Drops on soft solids: Free energy and double transition of contact angles

The equilibrium shape of liquid drops on elastic substrates is determined by minimising elastic and capillary free energies, focusing on thick incompressible substrates. The problem is governed by three length scales: the size of the drop $R$, the molecular size $a$, and the ratio of surface tension to elastic modulus $\gamma/E$. We show that the contact angles undergo two transitions upon changing the substrates from rigid to soft. The microscopic wetting angles deviate from Young's law when $\gamma/Ea \gg 1$, while the apparent macroscopic angle only changes in the very soft limit $\gamma/ER \gg 1$. The elastic deformations are worked out in the simplifying case where the solid surface energy is assumed constant. The total free energy turns out lower on softer substrates, consistent with recent experiments

Locking-Proof Tetrahedra

The simulation of incompressible materials suffers from locking when using the standard finite element method (FEM) and coarse linear tetrahedral meshes. Locking increases as the Poisson ratio gets close to 0.5 and often lower Poisson ratio values are used to reduce locking, affecting volume preservation. We propose a novel mixed FEM approach to simulating incompressible solids that alleviates the locking problem for tetrahedra. Our method uses linear shape functions for both displacements and pressure, and adds one scalar per node. It can accommodate nonlinear isotropic materials described by a Young\u27s modulus and any Poisson ratio value by enforcing a volumetric constitutive law. The most realistic such material is Neo-Hookean, and we focus on adapting it to our method. For , we can obtain full volume preservation up to any desired numerical accuracy. We show that standard Neo-Hookean simulations using tetrahedra are often locking, which, in turn, affects accuracy. We show that our method gives better results and that our Newton solver is more robust. As an alternative, we propose a dual ascent solver that is simple and has a good convergence rate. We validate these results using numerical experiments and quantitative analysis

Numerical Methods for Fluid-Structure Interaction, and their Application to Flag Flapping

This thesis is divided into two parts. Part I is devoted to the development of numerical techniques for simulating fluid-structure interaction (FSI) systems and for educing important physical mechanisms that drive these systems’ behavior; part II discusses the application of many of these techniques to investigate a specific FSI system. Within part I, we first describe a procedure for accurately computing the stresses on an immersed surface using the immersed-boundary method. This is a key step to simulating FSI problems, as the surface stresses simultaneously dictate the motion of the structure and enforce the no-slip boundary condition on the fluid. At the same time, accurate stress computations are also important for applications involving rigid bodies that are either stationary or moving with prescribed kinematics (e.g., characterizing the performance of wings and aerodynamic bodies in unsteady flows or understanding and controlling flow separation around bluff bodies). Thus, the method is first formulated for the rigid-body prescribed-kinematics case. The procedure described therein is subsequently incorporated into an immersed boundary method for efficiently simulating FSI problems involving arbitrarily large structural motions and rotations. While these techniques can be used to perform high-fidelity simulations of FSI systems, the resulting data often involves a range of spatial and temporal scales in both the structure and the fluid and are thus typically difficult to interpret directly. The remainder of part I is therefore devoted to extending tools regularly used for understanding complex flows to FSI systems. We focus in particular on the application of global linear stability analysis and snapshot-based data analysis (such as dynamic mode decomposition and proper orthogonal decomposition) to FSI problems. To our knowledge, these techniques had not been applied to deforming-body problems in a manner that that accounts for both the fluid and structure leading up to this work. Throughout part I, our methods are derived in the context of fairly general FSI systems and are validated using results from the literature for flapping flags in both the conventional configuration (in which the flag is pinned or clamped at its leading edge with respect to the oncoming flow) and the inverted configuration (in which the flag is clamped at its trailing edge). In part II, we apply many of the techniques developed in part I to uncover new physical mechanisms about inverted-flag flapping. We identify the instability-driving mechanism responsible for the initiation of flapping and further characterize the large-amplitude and chaotic flapping regimes that the system undergoes for a range of physical parameters.</p

