chain segment motions deactivate triplet excitons. In the current work, it is revealed that polystyrene (PS) can inhibit triplet thermal deactivation of coronene (Cor), and it is the serious oxygen diffusion and quenching that disables RTP emission of Cor/polymers. In view of oxygen barrier function of rubbers, PS−polyisoprene−PS tri‐block elastomers (SIS) are used as Cor's doping matrices. The results show that Cor/SIS sheets show bright and ultralong afterglow with RTP lifetime up to 3.64 s in air after brief 365 nm light excitation. More impressively, Cor/SIS and its red fluorescent dye doped sheets all exhibit ultralong room temperature afterglow under large dynamic elastic deformation. Further, all these sheets exhibit long‐wave blue light excited afterglow despite Cor/SIS having no visible light absorption band, and the unique photoexcitation and emission mechanism is verified. This work not only provides the development strategy of the latest elastic RTP materials, but also will evoke a fresh understanding on organic doped RTP polymers.

A Study on the Dynamic Response and Deformation of Slopes Supported by Anti-Slide Piles Subjected to Seismic Waves with Different Spectral Characteristics

The long-term stability of slopes in areas with strong earthquakes not only is very important for people’s lives and the safety of property, but also it enables restoration of the ecological environment in the landslide areas, which is very important for sustainable development. The most commonly used seismic-support method, anti-slide piles, provides outstanding seismic performance. However, piles still deform and fail during earthquakes, which can lead to instability of the slope. The dynamic response of a slope reinforced with anti-slide piles is crucial for maintaining the long-term stability of the slope in a strong-earthquake area and, thus, for promoting its sustainable development. However, current research is focused mainly on the stability of the slope, and there have been few studies on the dynamic response of anti-slide piles. For this reason, we have undertaken the present study of a bedding-rock slope supported by a single row of anti-slide piles. By changing the frequency, amplitude, and duration of the input seismic waves, we have systematically explored the influence of their spectral characteristics on the dynamic response of the anti-slide piles and the slope using numerical simulations combined with the wavelet-transform method. Our results show that the spectral characteristics of the seismic waves significantly affect the deformations of the anti-slide piles. Low-frequency and high-amplitude seismic waves have stronger destructive effects on slopes, and high-amplitude seismic waves can generate multi-level sliding surfaces that extend to deeper levels. The low-frequency component of the seismic wave controls the overall deformation of the slope, and the high-frequency component controls the local deformations. An increase in the proportion and duration of low frequencies in seismic waves is the main cause of slope deformation and failure. The present work, thus, provides a useful reference for the design of a slope supported by anti-slide piles in an area with strong earthquakes, as well as for the maintenance of the long-term stability of such a slope, therefore, encouraging the sustainable development of related areas.

Measurement of dynamic deformation during shock loading using a fiber-optic loop-sensor

Abstract Characterizing materials under shock loading has been of interest in fields such as protective material development, biomechanics to study the injury mechanics and high-speed aerodynamic structures. However, shock loading of material is a very short duration phenomenon and it is extremely challenging to develop sensors for dynamic measurements under such loading conditions. Optical fiber sensors that present the possibilities to allow high resolution measurement of force or displacement in such high strain rate loading conditions. This work studies the possibility of developing a single mode optical fiber sensor based on the principle of power losses from the curved section for dynamic measurements under shock loading conditions. The strain measurement results obtained from the optical sensors are validated with the controlled digital image correlation measurements are found to be in close correlation. The sensor was able to provide time sensitivity of better than 1 ms. The results show that the fiber sensor has the characteristics of high sensitivity and high precision, which can be used to measure fine vibration in real-time.

