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This book considers the kinematics and dynamics of the flows of fluids exhibiting a yield stress. Continuum mechanics governing the fluid mechanics is described. Two chapters are dedicated to analytical solutions to several steady and unsteady flows of viscoplastic fluids, including flows with pressure-dependent rheological parameters. Perturbation methods, variational inequalities to solve fluid flow problems, and the use of energy methods are discussed.

Classical mechanics. Field theory --- Fluid mechanics --- Solid state physics --- Physics --- Applied physical engineering --- toegepaste mechanica --- ingenieurswetenschappen --- fysica --- mechanica --- vloeistoffen --- Fluid mechanics. --- Viscoplasticity. --- Mechanics, Applied.

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This book contains geometrical and thermodynamical issues indispensable for development of a rational theory of thermoviscoplasticity. Geometrical picture of coupled thermomagnetomechanical histories of damaged solids is built both by means of Kroener's incompatibility approach as well by Eshelbian implanting eigenstrains. Duality of Euclidean anholonomic and non-Euclidean natural state space is also outlined in this book. Damaged inelastic materials of differential type, discrete and infinitesimal memory are obtained from principle of thermo-inelastic memory. Issue of plastic spin is considered. Postulate of minimal plastic work and corresponding non-associativity 4-tensor are then used to show whether associativity of flow rule holds. Postulates of Drucker, Iliushin and Hill are discussed. Thermodynamics of inelasticity is extensively discussed in classical, rational, extended and endochronic version with account to statistical thermodynamics. A non-steady aging is used in endochronic thermodynamics to cover creep-pasticity coupled inelastic histories. Multiaxial dynamic experiments with cylindrical, ``bichierino'' and cruciform specimen from austenitic stainless steels are analyzed. Quasi-rate independence and Rabotnov's plastic delay is combined with tensor representation. Inelastic ferromagnetics are treated by means of extended as well endochronic thermodynamics. For low cycle fatigue the experimentally observed displacement of magnetic induction history with respect to stress history is analyzed. Self consistent method applied to inelastic polycrystals is based on constrained micro-rotations and free meso-rotations. A special attention is devoted to slight disorder of polycrystal grains. The theory is confronted with classical J2-theory. Different inelastic multiaxial stress histories are analyzed and corresponding active slip systems determined. For numerical results micro quasi rate independence and relaxed Taylor's model are used. The theory of inelastic micromorphic polycrystals with couple stresses needs a very small number of necessary material constants. Nonproportionality of strain history as well as intergranular continuity are related to antisymmetry of stress tensor. Key topics: * Includes a detailed description of the geometry of thermo-deformation with local evolving natural state configuration * Provides a comparative review of various models of thermodynamics (classical, rational, endochronic, statistical) with special approach to inelastic high speed histories * Introduces quasi-rate independence and its application to plastic waves, ratcheting, and diffuse localization * Explores the sensor representation approach to thermo-inelastic coupled fields connected to a generalized associativity of flow rule as well as a comparison with the J2-approach * Examines micromechanics based on micro grain approach leading to reduced number of material constants * Provides biaxial cruciform specimen Hopkinson bar results * Reexamines the Hill’s yield function for nonproportional stress-thermo-strain histories This book is intended for material science experts and professionals interested in impact experiments, continuum mechanics researchers, engineers in research institutes and graduate and Phd students aiming to apply FEM to calculate strength of structures at time varying thermo-mechanical excitations.

Thermodynamics. --- Viscoplasticity. --- Thermodynamics --- Viscoplasticity --- Physics --- Physical Sciences & Mathematics --- Plasticity. --- Thermomechanical treatment. --- Engineering. --- Mathematical models. --- Mechanics. --- Mechanics, Applied. --- Continuum mechanics. --- Theoretical and Applied Mechanics. --- Mathematical Modeling and Industrial Mathematics. --- Continuum Mechanics and Mechanics of Materials. --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Models, Mathematical --- Simulation methods --- Construction --- Industrial arts --- Technology --- Cohesion --- Deformations (Mechanics) --- Plastics --- Rheology --- Plasticity --- Viscosity --- Mechanics, applied. --- Solid Mechanics.

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In this book, we shall consider the kinematics and dynamics of the flows of fluids exhibiting a yield stress. To highlight the principal characteristics of such fluids, the first chapter emphasizes the role played by the yield stress. Next, a careful description of the continuum mechanics behind the constitutive equations for incompressible and compressible viscoplastic fluids is given in Chapters 2–4. In Chapters 5 and 6 analytical solutions to several steady and unsteady flows of Bingham fluids are presented. The subsequent Chapters 7–10 are concerned with the development of variational principles and their numerical solutions, along with perturbation methods which play a significant role in numerical simulations.

