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Author: Jörg Schröder Publisher: Springer Science & Business Media ISBN: 3709101743 Category : Technology & Engineering Languages : en Pages : 361
Book Description
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.
Author: Jörg Schröder Publisher: Springer Science & Business Media ISBN: 3709101743 Category : Technology & Engineering Languages : en Pages : 361
Book Description
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.
Author: Boyan Sirakov Publisher: World Scientific ISBN: 9813272899 Category : Mathematics Languages : en Pages : 5393
Book Description
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Author: Arkadi Berezovski Publisher: Springer ISBN: 3319569341 Category : Science Languages : en Pages : 222
Book Description
This book describes an effective method for modeling advanced materials like polymers, composite materials and biomaterials, which are, as a rule, inhomogeneous. The thermoelastic theory with internal variables presented here provides a general framework for predicting a material’s reaction to external loading. The basic physical principles provide the primary theoretical information, including the evolution equations of the internal variables. The cornerstones of this framework are the material representation of continuum mechanics, a weak nonlocality, a non-zero extra entropy flux, and a consecutive employment of the dissipation inequality. Examples of thermoelastic phenomena are provided, accompanied by detailed procedures demonstrating how to simulate them.
Author: Felix Dillenberger Publisher: Springer Nature ISBN: 3658281995 Category : Technology & Engineering Languages : en Pages : 238
Book Description
A requirement for the safe design of thermoplastic parts is the ability to precisely predict mechanical behaviour by finite element simulations. Typical examples include the engineering of relevant components in automotive applications. For this purpose adequate material models are essential. In this context, the present work introduces a material modelling approach for short fibre reinforced thermoplastics (SFRTPs). SFRTP parts are processed cost-effectively by injection moulding and show a varying degree of anisotropy due to the locally inhomogeneous fibre distributions that arise during the moulding process. The presented material model considers linear-elastic behaviour and non-linear orthotropic stress-state dependent viscoplastic deformation for arbitrary fibre distributions. The constitutive equations are verified with the experiments of a PPGF30 material regarding different stress-states and orientations.
Author: Jörg Schröder Publisher: Springer ISBN: 3319319256 Category : Mathematics Languages : en Pages : 239
Book Description
The book presents an overview of the state of research of advanced finite element technologies. Besides the mathematical analysis, the finite element development and their engineering applications are shown to the reader. The authors give a survey of the methods and technologies concerning efficiency, robustness and performance aspects. The book covers the topics of mathematical foundations for variational approaches and the mathematical understanding of the analytical requirements of modern finite element methods. Special attention is paid to finite deformations, adaptive strategies, incompressible, isotropic or anisotropic material behavior and the mathematical and numerical treatment of the well-known locking phenomenon. Beyond that new results for the introduced approaches are presented especially for challenging nonlinear problems.
Author: Wulff Possart Publisher: John Wiley & Sons ISBN: 3527341854 Category : Technology & Engineering Languages : en Pages : 538
Book Description
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
Author: Gianpetro Del Piero Publisher: Springer ISBN: 370912770X Category : Science Languages : en Pages : 278
Book Description
An updated account of the state of the art in the subject, presenting recent progress in two active and related areas of continuum mechanics: fracture mechanics and structured deformations.
Author: David Yang Gao Publisher: Springer ISBN: 3319580175 Category : Mathematics Languages : en Pages : 374
Book Description
This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. A ground-breaking methodological theory, canonical duality theory can be used for modeling complex systems within a unified framework and for solving a large class of challenging problems in multidisciplinary fields in engineering, mathematics, and the sciences. This volume places a particular emphasis on canonical duality theory’s role in bridging the gap between non-convex analysis/mechanics and global optimization. With 18 total chapters written by experts in their fields, this volume provides a nonconventional theory for unified understanding of the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization. Additionally, readers will find a unified methodology and powerful algorithms for solving challenging problems in complex systems with real-world applications in non-convex analysis, non-monotone variational inequalities, integer programming, topology optimization, post-buckling of large deformed structures, etc. Researchers and graduate students will find explanation and potential applications in multidisciplinary fields.
Author: Jörg Schröder
Author: Jörg Schröder
Author: Boyan Sirakov
Author: Arkadi Berezovski
Author: Felix Dillenberger
Author: Jörg Schröder
Author: Wulff Possart
Author: Gianpetro Del Piero
Author: 
Author: 
Author: David Yang Gao