Application of configurational mechanics to crack propagation

Crack initiation and propagation is an essential aspect in the mechanical behavior of a large variety of materials and structures in all fields of Engineering and, in particular, the prediction of crack trajectories is one of the major challenges of existing numerical methods. Classical procedures to fix crack direction have been based on local criteria such as maximum (tensile) hope stress. However, Fracture Mechanics principles suggest that global criteria should be used instead, such as maximizing structural energy release rates. An emerging trend along this way is based on Configurational Mechanics, which describes a dual version of the mechanical problem in terms of configurational pseudo-stresses, pseudo-forces, etc. all with a physical meaning related to the change in global structural elastic energy caused by changes in the structural geometry (configuration). In the FEM context, these concepts are applied to optimize the total energy of the mesh with respect to reference coordinates using the discrete configurational forces. Configurational stresses given by Eshelby’s energy-momentum tensor may be integrated using standard expressions to give configurational nodal forces. Adequate treatment of these forces in the context of iterative FE calculations, may lead to prediction of crack trajectories in terms of global structural energy

Three-dimensional CFD simulations with large displacement of the geometries using a connectivity-change moving mesh approach

This paper deals with three-dimensional (3D) numerical simulations involving 3D moving geometries with large displacements on unstructured meshes. Such simulations are of great value to industry, but remain very time-consuming. A robust moving mesh algorithm coupling an elasticity-like mesh deformation solution and mesh optimizations was proposed in previous works, which removes the need for global remeshing when performing large displacements. The optimizations, and in particular generalized edge/face swapping, preserve the initial quality of the mesh throughout the simulation. We propose to integrate an Arbitrary Lagrangian Eulerian compressible flow solver into this process to demonstrate its capabilities in a full CFD computation context. This solver relies on a local enforcement of the discrete geometric conservation law to preserve the order of accuracy of the time integration. The displacement of the geometries is either imposed, or driven by fluid–structure interaction (FSI). In the latter case, the six degrees of freedom approach for rigid bodies is considered. Finally, several 3D imposed-motion and FSI examples are given to validate the proposed approach, both in academic and industrial configurations

On 3-D inelastic analysis methods for hot section components (base program)

A 3-D Inelastic Analysis Method program is described. This program consists of a series of new computer codes embodying a progression of mathematical models (mechanics of materials, special finite element, boundary element) for streamlined analysis of: (1) combustor liners, (2) turbine blades, and (3) turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain)and global (dynamics, buckling) structural behavior of the three selected components. Three computer codes, referred to as MOMM (Mechanics of Materials Model), MHOST (Marc-Hot Section Technology), and BEST (Boundary Element Stress Technology), have been developed and are briefly described in this report

Robust interactive simulation of deformable solids with detailed geometry using corotational FEM

This thesis focuses on the interactive simulation of highly detailed deformable solids modelled with the Corotational Finite Element Method. Starting from continuum mechanics we derive the discrete equations of motion and present a simulation scheme with support for user-in-the-loop interaction, geometric constraints and contact treatment. The interplay between accuracy and computational cost is discussed in depth, and practical approximations are analyzed with an emphasis on robustness and efficiency, as required by interactive simulation. The first part of the thesis focuses on deformable material discretization using the Finite Element Method with simplex elements and a corotational linear constitutive model, and presents our contributions to the solution of widely reported robustness problems in case of large stretch deformations and finite element degeneration. First,we introduce a stress differential approximation for quasi-implicit corotational linear FEM that improves its results for large deformations and closely matches the fullyimplicit solution with minor computational overhead. Next, we address the problem ofrobustness and realism in simulations involving element degeneration, and show that existing methods have previously unreported flaws that seriously threaten robustness and physical plausibility in interactive applications. We propose a new continuous-time approach, degeneration-aware polar decomposition, that avoids such flaws and yields robust degeneration recovery. In the second part we focus on geometry representation and contact determination for deformable solids with highly detailed surfaces. Given a high resolution closed surface mesh we automatically build a coarse embedding tetrahedralization and a partitioned representation of the collision geometry in a preprocess. During simulation, our proposed contact determination algorithm finds all intersecting pairs of deformed triangles using a memory-efficient barycentric bounding volume hierarchy, connects them into potentially disjoint intersection curves and performs a topological flood process on the exact intersection surfaces to discover a minimal set of contact points. A novel contact normal definition is used to find contact point correspondences suitable for contact treatment.Aquesta tesi tracta sobre la simulació interactiva de sòlids deformables amb superfícies detallades, modelats amb el Mètode dels Elements Finits (FEM) Corotacionals. A partir de la mecànica del continuu derivem les equacions del moviment discretes i presentem un esquema de simulació amb suport per a interacció d'usuari, restriccions geomètriques i tractament de contactes. Aprofundim en la interrelació entre precisió i cost de computació, i analitzem aproximacions pràctiques fent èmfasi en la robustesa i l'eficiència necessàries per a la simulació interactiva. La primera part de la tesi es centra en la discretització del material deformable mitjançant el Mètode dels Elements Finits amb elements de tipus s'implex i un model constituent basat en elasticitat linial corotacional, i presenta les nostres contribucions a la solució de problemes de robustesa àmpliament coneguts que apareixen en cas de sobreelongament i degeneració dels elements finits. Primer introduïm una aproximació dels diferencials d'estress per a FEM linial corotacional amb integració quasi-implícita que en millora els resultats per a deformacions grans i s'apropa a la solució implícita amb un baix cost computacional. A continuació tractem el problema de la robustesa i el realisme en simulacions que inclouen degeneració d'elements finits, i mostrem que els mètodes existents presenten inconvenients que posen en perill la robustesa plausibilitat de la simulació en aplicacions interactives. Proposem un enfocament nou basat en temps continuu, la descomposició polar amb coneixement de degeneració, que evita els inconvenients esmentats i permet corregir la degeneració de forma robusta. A la segona part de la tesi ens centrem en la representació de geometria i la determinació de contactes per a sòlids deformables amb superfícies detallades. A partir d'una malla de superfície tancada construím una tetraedralització englobant de forma automàtica en un preprocés, i particionem la geometria de colisió. Proposem un algorisme de detecció de contactes que troba tots els parells de triangles deformats que intersecten mitjançant una jerarquia de volums englobants en coordenades baricèntriques, els connecta en corbes d'intersecció potencialment disjuntes i realitza un procés d'inundació topològica sobre les superfícies d'intersecció exactes per tal de descobrir un conjunt mínim de punts de contacte. Usem una definició nova de la normal de contacte per tal de calcular correspondències entre punts de contacte útils per al seu tractament.Postprint (published version

