Generation of a Virtual Cell using a Phase Field Approach to Model Amoeboid Crawling.

The process of chemotaxis of living cells is complex. Cells follow gradients of an external signal because the interior of the cells gets polarized. The description of the exterior and the interior of the cell together with its motion for the convenient realization of the computational modeling of the whole process is a complex technical problem. Here, we employ a phase field model to characterize the interior of the cell, permitting the integration of stochastic partial differential equations, responsible for the polarization in the interior of the cell, and simultaneously, the calculation of the shape deformations of the cell, including its locomotion. We detail the mathematical description of the process and the procedure to calculate numerically the phase field with a simple reaction-diffusion equation for a single concentration.

Microcrack behavior in bone: Stress field analysis at osteon cement line tips.

Bone microstructure governs microcrack propagation complexity. Current research, relying on linear elastic fracture mechanics, inadequately considers authentic multi-level structures, like cement lines and osteons, impacting stress intensity at cracks. This study, by constructing models encompassing single or multiple osteons, delves into the influence of factors like crack length, osteon radius, and modulus ratio on the stress intensity factor at the crack tip. Employing a fracture mechanics phase-field approach to simulate crack propagation paths, it particularly explores the role of cement lines as weak interfaces in crack extension. The aim is to comprehensively and systematically elucidate the critical factors of bone microstructure in the context of crack propagation.

Engineering Multiphase Phase Transitions for Exceptional Electrocaloric Performance and Ultraweak Electrostrictive Response in Ferroelectrics.

In the pursuit of eco-friendly alternatives for refrigeration technology, electrocaloric materials have emerged as promising candidates for efficient solid-state refrigeration due to their high efficiency and integrability. However, current advancements in electrocaloric effects (ECEs) are often constrained by high temperatures and elevated electric fields (E-field), limiting practical applicability. Informed by phase-field simulation, this study introduces a (1-x)Pb(Yb1/2Nb1/2)O3-xPb(Mg1/3Nb2/3)O3 system, strategically engineered to incorporate highly ordered YN and disordered MN mixtures. The synergistic interplay between E-field/temperature-induced polarization reorientation and cation shift initiates multiple ferroelectric-antiferroelectric-paraelectric phase transitions. Our results demonstrate that under a moderate E-field of 50 kV cm-1, the x = 0.22 composition achieves remarkable performance with a giant temperature change (ΔT) of 3.48 K, a robust ECE strength (ΔT/ΔE) of 0.095 K cm kV-1, and a wide temperature span (Tspan) of 38 °C. Notably, the disrupted lattice structure contributes to ultralow electrostrains below 0.008%, with an average electrostrictive coefficient Q33 of 0.007 m4 C-2. The significantly weakened electrostrictive activity favors enhancing the performance stability of subsequent devices. This work introduces an innovative strategy for developing robust electrocaloric materials, offering substantial ΔT and low electrostrains, presenting promising advancements in ECE applications with an extended lifetime.

The diffuse interface description of fluid lipid membranes captures key features of the hemifusion pathway and lateral stress profile.

Topological transitions of lipid membranes are ubiquitous in key biological processes for cell life, like neurotransmission, fertilization, morphogenesis, and viral infections. Despite this, they are not well understood due to their multiscale nature, which limits the use of molecular models and calls for a mesoscopic approach such as the celebrated Canham-Helfrich one. Unfortunately, such a model cannot handle topological transitions, hiding the crucial involved forces and the appearance of the experimentally observed hemifused intermediates. In this work, we describe the membrane as a diffuse interface preserving the Canham-Helfrich elasticity. We show that pivotal features of the hemifusion pathway are captured by this mesoscopic approach, e.g. a (meta)stable hemifusion state and the fusogenic behavior of negative monolayer spontaneous curvatures. The membrane lateral stress profile is calculated as a function of the elastic rigidities, yielding a coarse-grained version of molecular models findings. Insights into the fusogenic mechanism are reported and discussed.

Simulation of Frost-Heave Failure of Air-Entrained Concrete Based on Thermal-Hydraulic-Mechanical Coupling Model.