파티클 시뮬레이션을 이용한 물리 기반 비강체 정합 기술

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2013. 8. 신영길.Recent advances in computing hardware have enabled the application of physically based simulation techniques to various research fields for improved accuracy. In this paper, we present a novel physically based non-rigid registration method using smoothed particle hydrodynamics (SPH) for hepatic metastasis volume-preserving registration between follow-up liver CT images. Our method models the liver and hepatic metastasis as a set of particles carrying their own physical properties. Based on the fact that the hepatic metastasis is stiffer than other normal cells in the liver parenchyma, the candidate regions of hepatic metastasis are modeled with particles of higher stiffness compared to the liver parenchyma. Particles placed in the liver and candidate regions of hepatic metastasis in the source image are transformed along a gradient vector flow (GVF)-based force field calculated in the target image. In this transformation, the particles are physically interacted and deformed by a novel deformable particle method which is proposed to preserve the hepatic metastasis to the best. In experimental results using 10 clinical datasets, our method matches the liver effectively between follow-up CT images as well as preserves the volume of hepatic metastasis almost completely, enabling the accurate assessment of the volume change of the hepatic metastasis. These results demonstrated a potential of the proposed method that it can deliver a substantial aid in measuring the size change of index lesion (i.e., hepatic metastasis) after the chemotheraphy of metastasis patients in radiation oncology.최근 컴퓨팅 하드웨어의 발달은 정확도 향상을 위해 물리 기반의 시뮬레이션 기술을 다양한 연구 분야에 적용할 수 있게 하였다. 본 논문에서는 입자를 이용하여 시뮬레이션하는 방법 중 하나인 입자 보간 방식의 유체역학(smoothed particle hydrodynamics) 기술을 이용하여, 후속 컴퓨터 단층촬영 영상(computed tomography) 사이에 간전이(hepatic metastasis) 체적을 보전하는 물리 기반의 비정형체 정합 기술을 제안한다. 제안 방법은 간과 간전이를 물리적 속성을 동반하는 일련의 입자로 표현하며, 간전이가 정상 간에 비해 강한 탄성을 보인다는 사실에 기반하여 간전이로 짐작되는 부위를 상대적으로 강한 탄성을 갖는 입자로 표현하였다. 초기에 간과 간전이 후보 영역을 나타내는 입자들은 입력 영상의 해당 영역에 위치되며, 정합하고자 하는 대상 영상으로 부터 경사도 벡터 흐름(gradient vector flow) 방법으로 계산된 힘의 장을 따라 이동된다. 이 때, 각 입자는 간전이의 체적을 최대한 보존하기 위해 제안된 변형 가능 입자 방식에 따라 서로 물리적으로 상호작용하며 변형된다. 10명의 환자 데이터를 이용한 실험 결과에 따르면, 후속 컴퓨터 단층촬영(CT) 영상 간의 정합 과정에서 간의 모양을 효과적으로 일치시킬 뿐만 아니라 간전이의 체적을 거의 완벽하게 보존하여 간전이의 체적 변화를 정확하게 진단할 수 있게 하였다. 이 결과는 간전이 환자가 화학 요법을 시행 한 후 암의 진행 상태를 판단하기 위해 간전이의 크기 변화를 측정하는데 도움을 줄 수 있는 방법임을 시사한다.I. Introduction 1.1 Motivation 1 1.2 Dissertation Goals 3 1.3 Main Contribution 4 1.4 Organization of the Dissertation 5 II. Background 2.1 Medical Image Registration 6 2.1.1 Transformation Models 8 2.1.2 Similarity Metrics 18 2.1.3 Optimization 23 2.1.4 Physically Based Non-Rigid Registration 25 2.2 Smoothed Particle Hydrodynamics 29 2.2.1 Formulation of SPH 30 2.2.2 Kernels 33 2.2.3 Applications 35 III. Volume-Preserving Deformation of Particles 3.1 SPH for Deformable Objects 40 3.2 Volume-Preserving Deformable Particle 44 IV. Non-Rigid Registration with the Deformable Particles 4.1 Automatic Detection of Liver and Candidate Regions of Metastasis 50 4.2 Placement of Initial Particles in Source Image 53 4.3 Generation of GVF-based Force Field in Target Image 55 4.4 Non-Rigid Registration with Particles 58 4.5 Computation of Deformation Field 60 V. Implementation 5.1 Workflow 62 5.2 Neighbor Search 65 5.3 Time Integrator and Time Step 67 5.4 Terminating Condition 69 VI. Results 6.1 Phantom Study 71 6.2 General Observations based on Visual Assessment 73 6.3 Evaluation of Registration Performance 74 6.4 Evaluation of Metastasis Detection Accuracy 77 6.5 Evaluation of Volume Preservation 79 6.6 Parameter Study 80 VII. Conclusion 86 Bibliography 89Docto

Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

The 6th ECCOMAS Young Investigators Conference YIC2021 will take place from July 7th through 9th, 2021 at Universitat Politècnica de València, Spain. The main objective is to bring together in a relaxed environment young students, researchers and professors from all areas related with computational science and engineering, as in the previous YIC conferences series organized under the auspices of the European Community on Computational Methods in Applied Sciences (ECCOMAS). Participation of senior scientists sharing their knowledge and experience is thus critical for this event.YIC 2021 is organized at Universitat Politécnica de València by the Sociedad Española de Métodos Numéricos en Ingeniería (SEMNI) and the Sociedad Española de Matemática Aplicada (SEMA). It is promoted by the ECCOMAS.The main goal of the YIC 2021 conference is to provide a forum for presenting and discussing the current state-of-the-art achievements on Computational Methods and Applied Sciences,including theoretical models, numerical methods, algorithmic strategies and challenging engineering applications.Nadal Soriano, E.; Rodrigo Cardiel, C.; Martínez Casas, J. (2022). Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. https://doi.org/10.4995/YIC2021.2021.15320EDITORIA

Mechanics of Materials

All up-to-date engineering applications of advanced multi-phase materials necessitate a concurrent design of materials (including composition, processing routes, microstructures and properties) with structural components. Simulation-based material design requires an intensive interaction of solid state physics, material physics and chemistry, mathematics and information technology. Since mechanics of materials fuses many of the above fields, there is a pressing need for well founded quantitative analytical and numerical approaches to predict microstructure-process-property relationships taking into account hierarchical stationary or evolving microstructures. Owing to this hierarchy of length and time scales, novel approaches for describing/ modelling non-equilibrium material evolution with various degrees of resolution are crucial to linking solid mechanics with realistic material behavior. For example, approaches such as atomistic to continuum transitions (scale coupling), multiresolution numerics, and handshaking algorithms that pass information to models with different degrees of freedom are highly relevant in this context. Many of the topics addressed were dealt with in depth in this workshop

Modeling brittle fracture, slip weakening, and variable friction in geomaterials with an embedded strong discontinuity finite element.

Localized shear deformation plays an important role in a number of geotechnical and geological processes. Slope failures, the formation and propagation of faults, cracking in concrete dams, and shear fractures in subsiding hydrocarbon reservoirs are examples of important effects of shear localization. Traditional engineering analyses of these phenomena, such as limit equilibrium techniques, make certain assumptions on the shape of the failure surface as well as other simplifications. While these methods may be adequate for the applications for which they were designed, it is difficult to extrapolate the results to more general scenarios. An alternative approach is to use a numerical modeling technique, such as the finite element method, to predict localization. While standard finite elements can model a wide variety of loading situations and geometries quite well, for numerical reasons they have difficulty capturing the softening and anisotropic damage that accompanies localization. By introducing an enhancement to the element in the form of a fracture surface at an arbitrary position and orientation in the element, we can regularize the solution, model the weakening response, and track the relative motion of the surfaces. To properly model the slip along these surfaces, the traction-displacement response must be properly captured. This report focuses on the development of a constitutive model appropriate to localizing geomaterials, and the embedding of this model into the enhanced finite element framework. This modeling covers two distinct phases. The first, usually brief, phase is the weakening response as the material transitions from intact continuum to a body with a cohesionless fractured surface. Once the cohesion has been eliminated, the response along the surface is completely frictional. We have focused on a rate- and state-dependent frictional model that captures stable and unstable slip along the surface. This model is embedded numerically into the element using a generalized trapezoidal formulation. While the focus is on the constitutive model of interest, the framework is also developed for a general surface response. This report summarizes the major research and development accomplishments for the LDRD project titled 'Cohesive Zone Modeling of Failure in Geomaterials: Formulation and Implementation of a Strong Discontinuity Model Incorporating the Effect of Slip Speed on Frictional Resistance'. This project supported a strategic partnership between Sandia National Laboratories and Stanford University by providing funding for the lead author, Craig Foster, during his doctoral research

Microsphere Traction Force Microscopy

This work is a culmination of our efforts in understanding cellular mechanics at the scale of single cells and small tissues. We developed methods to quantify cell-generated traction forces using cell-sized, synthetic, functionalized hydrogel microspheres. Cell-sized solid microspheres can provide information regarding cell-generated normal and shear forces while allowing natural cell-cell interactions and facilitating a convex cell-hydrogel interface. Therefore, they are a better mimic than the current methods for understanding the natural cell-cell interactions in a physiologically relevant geometry. In the analysis of the microsphere deformations, we use a boundary spectral method based on spherical harmonics decomposition of the traction field on the spherical gel surface. Using the techniques developed here, we measure the boundary traction profiles that mammalian cells exert on the synthetic microspherical hydrogel bodies. In this report, we briefly review the state of the art in cellular force quantification methods and discuss the contributions of our work to the field and its strengths as well as its limitations