Modelling mitral valvular dynamics–current trend and future directions

Dysfunction of mitral valve causes morbidity and premature mortality and remains a leading medical problem worldwide. Computational modelling aims to understand the biomechanics of human mitral valve and could lead to the development of new treatment, prevention and diagnosis of mitral valve diseases. Compared with the aortic valve, the mitral valve has been much less studied owing to its highly complex structure and strong interaction with the blood flow and the ventricles. However, the interest in mitral valve modelling is growing, and the sophistication level is increasing with the advanced development of computational technology and imaging tools. This review summarises the state-of-the-art modelling of the mitral valve, including static and dynamics models, models with fluid-structure interaction, and models with the left ventricle interaction. Challenges and future directions are also discussed

Enhancing Mesh Deformation Realism: Dynamic Mesostructure Detailing and Procedural Microstructure Synthesis

Propomos uma solução para gerar dados de mapas de relevo dinâmicos para simular deformações em superfícies macias, com foco na pele humana. A solução incorpora a simulação de rugas ao nível mesoestrutural e utiliza texturas procedurais para adicionar detalhes de microestrutura estáticos. Oferece flexibilidade além da pele humana, permitindo a geração de padrões que imitam deformações em outros materiais macios, como couro, durante a animação. As soluções existentes para simular rugas e pistas de deformação frequentemente dependem de hardware especializado, que é dispendioso e de difícil acesso. Além disso, depender exclusivamente de dados capturados limita a direção artística e dificulta a adaptação a mudanças. Em contraste, a solução proposta permite a síntese dinâmica de texturas que se adaptam às deformações subjacentes da malha de forma fisicamente plausível. Vários métodos foram explorados para sintetizar rugas diretamente na geometria, mas sofrem de limitações como auto-interseções e maiores requisitos de armazenamento. A intervenção manual de artistas na criação de mapas de rugas e mapas de tensão permite controle, mas pode ser limitada em deformações complexas ou onde maior realismo seja necessário. O nosso trabalho destaca o potencial dos métodos procedimentais para aprimorar a geração de padrões de deformação dinâmica, incluindo rugas, com maior controle criativo e sem depender de dados capturados. A incorporação de padrões procedimentais estáticos melhora o realismo, e a abordagem pode ser estendida além da pele para outros materiais macios.We propose a solution for generating dynamic heightmap data to simulate deformations for soft surfaces, with a focus on human skin. The solution incorporates mesostructure-level wrinkles and utilizes procedural textures to add static microstructure details. It offers flexibility beyond human skin, enabling the generation of patterns mimicking deformations in other soft materials, such as leater, during animation. Existing solutions for simulating wrinkles and deformation cues often rely on specialized hardware, which is costly and not easily accessible. Moreover, relying solely on captured data limits artistic direction and hinders adaptability to changes. In contrast, our proposed solution provides dynamic texture synthesis that adapts to underlying mesh deformations. Various methods have been explored to synthesize wrinkles directly to the geometry, but they suffer from limitations such as self-intersections and increased storage requirements. Manual intervention by artists using wrinkle maps and tension maps provides control but may be limited to the physics-based simulations. Our research presents the potential of procedural methods to enhance the generation of dynamic deformation patterns, including wrinkles, with greater creative control and without reliance on captured data. Incorporating static procedural patterns improves realism, and the approach can be extended to other soft-materials beyond skin

TacIPC: Intersection- and Inversion-free FEM-based Elastomer Simulation For Optical Tactile Sensors

Tactile perception stands as a critical sensory modality for human interaction with the environment. Among various tactile sensor techniques, optical sensor-based approaches have gained traction, notably for producing high-resolution tactile images. This work explores gel elastomer deformation simulation through a physics-based approach. While previous works in this direction usually adopt the explicit material point method (MPM), which has certain limitations in force simulation and rendering, we adopt the finite element method (FEM) and address the challenges in penetration and mesh distortion with incremental potential contact (IPC) method. As a result, we present a simulator named TacIPC, which can ensure numerically stable simulations while accommodating direct rendering and friction modeling. To evaluate TacIPC, we conduct three tasks: pseudo-image quality assessment, deformed geometry estimation, and marker displacement prediction. These tasks show its superior efficacy in reducing the sim-to-real gap. Our method can also seamlessly integrate with existing simulators. More experiments and videos can be found in the supplementary materials and on the website: https://sites.google.com/view/tac-ipc