Applied Mathematics and Mechanics 2019

Dear Colleagues,

The advances in technology and material science have required constitutive modeling of modern materials and the formulation of computational tools necessary for their analyses. For example, many new designs, such as microelectromechanical and nanoelectromechanical systems (MEMS and NEMS), smart materials and multifunctional materials, are inherently multiphysic and require rigorous constitutive modeling. Successful experimental demonstration of negative electrical permittivity, magnetic permeability, effective elastic modulus, and mass density in metamaterials and extreme solids are other examples that emphasize the importance of classical applied mechanics fields, such as continuum mechanics in recent years. Of particular importance have been multiscale and homogenization approaches, given the role of specific microstructural designs on the response of modern materials. There has also been a greater emphasis in nondeterministic approaches, given the higher sensitivity of the aforementioned materials to design deviations and the importance on the stochastic distribution on small scale features in overall response, for example, in fracture mechanics and turbulence. Such advances have, in turn, necessitated the formulation of computational methods capable of efficient and accurate rendering of these material models. Theoretical and computational tools, including but not limited to multiscale and high-order methods, rigorous analysis of numerical errors and efficiency, homogenization schemes, and efficient approaches for the solution of discrete lattices, periodic media, and ordinary, partial and stochastic partial differential equations are a few of the relevant topics.

Prof. Dr. Reza Abedi
Dr. Raj Kumar Pal
Guest Editors

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• Solid mechanics
• Fluid mechanics
• Thermodynamics
• Fracture mechanics
• Continuum mechanics
• Constitutive models for modern materials
• Multiphysics problems
• Homogenization
• Multiscale methods
• Stochastic partial differential equations
• Computational mechanics including error and efficiency analysis
• Finite element methods
• Metamaterials
• Wave propagation
• Granular media
• Instabilities in solids
• Acoustics and ultrasonics
• Smart materials