Mott Transition and Quantum Critical Metamagnetism on Compressible Lattices

Solid state phase transitions, which are amenable to pressure, generically, have an intrinsic coupling of the order parameter to the elastic degrees of freedom. The applied pressure primarily affects the lattice by varying the lattice spacing which, in turn, modifies the coupling constants of the critical degrees of freedom. Therefore, a coupling of the strain to the order parameter can strongly affect the phase transition. In this Thesis we investigate this influence on the finite temperature critical point of the Mott metal-insulator transition and the zero temperature quantum critical metamagnetic endpoint. The universality class of the Mott endpoint is a topic which is still under debate. In this Thesis, we show that the nature of the Mott transition is drastically changed when interacting with a compressible lattice. The expected Ising criticality of the electronic system is preempted by an isostructural instability. Due to long ranged shear forces, in the vicinity of the critical endpoint an elastic Landau regime emerges, where the system shows mean-field behavior. The smoking gun criterion to detect the elastic Landau regime is the breakdown of Hooke's law, i.e. a non-linear stress-strain relation. Furthermore, the specific heat coefficient exhibits a finite mean field jump at the transition. For the family of organic salts Kappa-(BEDT-TTF)_2 X, we determine the extent of the elastic Landau regime as \Delta T^\star \approx 2.5 K and \Delta p^\star \approx 50 bar based on thermal expansion experiments. In the second part, we investigate the quantum critical endpoint of itinerant metamagnets. Recently, it was suggested that quantum critical metamagnetism is a generic feature in itinerant ferromagnets such as UCoAl and UGe_2. Within the framework of spin fluctuation theory, we determine the free energy and its temperature dependence, obtained by fluctuation renormalizations, and deduce the critical thermodynamics. Importantly, the compressibility shows the same behavior as the susceptibility which, by definition, diverges at a metamagnetic transition. Therefore, the metamagnetic quantum critical endpoint is intrinsically unstable towards an isostructural transition. This isostructural transition preempts the metamagnetic quantum critical endpoint and the elastic degrees of freedom crucially alter the critical thermodynamics. Most importantly, at the critical field we obtain for lowest but finite temperatures a regime of critical elasticity which is characterized by unusual power laws of the thermodynamic quantities. Whereas the thermal expansion has a much stronger temperature divergence for fields close to the critical field, the specific heat divergence is cut off upon entering this regime. As a consequence, the Grüneisen parameter diverges with an unusual high power of temperature

Material length scales in gradient-dependent plasticity/damage and size effects: theory and computation

Structural materials display a strong size-dependence when deformed non-uniformly into the inelastic range: smaller is stronger. This effect has important implications for an increasing number of applications in structural failure, electronics, functional coatings, composites, micro-electro-mechanical systems (MEMS), nanostructured materials, micro/nanometer fabrication technologies, etc. The mechanical behavior of these applications cannot be characterized by classical (local) continuum theories because they incorporate no ‘material length scales’ and consequently predict no size effects. On the other hand, it is still not possible to perform quantum and atomistic simulations on realistic time and structures. It is therefore necessary to develop a scale-dependent continuum theory bridging the gap between the classical continuum theories and the atomistic simulations in order to be able to design the size-dependent structures of modern technology. Nonlocal rate-dependent and gradient-dependent theories of plasticity and damage are developed in this work for this purpose. We adopt a multi-scale, hierarchical thermodynamic consistent framework to construct the material constitutive relations for the scale-dependent plasticity/damage behavior. Material length scales are implicitly and explicitly introduced into the governing equations through material rate-dependency (viscosity) and coefficients of spatial higher-order gradients of one or more material state variables, respectively. The proposed framework is implemented into the commercially well-known finite element software ABAQUS. The finite element simulations of material instability problems converge to meaningful results upon further refinement of the finite element mesh, since the width of the fracture process zone (shear band) is determined by the intrinsic material length scale; while the classical continuum theories fail to address this problem. It is also shown that the proposed theory is successful for the interpretation of indentation size effects in micro/nano-hardness when using pyramidal and spherical indenters and gives sound interpretations of the size effects in micro-torsion of thin wires and micro-bending of thin beams. Future studies should be directed toward incorporation of the size effects into design procedures and code recommendations of modern engineering structures (e.g. for MEMS, NEMS, coatings, thin films), fiber composites (e.g. for aircrafts and ships), etc