IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves

Composites have been found to be the most promising and discerning material available in this century. Presently, composites reinforced with fibers of synthetic or natural materials are gaining more importance as demands for lightweight materials with high strength for specific applications are growing in the market. Fiber-reinforced polymer composite offers not only high strength to weight ratio, but also reveals exceptional properties such as high durability; stiffness; damping property; flexural strength; and resistance to corrosion, wear, impact, and fire. These wide ranges of diverse features have led composite materials to find applications in mechanical, construction, aerospace, automobile, biomedical, marine, and many other manufacturing industries. Performance of composite materials predominantly depends on their constituent elements and manufacturing techniques, therefore, functional properties of various fibers available worldwide, their classifications, and the manufacturing techniques used to fabricate the composite materials need to be studied in order to figure out the optimized characteristic of the material for the desired application. An overview of a diverse range of fibers, their properties, functionality, classification, and various fiber composite manufacturing techniques is presented to discover the optimized fiber-reinforced composite material for significant applications. Their exceptional performance in the numerous fields of applications have made fiber-reinforced composite materials a promising alternative over solitary metals or alloys.

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Fiber-Reinforced Polymer Composites: Manufacturing, Properties, and Applications.

Three-dimensional Problems of the Theory of Elasticity. By A. I. Lur’e.1964. (Interscience Publishers)

One of the research direction of Horst Lippmann during his whole scientific career was devoted to the possibilities to explain complex material behavior by generalized continua models. A representative of such models is the Cosserat continuum. The basic idea of this model is the independence of translations and rotations (and by analogy, the independence of forces and moments). With the help of this model some additional effects in solid and fluid mechanics can be explained in a more satisfying manner. They are established in experiments, but not presented by the classical equations. In this paper the Cosserat-type theories of plates and shells are debated as a special application of the Cosserat theory.

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On generalized Cosserat-type theories of plates and shells: a short review and bibliography

/pdf/mechanics-of-composite-structural-elements-1aqvsalpmk.pdf

Mechanics of Composite Structural Elements

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Foundations of Micropolar Mechanics

We discuss the general linear six-parametric theory of plates based on the direct approach. We consider the plate as a deformable surface. Each material point of the surface can be regarded as an infinitesimal small rigid body with six degrees of freedom. The kinematics of the plate is described by using the vector of translation and the vector of rotation as the independent variables. The relations between the equilibrium conditions of a three-dimensional micropolar plate-like body and the two-dimensional equilibrium equations of the deformable surface are established. Using the three-dimensional constitutive equations of a micropolar material we discuss the determination of the effective stiffness tensors appearing in the two-dimensional constitutive equations.

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On the linear theory of micropolar plates

State of the Art and prospects in generalized GCM- Microstructure, homogenisation and GCM modelling- Application of GCM to intertwined fabrics- GCM modelling of granular materials- Scaling effects and metamaterials-Applications of GCM in the strength of materials- Application of GCM in 3D periodic structures- GCM and numerics- Hierarchy of scales in modelling materials-Fractals and GCM- Nonlinear waves in Cosserat continuum- Analytical and numerical solutions for problems of the theory of asymmetric elasticity and their applications for experimental studies- Kinetics of chemical reactions in deformable solids with dynamic loading- Constitutive models of mechanical behaviour of media with stress state dependent material properties- Theory of continuously distributed disclinations and dislocations in micropolar media- On one model of generalised continuum and its thermodynamical interpretation- Mechanics of carbon nanostructures- The influence of the Cosserat concept on the theory of strength of materials-Visualization at studying hydrodynamic instability in strong -Nonlinear dynamic processes in media with internal structure- On the Application of Generalized Continua Models to Structural Mechanics- An Axiomatic Framework for Gradient-Materials- Logarithmic Deformation Measures and Tensors Applied to Generalized Continua- Modelling and Simulation Aspects of Generalised Multiphysics Continuum Models- A Micro-Macro-Based Investigation of Micropolar Media- Micromechanical Interpretation of Kinematically Extended Continua- Subgrid Interaction and Homogenisation: New Invariance Conditions in Gradient Elasticity- Numerical Considerations of FE^2 Problems- Dispersive Waves in Generalized Continua: Experimental and Theoretical Investigations- Generalized Continua Applied to Nano-size Objects

Holm Altenbach

Papers

On generalized Cosserat-type theories of plates and shells: a short review and bibliography

Mechanics of Composite Structural Elements

Foundations of Micropolar Mechanics

On the linear theory of micropolar plates

Mechanics of Generalized Continua