Dynamic deformation and fracture of brass: Experiments and dislocation-based model

In this work, we perform a comprehensive study of the dynamic deformation and fracture of brass, including Taylor tests with classical and profiled cylinders and ball throwing experiments reaching the strain rates of about (0.1−1)/μs, as well as atomistic and continuum-level numerical modeling. Molecular dynamics (MD) simulations are used to construct the equation of state (EOS) of brass and to study its fracture characteristics at shear deformation under negative pressure. An original model of fracture under combined tensile-shear loading is formulated, which takes into account both the accumulation of empty volume in the process of lattice loosening due to the lattice defect production in the course of plastic deformation and further mechanical growth of voids controlled by the dislocation plasticity. This atomic-scale model is transmitted to the macroscopic experiment-scale level and embedded into 3D dislocation plasticity model to describe the dynamic deformation and fracture of brass using the numerical scheme of smoothed particle hydrodynamics (SPH). A part of experimental data is used to find the optimal parameters of the dislocation plasticity model by means of the Bayesian global optimization method accelerated with the help of artificial-neural-network (ANN)-based emulator of the 3D model. Another part of experimental data is used to fit the fracture model parameter. The remaining experimental data, which are not used in the parameterization, are applied to verify the parameterized model. The developed physical-based model provides correct and meaningful description of the dynamic deformation and fracture of brass, while the developed formalized approach to its parameterization opens a way to wider use of this type of models in the engineering applications, including studies on dynamic performance and high-speed processing technologies.

Fragmentation behavior and velocity formula for secondary fragments from RC slabs during contact explosions

The failure process of reinforced concrete (RC) slabs under contact explosion is dominated by localized damages, accompanied by numerous flying fragments. These concrete fragments pose a significant threat to personnel and equipment, as well as causing dynamic deformation and failure of the retrofitting materials used to restrain the fragments. The behavior of concrete fragmentation during explosions has been seldom studied experimentally, and few fragment velocity formulas exist that incorporate multiple factors. In this paper, the fragmentation process is recorded using two high-speed cameras, revealing that concrete fragmentation during explosions exhibits notable zoning characteristics, with the maximum velocity observed at the center of the fragment cloud’s front. To predict this maximum velocity, a model is derived from dimensional analysis. Utilizing this model, velocity prediction formulas are proposed and validated by 29 contact explosion tests. The formulas consider the explosive-rebar position, slab thickness, explosive mass and explosive shape, and are further improved by considering the concrete cover. The results indicate that, when the slab is not breached, the deceleration of rebar on fragments is weak. However, once the slab is breached, this deceleration becomes increasingly significant as the defined scaled thickness (TS) decreases. In the limiting case, the fragment velocity when the charge is located above the rebar is 0.636 times that of when the charge avoids the rebar. Fragments when the charge avoids the rebar, should be regarded as the most unfavorable case in secondary fragment hazards assessment and structural design.

Dynamic Impact Deformation Characteristics of Multi-Layer Metallic Materials Based on a New Combustion Propulsion Pattern

Dynamic Impact Deformation Characteristics of Multi-Layer Metallic Materials Based on a New Combustion Propulsion Pattern

Phase reversion mediated the dual heterogeneity of grain size and dislocation density in an equiatomic CrCoNi medium-entropy alloy

An ultra-high strain rate (104 s-1) dynamic plastic deformation treatment at liquid nitrogen temperature (LNT-DPD) followed by annealing is carried out to obtain dual heterogeneity of grain size and dislocation density in an equiatomic CrCoNi medium entropy alloy (MEA). Such extreme loading conditions resulted in extensive phase transformation in this MEA. Subsequent annealing at 650°C for 1 h further induced reverse phase transformation and partial recrystallization, forming a complex heterogeneous microstructure characterized by nested trimodal grain sizes and partitioned dislocation density. A superior yield strength of ∼800MPa and a good ductility of ∼40% were simultaneously achieved in this heterogeneous alloy. In order to reveal the effects of grain size and dislocation density distributions on the mechanical property improvements, the underlying deformation mechanisms were systematically discussed. High density of geometrically necessary dislocations (GNDs) would be induced in complex heterogeneous structures during tensile deformation due to strain gradients or partitioning between different regions, which would lead to additional strengthening and work hardening. These results provide a novel approach to overcome the strength-ductility trade-off dilemma for FCC-structured MEAs.

