This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

The aim of the present chapter is to provide an in-depth survey of arbitrary Lagrangian–Eulerian (ALE) methods, including both conceptual aspects of the mixed kinematical description and numerical implementation details. Applications are discussed in fluid dynamics, nonlinear solid mechanics and coupled problems describing fluid–structure interaction. The need for an adequate mesh-update strategy is underlined, and various automatic mesh-displacement prescription algorithms are reviewed. This includes mesh-regularization methods essentially based on geometrical concepts, as well as mesh-adaptation techniques aimed at optimizing the computational mesh according to some error indicator. Emphasis is then placed on particular issues related to the modeling of compressible and incompressible flow and nonlinear solid mechanics problems. This includes the treatment of convective terms in the conservation equations for mass, momentum, and energy, as well as a discussion of stress-update procedures for materials with history-dependent constitutive behavior.


Keywords:

ALE description;
convective transport;
finite elements;
stabilization techniques;
mesh regularization and adaptation;
fluid dynamics;
nonlinear solid mechanics;
stress-update procedures;
fluid–structure interaction

https://onlinelibrary.wiley.com/doi/pdf/10.1002/0470091355.ecm009

Arbitrary Lagrangian–Eulerian Methods

In the field of computational biomechanics, investigators have primarily used commercial software that is neither geared toward biological applications nor sufficiently flexible to follow the latest developments in the field This lack of a tailored software environment has hampered research progress, as well as dissemination of models and results To address these issues, we developed the FEBio software suite (http://mrlsciutahedu/software/febio), a nonlinear implicit finite element (FE) framework, designed specifically for analysis in computational solid biomechanics This paper provides an overview of the theoretical basis of FEBio and its main features FEBio offers modeling scenarios, constitutive models, and boundary conditions, which are relevant to numerous applications in biomechanics The open-source FEBio software is written in C++, with particular attention to scalar and parallel performance on modern computer architectures Software verification is a large part of the development and maintenance of FEBio, and to demonstrate the general approach, the description and results of several problems from the FEBio Verification Suite are presented and compared to analytical solutions or results from other established and verified FE codes An additional simulation is described that illustrates the application of FEBio to a research problem in biomechanics Together with the pre- and postprocessing software PREVIEW and POSTVIEW, FEBio provides a tailored solution for research and development in computational biomechanics

/pdf/febio-finite-elements-for-biomechanics-2r5v7f7rae.pdf

FEBio: finite elements for biomechanics.

Variational and momentum preservation aspects of Smooth Particle Hydrodynamic formulations

Physically based deformable models have been widely embraced by the Computer Graphics community. Many problems outlined in a previous survey by Gibson and Mirtich [ GM97] have been addressed, thereby making these models interesting and useful for both offline and real-time applications, such as motion pictures and video games. In this paper, we present the most significant contributions of the past decade, which produce such impressive and perceivably realistic animations and simulations: finite element/difference/volume methods, mass-spring systems, meshfree methods, coupled particle systems and reduced deformable models based on modal analysis. For completeness, we also make a connection to the simulation of other continua, such as fluids, gases and melting objects. Since time integration is inherent to all simulated phenomena, the general notion of time discretization is treated separately, while specifics are left to the respective models. Finally, we discuss areas of application, such as elastoplastic deformation and fracture, cloth and hair animation, virtual surgery simulation, interactive entertainment and fluid/smoke animation, and also suggest areas for future research.

/pdf/physically-based-deformable-models-in-computer-graphics-rjirdt191n.pdf

Physically Based Deformable Models in Computer Graphics

Designing engineering components that make optimal use of materials requires consideration of the nonlinear characteristics associated with both manufacturing and working environments. The modeling of these characteristics can only be done through numerical formulation and simulation, and this requires an understanding of both the theoretical background and associated computer solution techniques. By presenting both nonlinear continuum analysis and associated finite element techniques under one roof, Bonet and Wood provide, in this edition of this successful text, a complete, clear, and unified treatment of these important subjects. New chapters dealing with hyperelastic plastic behavior are included, and the authors have thoroughly updated the FLagSHyP program, freely accessible at www.flagshyp.com. Worked examples and exercises complete each chapter, making the text an essential resource for postgraduates studying nonlinear continuum mechanics. It is also ideal for those in industry requiring an appreciation of the way in which their computer simulation programs work.

https://cdn.preterhuman.net/texts/science_and_technology/physics/Mechanics/Nonlinear%20Continuum%20Mechanics%20For%20Finite%20Element%20Analysis%20-%20Bonet,%20Wood.pdf

Nonlinear Continuum Mechanics for Finite Element Analysis

Designing engineering components that make optimal use of materials requires consideration of the nonlinear static and dynamic characteristics associated with both manufacturing and working environments. The modeling of these characteristics can only be done through numerical formulation and simulation, which requires an understanding of both the theoretical background and associated computer solution techniques. By presenting both the nonlinear solid mechanics and the associated finite element techniques together, the authors provide, in the first of two books in this series, a complete, clear, and unified treatment of the static aspects of nonlinear solid mechanics. Alongside a range of worked examples and exercises are user instructions, program descriptions, and examples for the FLagSHyP MATLAB computer implementation, for which the source code is available online. While this book is designed to complement postgraduate courses, it is also relevant to those in industry requiring an appreciation of the way their computer simulation programs work.

Nonlinear Solid Mechanics for Finite Element Analysis: Statics

Superplastic forming is a manufacturing process whereby titanium or aluminium sheet is blow formed into a die to produce very light and strong aerospace components. Of crucial importance is the prediction of the final thickness distribution and the pressure cycle necessary to maintain superplasticity. This paper discusses a finite element based solution to these problems and presents examples for typical components including diffusion bonding effects.

Richard D. Wood

Papers

Nonlinear Continuum Mechanics for Finite Element Analysis

Nonlinear Solid Mechanics for Finite Element Analysis: Statics

Numerical simulation of the superplastic forming of thin sheet components using the finite element method

Simulating superplastic forming

Pressure-control algorithms for the numerical simulation of superplastic forming