Higher Gradient Materials and Related Generalized Continua

Description

This book discusses recent findings and advanced theories presented at two workshops at TU Berlin in 2017 and 2018. It underlines several advantages of generalized continuum models compared to the classical Cauchy continuum, which although widely used in engineering practice, has a number of limitations, such as: • The structural size is very small. • The microstructure is complex. • The effects are localized. As such, the development of generalized continuum models is helpful and results in a better description of the behavior of structures or materials. At the same time, there are more and more experimental studies supporting the new models because the number of material parameters is higher. Front Matter ....Pages i-xvi A Computational Approach for Determination of Parameters in Generalized Mechanics (Bilen Emek Abali, Hua Yang, Panayiotis Papadopoulos)....Pages 1-18 Extensible Beam Models in Large Deformation Under Distributed Loading: A Numerical Study on Multiplicity of Solutions (Francesco dell’Isola, Alessandro Della Corte, Antonio Battista, Emilio Barchiesi)....Pages 19-41 On the Characterization of the Nonlinear Reduced Micromorphic Continuum with the Local Material Symmetry Group (Victor A. Eremeyev)....Pages 43-54 Structural Modeling of Nonlinear Localized Strain Waves in Generalized Continua (Vladimir I. Erofeev, Anna V. Leontyeva, Alexey O. Malkhanov, Igor S. Pavlov)....Pages 55-68 A Diffusion Model for Stimulus Propagation in Remodeling Bone Tissues (Ivan Giorgio, Ugo Andreaus, Faris Alzahrani, Tasawar Hayat, Tomasz Lekszycki)....Pages 69-94 A C1 Incompatible Mode Element Formulation for Strain Gradient Elasticity (Rainer Glüge)....Pages 95-120 A Comparison of Boundary Element Method and Finite Element Method Dynamic Solutions for Poroelastic Column (Leonid A. Igumnov, Aleksandr A. Ipatov, Andrey N. Petrov, Svetlana Yu. Litvinchuk, Aron Pfaff, Victor A. Eremeyev)....Pages 121-134 From Generalized Theories of Media with Fields of Defects to Closed Variational Models of the Coupled Gradient Thermoelasticity and Thermal Conductivity (Sergey Lurie, Petr Belov)....Pages 135-154 Mathematical Modeling of Elastic Thin Bodies with one Small Size (Mikhail Nikabadze, Armine Ulukhanyan)....Pages 155-199 Application of Eigenvalue Problems Under the Study of Wave Velocity in Some Media (Mikhail Nikabadze, Armine Ulukhanyan)....Pages 201-220 Theoretical Estimation of the Strength of Thin-film Coatings (Sergey N. Romashin, Victoria Yu. Presnetsova, Larisa Yu Frolenkova, Vladimir S. Shorkin, Svetlana I. Yakushina)....Pages 221-231