Microstructure and dynamic deformation mechanism of laser powder bed fusion of 316L-containing Ti–6Al–4V with dual-phase heterostructure

In this paper, 316L-containing Ti–6Al–4V alloy was fabricated by laser powder bed fusion (LPBF) through mixing Ti–6Al–4V and 4.5 wt% 316L powders, and the dynamic compressive mechanical properties and deformation mechanism at different strain rates were studied. The results show that the volume fraction of β phase sharply increases from 1.8% (in TC4) to 61.4% (in HST), and micro- and submicron-sized grains coexist in the HST alloy, producing heterostructure in the form of bimodal grain size distribution. The presence of the heterostructure led to superior heterogeneous deformation induced stress, thus facilitating the additional strain hardening and deformation coordinating ability, thus made the HST alloy achieved ultimate compressive stress of ∼1750 MPa and fracture strain of ∼17%, showing excellent comprehensive mechanical properties. Under quasi-static load, the deformation mode of HST alloy is mainly attributed to progressive deformation-induced martensitic transformation. However, at high strain rates, the impact loading inhibited the activation of progressive DIMT, and thus the deformation mode changed to combination of dislocation slipping and deformation twinning.

A Variable Horizon Model Predictive Control for Magnetorheological Semi-Active Suspension with Air Springs

To improve the characteristics of traditional model predictive control (MPC) semi-active suspension that cannot achieve the optimal suspension control effect under different conditions, a variable horizon model predictive control (VHMPC) method is devised for magnetorheological semi-active suspension with air springs. Mathematical models are established for the magnetorheological dampers and air springs. Based on the improved hyperbolic tangent model, a forward model is established for the magnetorheological damper. The adaptive fuzzy neural network method is used to establish the inverse model of the magnetorheological damper. The relationship between different road excitation frequencies and the control effect of magnetorheological semi-active suspension with air springs is simulated, and the optimal prediction horizons under different conditions are obtained. The VHMPC method is designed to automatically switch the predictive horizon according to the road surface excitation frequency. The results demonstrate that under mixed conditions, compared with the traditional MPC, the VHMPC can improve the smoothness of the suspension by 2.614% and reduce the positive and negative peaks of the vertical vibration acceleration by 11.849% and 6.938%, respectively. Under variable speed road conditions, VHMPC improved the sprung mass acceleration, dynamic tire deformation, and suspension deflection by 7.191%, 7.936%, and 22.222%, respectively, compared to MPC.

Constructing Long and Stable Ag‐Al2O3 Core–Shell Nanowires for Humidity Sensing and Triboelectric Energy Generation

Silver nanowires (AgNWs) are a promising alternative material to indium tin oxide as flexible transparent electrodes owing to their excellent optoelectrical properties and mechanical performance. However, the main challenge is the poor stability under diverse environments, ranging from high humidity, chemical exposure, and dynamic mechanical deformation. Herein, ultralong AgNWs (≈100 μm) have been synthesized via controlling growth kinetics by a facile acetic acid‐assisted solvothermal method, further decorated with a thin Al2O3 layer by electrodeposition to form a core–shell architecture. The resultant films based on Ag‐Al2O3 core–shell nanowires (NWs) possess a higher conductivity while preserving the optical transparency due to the enhanced NWs contact. More importantly, the constructed films exhibit strong resistance to various conditions, such as exposure to high temperature/humidity and immersion in NaCl, HCl, and Na2S solutions. The laser‐etched interdigital electrodes based on the chemically stable AgNWs are further integrated with graphene oxide layer for humidity sensing and respiration monitoring. Furthermore, the developed NWs with superior mechanical stability are constructed as triboelectric nanogenerators for electricity generation, and reliable output performance has been demonstrated. This work provides a convenient, scalable, and cost‐effective solution that offers great potential for designing robust, transparent electrodes for next‐generation flexible electronics.