The internal pore structural characteristics and microbubble distribution features of concrete have a significant impact on its frost resistance, but their size is relatively small compared to aggregates, making them difficult to visually represent in the mesoscopic numerical model of concrete. Therefore, based on the ice-crystal phase transition mechanism of pore water and the theory of fine-scale inclusions, this paper establishes an estimation model for effective thermal conductivity and permeability coefficients that can reflect the distribution characteristics of the internal pore size and the content of microbubbles in porous media and explores the evolution mechanism of effective thermal conductivity and permeability coefficients during the freezing process. The segmented Gaussian integration method is adopted for the calculation of integrals involving pore size distribution curves. In addition, based on the concept that the fracture phase represents continuous damage, a switching model for the permeability coefficient is proposed to address the fundamental impact of frost cracking on permeability. Finally, the proposed estimation models for thermal conductivity and permeability are applied to the cement mortar and the interface transition zone (ITZ), and a thermal-hydraulic-mechanical coupling finite element model of concrete specimens at the mesoscale based on the fracture phase-field method is established. After that, the frost-cracking mechanism in ordinary concrete samples during the freezing process is explored, as well as the mechanism of microbubbles in relieving pore pressure and the adverse effect of accelerated cooling on frost cracking. The results show that the cracks first occurred near the aggregate on the concrete sample surface and then extended inward along the interface transition zone, which is consistent with the frost-cracking scenario of concrete structures in cold regions.

What is the physical origin of the gradient flow structure of variational fracture models?

We investigate a physical characterization of the gradient flow structure of variational fracture models for brittle materials: a Griffith-type fracture model and an irreversible fracture phase field model. We derive the Griffith-type fracture model by assuming that the fracture energy in Griffith's theory is an increasing function of the crack tip velocity. Such a velocity dependence of the fracture energy is typically observed in polymers. We also prove an energy dissipation identity of the Griffith-type fracture model, in other words, its gradient flow structure. On the other hand, the irreversible fracture phase field model is derived as a unidirectional gradient flow of a regularized total energy. We have considered the time relaxation parameter a mathematical approximation parameter, which we should choose as small as possible. In this research, however, we reveal the physical origin of the gradient flow structure of the fracture phase field model (F-PFM) and show that the small time relaxation parameter is characterized as the rate of velocity dependence of the fracture energy. It is verified by comparing the energy dissipation properties of those two models and by analysing a travelling wave solution of the irreversible F-PFM. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.

Grain orientation and shape evolution of ferroelectric ceramic thick films simulated by phase-field method.

The orientation and shape of ceramics grains was always neglected, resulting in a lot of information during sintering has not been excavated. In this study, a modified phase-field model in order to express the anisotropy of grain boundary energy is developed. The effects of the anisotropy of grain boundary energy on the grain orientation and shape evolution are investigated in detail. The ferroelectric ceramic thick films are prepared by tape casting. The comparison of experiment and simulation results shows that the anisotropy of grain boundary energy results in uneven grain orientation and bimodal grain size distribution. The quantitative analysis of grain microstructures helps to establish a relationship with the degree of anisotropy of grain boundary energy. Our findings provide a new way to judge the degree of anisotropy by calculating the relevant parameters in the SEM images of ceramics materials.

Yardangs sculpted by erosion of heterogeneous material.

The recognizable shapes of landforms arise from processes such as erosion by wind or water currents. However, explaining the physical origin of natural structures is challenging due to the coupled evolution of complex flow fields and three-dimensional (3D) topographies. We investigate these issues in a laboratory setting inspired by yardangs, which are raised, elongate formations whose characteristic shape suggests erosion of heterogeneous material by directional flows. We combine experiments and simulations to test an origin hypothesis involving a harder or less erodible inclusion embedded in an outcropping of softer material. Optical scans of clay objects fixed within flowing water reveal a transformation from a featureless mound to a yardang-like form resembling a lion in repose. Phase-field simulations reproduce similar shape dynamics and show their dependence on the erodibility contrast and flow strength. Through visualizations of the flow fields and analysis of the local erosion rate, we identify effects associated with flow funneling and the turbulent wake that are responsible for carving the unique geometrical features. This highly 3D scouring process produces complex shapes from simple and commonplace starting conditions and is thus a candidate explanation for natural yardangs. The methods introduced here should be generally useful for geomorphological problems and especially those for which material heterogeneity is a primary factor.