Engineering. --- Engineering Fluid Dynamics. --- Fluid- and Aerodynamics. --- Continuum Mechanics and Mechanics of Materials. --- Materials. --- Hydraulic engineering. --- Ingénierie --- Matériaux --- Technologie hydraulique --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Civil Engineering --- Viscoplasticity. --- Fluid mechanics. --- Hydromechanics --- Fluids. --- Continuum mechanics. --- Continuum mechanics --- Plasticity --- Viscosity --- Mechanics. --- Mechanics, Applied. --- Solid Mechanics. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Engineering, Hydraulic --- Engineering --- Fluid mechanics --- Hydraulics --- Shore protection --- Mechanics --- Hydrostatics --- Permeability

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In this volume scientists and researchers from industry discuss the new trends in simulation and computing shell-like structures. The focus is put on the following problems: new theories (based on two-dimensional field equations but describing non-classical effects), new constitutive equations (for materials like sandwiches, foams, etc. and which can be combined with the two-dimensional shell equations), complex structures (folded, branching and/or self intersecting shell structures, etc.) and shell-like structures on different scales (for example: nano-tubes) or very thin structures (similar to membranes, but having a compression stiffness). In addition, phase transitions in shells and refined shell thermodynamics are discussed. The chapters of this book are the most exciting contributions presented at the EUROMECH 527 Colloquium “Shell-like structures: Non-classical Theories and Applications” held in Wittenberg, Germany.

Buckling (Mechanics). --- Dynamics. --- Engineering. --- Shells (Engineering). --- Viscoplasticity. --- Civil & Environmental Engineering --- Chemical & Materials Engineering --- Engineering & Applied Sciences --- Materials Science --- Civil Engineering --- Shells (Engineering) --- Elastic plates and shells. --- Elastic shells --- Plates, Elastic --- Shells, Elastic --- Structural shells --- Materials science. --- Computer mathematics. --- Continuum mechanics. --- Materials Science. --- Characterization and Evaluation of Materials. --- Continuum Mechanics and Mechanics of Materials. --- Computational Science and Engineering. --- Elastic waves --- Elasticity --- Plasticity --- Elastic plates and shells --- Structural analysis (Engineering) --- Plates (Engineering) --- Surfaces (Physics). --- Mechanics. --- Mechanics, Applied. --- Computer science. --- Solid Mechanics. --- Informatics --- Science --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Surface chemistry --- Surfaces (Technology) --- Computer mathematics --- Electronic data processing --- Mathematics --- Material science --- Physical sciences

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The use of machine learning in mechanics is booming. Algorithms inspired by developments in the field of artificial intelligence today cover increasingly varied fields of application. This book illustrates recent results on coupling machine learning with computational mechanics, particularly for the construction of surrogate models or reduced order models. The articles contained in this compilation were presented at the EUROMECH Colloquium 597, « Reduced Order Modeling in Mechanics of Materials », held in Bad Herrenalb, Germany, from August 28th to August 31th 2018. In this book, Artificial Neural Networks are coupled to physics-based models. The tensor format of simulation data is exploited in surrogate models or for data pruning. Various reduced order models are proposed via machine learning strategies applied to simulation data. Since reduced order models have specific approximation errors, error estimators are also proposed in this book. The proposed numerical examples are very close to engineering problems. The reader would find this book to be a useful reference in identifying progress in machine learning and reduced order modeling for computational mechanics.

supervised machine learning --- proper orthogonal decomposition (POD) --- PGD compression --- stabilization --- nonlinear reduced order model --- gappy POD --- symplectic model order reduction --- neural network --- snapshot proper orthogonal decomposition --- 3D reconstruction --- microstructure property linkage --- nonlinear material behaviour --- proper orthogonal decomposition --- reduced basis --- ECSW --- geometric nonlinearity --- POD --- model order reduction --- elasto-viscoplasticity --- sampling --- surrogate modeling --- model reduction --- enhanced POD --- archive --- modal analysis --- low-rank approximation --- computational homogenization --- artificial neural networks --- unsupervised machine learning --- large strain --- reduced-order model --- proper generalised decomposition (PGD) --- a priori enrichment --- elastoviscoplastic behavior --- error indicator --- computational homogenisation --- empirical cubature method --- nonlinear structural mechanics --- reduced integration domain --- model order reduction (MOR) --- structure preservation of symplecticity --- heterogeneous data --- reduced order modeling (ROM) --- parameter-dependent model --- data science --- Hencky strain --- dynamic extrapolation --- tensor-train decomposition --- hyper-reduction --- empirical cubature --- randomised SVD --- machine learning --- inverse problem plasticity --- proper symplectic decomposition (PSD) --- finite deformation --- Hamiltonian system --- DEIM --- GNAT