Anti-ballistic properties of hybrid UHMWPE fiber-reinforced composite armour

The ballistic performance of three hybrid composite plates, including ultra-high molecular weight polyethylene (UHMWPE), UHMWPE/Aramid, and UHMWPE/CFRP with similar surface density, was studied in the paper. These plates were tested under the impact of 7.62×25 mm full metal jacket (FMJ) bullets, with the dynamic back deformation (BFD) captured using Digital Image Correlation (DIC) technology. The effects of material combinations and striking faces on the dynamic response were discussed. The deformation and penetration mechanisms were analyzed using optical microscopy and micro-CT tomography. The results indicated that the UHMWPE/CFRP plate exhibited the lowest BFD, followed by UHMWPE and the UHMWPE/Aramid plate. When UHMWPE severed as the striking face, the fibers underwent through-thickness compression, which transitioned to in-plane tension and led to an elongated fracture of yarns. Similarly, Aramid fibers also experienced tensile fractures under similar conditions. In contrast, carbon fibers had brittle shear fractures when CFRP was the striking face. Additionally, the “V-shaped” cone traveling hinge velocity was calculated using DIC results, and the effects of the plate bending stiffness and wave impedance on protective performance were discussed. The findings emphasize the importance of an optimal material configuration to mitigate the propagation of compressive waves in the thickness direction and enhance bending stiffness, which is crucial for improving protection within ballistic limits.

Magnetic Field Enable Lithium Ions to Penetrate Lithophilic 3D Collectors and Enhance Electrochemical Performance

Abstract Lithium metal batteries, celebrated for their exceptional energy density, are promising for advanced energy storage. Nevertheless, the dynamic deformation of lithium metal during cycling often leads to the unchecked proliferation of lithium dendrites, compromising the solid electrolyte interface. This not only deteriorates cycle stability but also poses significant safety risks. In our approach, we develop a three-dimensional lithium-affinitive composite current collector, utilizing an external magnetic field. The lithiophilic nature of V2O5, coupled with the deformability support provided by nickel foam and the depth-enhancing influence of the magnetic field on lithium metal deposition, collectively contribute to a more controlled and stable lithium environment. Our findings indicate that this novel setup allows for a lithium metal deposition depth of up to 310 μm, markedly curtailing the growth of dendrites in successive cycles. Remarkably, batteries reassembled with this magnetically-enhanced, lithium pre-deposited current collector exhibits a coulombic efficiency of 98.3% after 320 cycles at 1 mA cm-2. Moreover, a full cell, equipped with LiFePO4, delivers an initial capacity of 158.4 mAh g-1 at 1 C.

Monte Carlo dose calculation for photon and electron radiotherapy on dynamically deforming anatomy.

Dose calculation in radiotherapy aims to accurately estimate and assess the dose distribution of a treatment plan. Monte Carlo (MC) dose calculation is considered the gold standard owing to its ability to accurately simulate particle transport in inhomogeneous media. However, uncertainties such as the patient's dynamically deforming anatomy can still lead to differences between the delivered and planned dose distribution. Development and validation of a deformable voxel geometry for MC dose calculations (DefVoxMC) to account for dynamic deformation in the dose calculation process of photon- and electron-based radiotherapy treatment plans for clinically motivated cases. DefVoxMC relies on the subdivision of a regular voxel geometry into dodecahedrons. It allows shifting the dodecahedrons' corner points according to the deformation in the patient's anatomy using deformation vector fields (DVF). DefVoxMC is integrated into the Swiss Monte Carlo Plan (SMCP) to allow the MC dose calculation of photon- and electron-based treatment plans on the deformable voxel geometry. DefVoxMC is validated in two steps. A compression test and a Fano test are performed in silico. Delta4 (for photon beams) and EBT4 film measurements in a cubic PMMA phantom (for electron beams) are performed on a TrueBeam in Developer Mode for clinically motivated treatment plans. During these measurements, table motion is used to mimic rigid dynamic patient motion. The measured and calculated dose distributions are compared using gamma passing rate (GPR) (3% / 2mm (global), 10% threshold). DefVoxMC is used to study the impact of patient-recorded breathing motion on the dose distribution for clinically motivated lung and breast cases, each prescribed 50Gy to 50% of the target volume. A volumetric modulated arc therapy (VMAT) and an arc mixed-beam radiotherapy (Arc-MBRT) plan are created for the lung and breast case, respectively. For the dose calculation, the dynamic deformation of the patient's anatomy is described by DVFs obtained from deformable image registration of the different phases of 4DCTs. The resulting dose distributions are compared to the ones of the static situation using dose-volume histograms and dose differences. DefVoxMC is successfully integrated into the SMCP to enable the MC dose calculation of photon- and electron-based treatments on a dynamically deforming patient anatomy. The compression and the Fano test agree within 1.0% and 0.1% with the expected result, respectively. Delta4 and EBT4 film measurements agree with the calculated dose by a GPR>95%. For the clinically motivated cases, breathing motion resulted in areas with a dose increase of up to 26.9Gy (lung) and up to 7.6Gy (breast) compared to the static situation. The largest dose differences are observed in high-dose-gradient regions perpendicular to the beam plane, consequently decreasing the planning target volume coverage (V95%) by 4.2% for the lung case and 2.0% for the breast case. A novel method for MC dose calculation for photon- and electron-based treatments on dynamically deforming anatomy is successfully developed and validated. Applying DefVoxMC to clinically motivated cases, we found that breathing motion has non-negligible impact on the dosimetric plan quality.