Phase-Field Simulation of Precipitation and Grain Boundary Segregation in Fe-Cr-Al Alloys under Irradiation.

A phase-field model for the precipitation of Fe-Cr-Al alloy is established incorporating grain boundary (GB) effects and irradiation-accelerated diffusion. The radiation source and grain boundary effect are incorporated to broaden the applicability of the Fe-Cr-Al precipitated phase-field model. The model is firstly employed to simulate the precipitation of the Cr-rich α' phase in a single-crystal alloy. The precipitation rate and the size distribution of the precipitated phase were analyzed. Subsequently, the model is utilized to simulate segregation at GBs in a double-crystal system, analyzing the enrichment of Cr and depletion of Al near these boundaries. The simulation results are consistent with experimental observations reported in the references. Finally, the model is applied to simulate the precipitation in a polycrystalline Fe-Cr-Al system. The simulated results revealed that the presence of GBs induces the formation of localized regions with enhanced Cr and Al content as well as depleted zones adjacent to these boundaries. GBs also diminish both the quantity and precipitation rate of the formed phase within the grains.

Analyzing the Effects of Cr and Mo on the Pearlite Formation in Hypereutectoid Steel Using Experiments and Phase Field Numerical Simulations.

In this study, we quantitatively investigate the impact of 1.4 wt.% chromium and 1.4 wt.% molybdenum additions on pearlitic microstructure characteristics in 1 wt.% carbon steels. The study was carried out using a combination of experimental methods and phase field simulations. We utilized MatCalc v5.51 and JMatPro v12 to predict transformation behaviors, and electron microscopy for microstructural examination, focusing on pearlite morphology under varying thermal conditions. Phase field simulations were carried out using MICRESS v7.2 software and, informed by thermodynamic data from MatCalc v5.51 and the literature, were conducted to replicate pearlite formation, demonstrating a good agreement with the experimental observations. In this work, we introduced a semi-automatic reliable microstructural analysis method, quantifying features like lamella dimensions and spacing through image processing by Fiji ImageJ v1.54f. The introduction of Cr resulted in longer, thinner, and more homogeneously distributed cementite lamellae, while Mo led to shorter, thicker lamellae. Phase field simulations accurately predicted these trends and showed that alloying with Cr or Mo increases the density and circularity of the lamellae. Our results demonstrate that Cr stabilizes pearlite formation, promoting a uniform microstructure, whereas Mo affects the morphology without enhancing homogeneity. The phase field model, validated by experimental data, provides insights into the morphological changes induced by these alloying elements, supporting the optimization of steel processing conditions.

Modeling fracture in multilayered teeth using the finite volume-based phase field method.

The present work, utilizing the finite volume-based phase field method (FV-based PFM), aims to investigate the initiation and propagation of cracks in the second molar of the left mandible under occlusal loading. By reconstructing cone beam computed tomography scans of the patient, the true morphology and internal mesostructure of the entire tooth are implemented into numerical simulations, including both 2D slice models and a realistic 3D model. Weibull functions are introduced to represent the tooth's heterogeneity, enabling the stochastic distribution characteristics of mechanical parameters. The results indicate that stronger heterogeneity leads to greater crack tortuosity, uneven damage distribution, and lower fracture stress. Additionally, different cusp angles (50° and 70°) and pre-existing fissure morphologies (i.e., U-shape, V-shape, IK-shape, I-shape, and IY-shape) also significantly affect the mechanical performance of the tooth. The study reveals that different cusp angles affect the location of crack initiation. Overall, this work demonstrates the utility of the FV-based PFM framework in capturing the complex fracture behavior of teeth, which can contribute to improved clinical treatment and prevention of tooth fractures. The insights gained from this study can inform the design of dental crown restorations and the optimization of cusp inclination and contact during clinical occlusal adjustments.

