Poly-, Quasi- and Rank-One Convexity in Applied Mechanics
Poly-, Quasi- and Rank-One Convexity in Applied Mechanics

Author: Jörg Schröder

Publisher: Springer Science & Business Media

Published: 2010-08-04

Total Pages: 361

ISBN-13: 3709101743

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Generalized convexity conditions play a major role in many modern mechanical applications. They serve as the basis for existence proofs and allow for the design of advanced algorithms. Moreover, understanding these convexity conditions helps in deriving reliable mechanical models. The book summarizes the well established as well as the newest results in the field of poly-, quasi and rank-one convexity. Special emphasis is put on the construction of anisotropic polyconvex energy functions with applications to biomechanics and thin shells. In addition, phase transitions with interfacial energy and the relaxation of nematic elastomers are discussed.

Mathematical Methods in Continuum Mechanics of Solids
Mathematical Methods in Continuum Mechanics of Solids

Author: Martin Kružík

Publisher: Springer

Published: 2019-03-02

Total Pages: 624

ISBN-13: 3030020657

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This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear or quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited. This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields.

Plasticity and Beyond
Plasticity and Beyond

Author: Jörg Schröder

Publisher: Springer Science & Business Media

Published: 2013-09-20

Total Pages: 417

ISBN-13: 3709116252

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The book presents the latest findings in experimental plasticity, crystal plasticity, phase transitions, advanced mathematical modeling of finite plasticity and multi-scale modeling. The associated algorithmic treatment is mainly based on finite element formulations for standard (local approach) as well as for non-standard (non-local approach) continua and for pure macroscopic as well as for directly coupled two-scale boundary value problems. Applications in the area of material design/processing are covered, ranging from grain boundary effects in polycrystals and phase transitions to deep-drawing of multiphase steels by directly taking into account random microstructures.

Trends in Applications of Mathematics to Mechanics
Trends in Applications of Mathematics to Mechanics

Author: Elisabetta Rocca

Publisher: Springer

Published: 2018-04-27

Total Pages: 374

ISBN-13: 331975940X

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This volume originates from the INDAM Symposium on Trends on Applications of Mathematics to Mechanics (STAMM), which was held at the INDAM headquarters in Rome on 5–9 September 2016. It brings together original contributions at the interface of Mathematics and Mechanics. The focus is on mathematical models of phenomena issued from various applications. These include thermomechanics of solids and gases, nematic shells, thin films, dry friction, delamination, damage, and phase-field dynamics. The papers in the volume present novel results and identify possible future developments. The book is addressed to researchers involved in Mathematics and its applications to Mechanics.

Variational Views in Mechanics
Variational Views in Mechanics

Author: Paolo Maria Mariano

Publisher: Springer Nature

Published: 2022-02-08

Total Pages: 315

ISBN-13: 3030900517

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This volume provides a timely survey of interactions between the calculus of variations and theoretical and applied mechanics. Chapters have been significantly expanded since preliminary versions appeared in a special issue of the Journal of Optimization Theory and Applications (184(1), 2020) on “Calculus of Variations in Mechanics and Related Fields”. The variety of topics covered offers researchers an overview of problems in mechanics that can be analyzed with variational techniques, making this a valuable reference for researchers in the field. It also presents ideas for possible future areas of research, showing how the mastery of these foundational mathematical techniques can be used for many exciting applications. Specific topics covered include: Topology optimization Identification of material properties Optimal control Plastic flows Gradient polyconvexity Obstacle problems Quasi-monotonicity Variational Views in Mechanics will appeal to researchers in mathematics, solid-states physics, and mechanical, civil, and materials engineering.

Adhesive Joints
Adhesive Joints

Author: Wulff Possart

Publisher: John Wiley & Sons

Published: 2019-02-11

Total Pages: 538

ISBN-13: 3527341854

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A comprehensive overview of adhesive bonding, providing both basic knowledge of polymer adhesives as well as insights into their mechanical and ageing properties. The book is unique in its up-to-date, self-contained summary of recent developments and in its integration of the theory, synthesis and mechanical properties of adhesive joints as well as their applications. Well-structured throughout, the first chapter introduces the initial state of adhesive joints and their formation, while subsequent chapters discuss the ageing and failure as well as the weathering of adhesive joints. In addition the issue of long-term behavior and lifetime predictions are considered. The text is rounded off by a look at future technological advances. The result is an essential reference for a wide range of disciplines

Constitutive Modelling and Failure Prediction for Silicone Adhesives in Façade Design
Constitutive Modelling and Failure Prediction for Silicone Adhesives in Façade Design

Author: Michael Drass

Publisher: Springer Nature

Published: 2020-02-21

Total Pages: 304

ISBN-13: 3658292555

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This book provides readers with an elementary understanding of the material behavior of structural silicones in façades. Based on extensive experimental investigations on a transparent structural silicone adhesive (TSSA), the material behavior, failure, and microscopic effects such as stress whitening, cavitation failure, and the Mullins effect are analyzed. In turn, novel hyperelastic material models are developed to account for nonlinear material behavior under arbitrary deformations. The development of a volumetric hyperelastic model makes it possible for the first time to approximate the structural behavior of TSSA under constrained tensile load and cavitation. The material models discussed here were implemented in a finite element code for validation, and their quality was confirmed by three-dimensional numerical simulations, in which an additional stretch-based failure criterion was evaluated for failure prediction. The numerical studies are in good agreement with the experimental results.

Mathematical Elasticity
Mathematical Elasticity

Author: Philippe G. Ciarlet

Publisher: SIAM

Published: 2022-01-22

Total Pages: 521

ISBN-13: 1611976782

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The first book of a three-volume set, Three-Dimensional Elasticity covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. It includes the known existence theorems, either via the implicit function theorem or via the minimization of the energy (John Ball’s theory). An extended preface and extensive bibliography have been added to highlight the progress that has been made since the volume’s original publication. While each one of the three volumes is self-contained, together the Mathematical Elasticity set provides the only modern treatise on elasticity; introduces contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells; and contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.

Shell Structures: Theory and Applications (Vol. 2)
Shell Structures: Theory and Applications (Vol. 2)

Author: Wojciech Pietraszkiewicz

Publisher: CRC Press

Published: 2009-09-22

Total Pages: 361

ISBN-13: 0203859766

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Shell Structures. Theory and Applications, Volume 2 contains 77 contributions from over 17 countries, reflecting a wide spectrum of scientific and engineering problems of shell structures. The papers are divided into six broad groups: 1. General lectures; 2. Theoretical modeling; 3. Stability; 4. Dynamics; 5. Numerical analysis; 6. Engineering

The Role of Mechanics in the Study of Lipid Bilayers
The Role of Mechanics in the Study of Lipid Bilayers

Author: David J. Steigmann

Publisher: Springer

Published: 2017-05-23

Total Pages: 338

ISBN-13: 3319563483

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This book is the first collection of lipid-membrane research conducted by leading mechanicians and experts in continuum mechanics. It brings the overall intellectual framework afforded by modern continuum mechanics to bear on a host of challenging problems in lipid membrane physics. These include unique and authoritative treatments of differential geometry, shape elasticity, surface flow and diffusion, interleaf membrane friction, phase transitions, electroelasticity and flexoelectricity, and computational modelling.