Design and manufacturing of a dynamically deformable liver phantom for radiotherapy

Phantoms representing anatomical deformations are necessary to investigate and improve dynamic treatments. In this study, we aimed to produce a deformable liver phantom by simulating respiratory motion.The dynamically DEformable Liver Phantom (DELP) is designed to create a human-specific respiratory model and to produce synchronised, repeatable motion with this model. For the deformation effect of this movement, an artificial liver was created using silicone material and mold. A stepper motor was used to compress the liver in the inferior direction according to an adjustable respiratory motion. Reference markers (fiducial) placed on the DELP helped to verify the movement and calculate the deformation. In dynamic deformation tests, the greatest amount of deformation was found in the edge region of the silicone liver. The average deformation was 3.45 ± 0.93 mm when 5 mm amplitude movement was applied and 5.98 ± 0.01 mm when 10 mm amplitude movement was applied.DELP is a deformable liver phantom with motion reproducibility. Its performance in radiotherapy application was evaluated using dosimetric equipment.

Quasi‐Static and Dynamic Deformation Behavior of Medium Manganese Automotive Steel under Interrupted Tension

Quasi‐Static and Dynamic Deformation Behavior of Medium Manganese Automotive Steel under Interrupted Tension

Grain disintegration and dynamic recrystallization during impact tests of additively manufactured nickel-based alloy 718

The high-temperature dynamic mechanical response of Alloy 718 produced via laser-powder bed fusion (LPBF) was investigated through compressive Split-Hopkinson Pressure Bar (SHPB) tests. Simulating the typical service conditions of Alloy 718, the tests were conducted at temperatures ranging from 298 K to 773 K and at strain rates of 1000 s−1 to 1500 s−1. Phenomenological material constitutive models, such as the modified versions of Johnson-Cook and Hensel-Spittel models, were developed based on the SHPB test results. Analysis of microstructural evolution under impact conditions highlighted that columnar grains with high Schmid factors tend to undergo preferential activation and dislocation pile-up. This process leads to the formation of adiabatic shear bands, grain disintegration, and intense lattice rotation, particularly at higher strain rates. Furthermore, increasing the dynamic deformation temperature facilitates the activation of discontinuous dynamic recrystallization (DRX), with strain accumulation promoting localized grain nucleation along heavily dislocated dendritic boundaries. Recognizing the limitations of phenomenological material constitutive models in accurately representing the underlying microstructural evolution, an artificial neural network (ANN)-based constitutive model employing a three-layer backpropagation learning algorithm was implemented, reducing the Average Absolute Relative Error (AARE) to 0.17%.

Insights into permafrost aggradation and thawing: A case study of Zonag Lake on the Qinghai–Tibet Plateau using SAR interferometry