Ferroelectric Texture of Individual Barium Titanate Nanocrystals.

Ferroelectric materials display exotic polarization textures at the nanoscale that could be used to improve the energetic efficiency of electronic components. The vast majority of studies were conducted in two dimensions on thin films that can be further nanostructured, but very few studies address the situation of individual isolated nanocrystals (NCs) synthesized in solution, while such structures could have other fields of applications. In this work, we experimentally and theoretically studied the polarization texture of ferroelectric barium titanate (BaTiO3, BTO) NCs attached to a conductive substrate and surrounded by air. We synthesized NCs of well-defined quasicubic shape and 160 nm average size that conserve the tetragonal structure of BTO at room temperature. We then investigated the inverse piezoelectric properties of such pristine individual NCs by vector piezoresponse force microscopy (PFM), taking particular care to suppress electrostatic artifacts. In all of the NCs studied, we could not detect any vertical PFM signal, and the maps of the lateral response all displayed larger displacement amplitude on the edges with deformations converging toward the center. Using field phase simulations dedicated to ferroelectric nanostructures, we were able to predict the equilibrium polarization texture. These simulations revealed that the NC core is composed of 180° up and down domains defining the polar axis that rotate by 90° in the two facets orthogonal to this axis, eventually lying within these planes forming a layer of about 10 nm thickness mainly composed of 180° domains along an edge. From this polarization distribution, we predicted the lateral PFM response, which was revealed to be in very good qualitative agreement with the experimental observations. This work positions PFM as a relevant tool to evaluate the potential of complex ferroelectric nanostructures to be used as sensors.

Development of bone surrogates by material extrusion-based additive manufacturing to mimic flexural mechanical behaviour and fracture prediction via phase-field approach.

BACKGROUND AND OBJECTIVE: The limited availability of human bone samples for investigation leads to the demand for alternatives. Bone surrogates are crucial in promoting research on the intricate mechanics of osseous tissue. However, solutions are restricted to commercial brands, which frequently fail to faithfully replicate the mechanical response of bone, or oversimplified customised simulants designed for a specific application. The manufacturing and assessment of reliable bone surrogates made of polylactic acid via material extrusion-based additive manufacturing are presented in this work. METHODS: An experimental and numerical study with 3D-printed dog-bone and prismatic specimens was carried out to characterise the polymeric feedstock and analyse the influence of process parameters under three-point bending and quasi-static conditions. Besides, three porcine rib samples were considered as a reference for the development of the artificial bones. Bone surrogates were manufactured from the 3D-scanned real bone geometries. In order to reproduce the trabecular and cortical bone, a lattice structure for the infill and a compact shell surrounding the core were employed. Infill density and shell thickness were evaluated through different printing configurations. Additionally, a computational analysis based on the phase-field approach was conducted to simulate the experimental tests and predict fracture. The modelling considered homogenisation of the infill material. RESULTS: Outcomes demonstrated the potential of the presented methodology. Maximum force and flexural stiffness were compared to real bone properties to find the optimal printing configuration, replicating the flexural mechanical behaviour of bone tissue. Certain configurations accurately reproduce the studied properties. Regarding the numerical model, strength and stiffness prediction was validated with experimental results. CONCLUSIONS: The presented methodology enables the manufacturing of artificial bones with accurate geometries and tailored mechanical properties. Furthermore, the described modelling strategy offers a powerful tool for designing bone surrogates.

Mesoscopic elasticity controls dynamin-driven fission of lipid tubules.

Mesoscale physics bridges the gap between the microscopic degrees of freedom of a system and its large-scale continuous behavior and highlights the role of a few key quantities in complex and multiscale phenomena, like dynamin-driven fission of lipid membranes. The dynamin protein wraps the neck formed during clathrin-mediated endocytosis, for instance, and constricts it until severing occurs. Although ubiquitous and fundamental for life, the cooperation between the GTP-consuming conformational changes within the protein and the full-scale response of the underlying lipid substrate is yet to be unraveled. In this work, we build an effective mesoscopic model from constriction to fission of lipid tubules based on continuum membrane elasticity and implicitly accounting for ratchet-like power strokes of dynamins. Localization of the fission event, the overall geometry, and the energy expenditure we predict comply with the major experimental findings. This bolsters the idea that a continuous picture emerges soon enough to relate dynamin polymerization length and membrane rigidity and tension with the optimal pathway to fission. We therefore suggest that dynamins found in in vivo processes may optimize their structure accordingly. Ultimately, we shed light on real-time conductance measurements available in literature and predict the fission time dependency on elastic parameters.