AbstractLakes on the Qinghai–Tibet Plateau (QTP) are important indicators of climate change. The water level and area of Zonag Lake have increased sharply since 2000, and the west lake bottom area was exposed after an outburst of flood in September 2011. The drained basin was exposed to the cold environment, causing rapid permafrost forming. In this paper, time‐series synthetic aperture radar interferometry (InSAR) was utilized to monitor the surface deformation of the drained basin using Sentinel‐1A images within a 4‐year period (2017–2020). This research focused on characterizing the spatial and temporal dynamics of ground deformation and exploring changes in the permafrost base around the drained basin based on the deformation information. The experimental results revealed spatially variable ground deformation, with long‐term deformation rates ranging from −78.3 mm/year to 72.8 mm/year and seasonal amplitudes of 0–14 mm. Subsidence was prominent in the lakeshore, the thermokarst region and the slope drainage area, indicative of the thawing of ice‐rich permafrost. Conversely, uplift was concentrated in the exposed unconsolidated sediment region, with a maximum displacement of 110 mm over the nearly 4‐year observation period, suggesting ground ice aggradation. The uplift information was used to estimate the change in the permafrost base in the drained basin, yielding a maximum value of 4 m. The estimated permafrost base change closely aligned with simulated results, with an error of 0.28 m. This study demonstrates the capability of InSAR in monitoring permafrost stability and improving the understanding of the dynamic permafrost formation process.

Achieving automated and high-precision in situ analysis of the dimensional accuracy and dynamic deformation of 3D-printed surgical templates: an in vitro study

PurposeTo demonstrate the viability of a coordinate-measuring machine (CMM) for the geometric analysis of 3D printed surgical templates.MethodsThe template was designed and modified by adding 18 cylindrical landmarks for CMM test and then classified into five groups according to the slicing software and resins (opaque and transparent): Streamflow-O, Streamflow-T, Shapeware-T, Rayware-T and Polydevs-T (N = 3). Three standing times (0 w, 1 w, and 2 w) were included to observe possible deformation. All the measurements were performed automatically by the CMM through a preset program. The Euclidian distance (dxyz) was regarded as the representation of global dimension accuracy, and displacements in the x-, y-, and z-axes were also calculated.ResultsThe average dxyz values of Streamflow-O, Streamflow-T, Shapeware-T, Rayware-T and Polydev-T are 32.6 μm, 31.3 μm, 56.4 μm, 96.4 μm, and 55.3 μm, respectively. Deviations were mainly induced by the upward bending of the free end region (positive direction of the z-axis). Different resins did not have a significant influence on the dimensional accuracy. Moreover, deformation appeared to be negligible after 2 weeks of storage, and the z-axis displacements were only approximately 30 μm at week 1 and 10 μm at week 2.ConclusionsThe deviations of the DLP-printed template are induced mainly by z-axis displacements and are determined by the processing accuracy. After 2 weeks, the dimensional stabilities of these templates are reliable, which is encouraging for clinicians. Moreover, the CMM is preliminarily demonstrated to be a feasible tool for achieving automated geometric analysis of surgical templates.

Fast and Compact Partial Differential Equation (PDE)-Based Dynamic Reconstruction of Extended Position-Based Dynamics (XPBD) Deformation Simulation

Dynamic simulation is widely applied in the real-time and realistic physical simulation field. How to achieve natural dynamic simulation results in real-time with small data sizes is an important and long-standing topic. In this paper, we propose a dynamic reconstruction and interpolation method grounded in physical principles for simulating dynamic deformations. This method replaces the deformation forces of the widely used eXtended Position-Based Dynamics (XPBD), which are traditionally derived from the gradient of the energy potential defined by the constraint function, with the elastic beam bending forces to more accurately represent the underlying deformation physics. By doing so, it establishes a mathematical model based on dynamic partial differential equations (PDE) for reconstruction, which are the differential equations involving both the parametric variable u and the time variable t. This model also considers the inertia forces caused by acceleration. The analytical solution to this model is then integrated with the XPBD framework, built upon Newton’s equations of motion. This integration reduces the number of design variables and data sizes, enhances simulation efficiency, achieves good reconstruction accuracy, and makes deformation simulation more capable. The experiment carried out in this paper demonstrates that deformed shapes at about half of the keyframes simulated by XPBD can be reconstructed by the proposed PDE-based dynamic reconstruction algorithm quickly and accurately with a compact and analytical representation, which outperforms static B-spline-based representation and interpolation, greatly shortens the XPBD simulation time, and represents deformed shapes with much smaller data sizes while maintaining good accuracy. Furthermore, the proposed PDE-based dynamic reconstruction algorithm can generate continuous deformation shapes, which cannot be generated by XPBD, to raise the capacity of deformation simulation.