Dislocation loop and irradiation-induced synergistic-competitive mechanism in Cu-rich precipitates: a phase-field study.

Both irradiation and dislocations have been proposed as routes to rationally manipulate spatial distribution and micromorphology of precipitate. An interesting effect emerges in Fe-10at.%Cu-3at.%Mn-1.5at.%Ni-1.5at.%Al alloy due to the synergistic-competitive roles of dislocation loop and irradiation. Base on cascade mixing, vacancy-interstitial atoms and dislocation stress field model, we examine nucleation and growth dynamics of Cu-rich precipitates, where both dislocation loop and irradiation act in conjunction. Analytical treatments identify regimes, where the distribution of elements and point defects due to irradiation and dislocations are specific to the Cu-rich precipitates. Simulation results reveal that density, size and distribution of Cu-rich precipitates are a manifestation of the competing effects of the dislocation loop and the irradiation rate. More specifically, the dislocation loop preferentially assists the formation of precipitates and new dislocations at lower irradiation rates. Only the irradiation induces the formation of Cu-rich precipitates with the irradiation rate continues to increase. Equipped with molecular dynamics, where reproduces major interaction features of the solutes with point defects under displacement cascade, can verify multi-component morphologies of Cu-rich precipitates. This modeling framework provides an avenue to explore the role of dislocation loop and irradiation on the microstructural evolution of Cu-rich precipitates.

Balancing Polarization and Breakdown for High Capacitive Energy Storage by Microstructure Design.

The compromise of contradictive parameters, polarization, and breakdown strength, is necessary to achieve a high energy storage performance. The two can be tuned, regardless of material types, by controlling microstructures: amorphous states possess higher breakdown strength, while crystalline states have larger polarization. However, how to achieve a balance of amorphous and crystalline phases requires systematic and quantitative investigations. Herein, the trade-off between polarization and breakdown field is comprehensively evaluated with the evolution of microstructure, i.e., grain size and crystallinity, by phase-field simulations. The results indicate small grain size (≈10-35 nm) with moderate crystallinity (≈60-80%) is more beneficial to maintain relatively high polarization and breakdown field simultaneously, consequently contributing to a high overall energy storage performance. Experimentally, therefore an ultrahigh energy density of 131 J cm-3 is achieved with a high efficiency of 81.6% in the microcrystal-amorphous dual-phase Bi3NdTi4O12 films. This work provides a guidance to substantially enhance dielectric energy storage by a simple and effective microstructure design.

Achieving Ultrahigh Electrocaloric Response in (Bi0.5Na0.5)TiO3-Based Ceramics through B-Site Defect Engineering.

Lead-free electrocaloric (EC) ferroelectrics are considered ideal for the next generation of environmentally friendly solid-state refrigeration materials. However, their inferior performance compared to lead-based materials significantly restricts their potential application. According to phase-field simulations, it is predicted that the pinning effect of a moderate number of defects can effectively enhance the reversible polarization response associated with the entropy change. Herein, sodium-bismuth titanate (BNT) ceramics with high spontaneous polarization are selected to construct B-site defects by introducing Li+ and Nb5+. Under an electric field of 6 kV mm-1, ultrahigh EC temperature changes of ΔTpos = 1.77 and ΔTneg = 1.49 K are achieved at 65 °C by direct measurement (ΔTneg > 1 K over 55-120 °C). Furthermore, ΔTneg remains above 0.70 K in the temperature range from 25 to 130 °C, exhibiting immense potential for practical applications. This study offers a promising direction for optimizing the EC response in defect systems.

"What makes blood clots break off?" A Back-of-the-Envelope Computation Toward Explaining Clot Embolization.

PURPOSE: One in four deaths worldwide is due to thromboembolic disease; that is, one in four people die from blood clots first forming and then breaking off or embolizing. Once broken off, clots travel downstream, where they occlude vital blood vessels such as those of the brain, heart, or lungs, leading to strokes, heart attacks, or pulmonary embolisms, respectively. Despite clots' obvious importance, much remains to be understood about clotting and clot embolization. In our work, we take a first step toward untangling the mystery behind clot embolization and try to answer the simple question: "What makes blood clots break off?" METHODS: To this end, we conducted experimentally-informed, back-of-the-envelope computations combining fracture mechanics and phase-field modeling. We also focused on deep venous clots as our model problem. RESULTS: Here, we show that of the three general forces that act on venous blood clots-shear stress, blood pressure, and wall stretch-induced interfacial forces-the latter may be a critical embolization force in occlusive and non-occlusive clots, while blood pressure appears to play a determinant role only for occlusive clots. Contrary to intuition and prior reports, shear stress, even when severely elevated, appears unlikely to cause embolization. CONCLUSION: This first approach to understanding the source of blood clot bulk fracture may be a critical starting point for understanding blood clot embolization. We hope to inspire future work that will build on ours and overcome the limitations of these back-of-the-envelope computations.

Development and Calibration of a Phenomenological Material Model for Steel-Fiber-Reinforced High-Performance Concrete Based on Unit Cell Calculations.

A phenomenological material model has been developed to facilitate the efficient numerical analysis of fiber-reinforced high-performance concrete (HPC). The formulation integrates an elasto-plastic phase-field model for simulating fractures within the HPC matrix, along with a superimposed one-dimensional elasto-plasticity model that represents the behavior of the embedded fibers. The Drucker-Prager plasticity and one-dimensional von-Mises plasticity formulations are incorporated to describe the nonlinear material behavior of both the HPC matrix and the fibers, respectively. Specific steps are undertaken during the development and calibration of the phenomenological material model. In the initial step, an experimental and numerical analysis of the pullout test of steel fibers embedded in an HPC matrix is conducted. This process is used to calibrate the micro-mechanical model based on the elasto-plastic phase-field formulation for fracture. In the subsequent step, virtual experiments based on an ellipsoidal unit cell, also with the resolution of fibers (used as a representative volume element, RVE), are simulated to analyze the impact of fiber-matrix interactions and their physical properties on the effective material behavior of fiber-reinforced HPC. In the final step, macroscopic boundary value problems (BVPs) based on a cuboid are simulated on a single scale using the developed phenomenological material model. The resulting macroscopic stress-strain characteristics obtained from both types of simulations, namely simulations of virtual experiments and macroscopic BVPs, are compared. This comparison is utilized for the calibration of material parameters to obtain a regularized solution and to assess the effectiveness of the presented phenomenological material model.

Fracture behavior of human cortical bone with high glycation content under dynamic loading.

The present study simulates the fracture behavior of diabetic cortical bone with high levels of advanced glycation end-products (AGEs) under dynamic loading. We consider that the increased AGEs in diabetic cortical bone degrade the materials heterogeneity of cortical bone through a reduction in critical energy release rates of the microstructural features. To simulate the initiation and propagation of cracks, we implement a phase field fracture framework on 2D models of human tibia cortical microstructure. The simulations show that the mismatch between the fracture properties (e.g., critical energy release rate) of osteons and interstitial tissue due to high AGEs contents can change crack growth trajectories. The results show crack branching in the cortical microstructure under dynamic loading is affected by the mismatches related to AGEs. In addition, we observe cortical features such as osteons and cement lines can prevent multiple cracking under dynamic loading even with changing the mismatches due to high AGEs. Furthermore, under dynamic loading, some toughening mechanisms can be activated and deactivated with different AGEs contents. In conclusion, the current findings present that the combination of the loading type and materials heterogeneity of microstructural features can change the fracture response of diabetic cortical bone and its fragility.