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Stability of microstructure for tetragonal to monoclinic martensitic transformations

Pavel Belik, Mitchell Luskin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We give an analysis of the stability and uniqueness of the simply laminated microstructure for all three tetragonal to monoclinic martensitic transformations. The energy density for tetragonal to monoclinic transformations has four rotationally invariant wells since the transformation has four variants. One of these tetragonal to monoclinic martensitic transformations corresponds to the shearing of the rectangular side, one corresponds to the shearing of the square base, and one corresponds to...

Stress equations of motion of Ignaczak type for the second axisymmetric problem of micropolar elastodynamics

Janusz Dyszlewicz (1997)

Applicationes Mathematicae

A second axially-symmetric initial-boundary value problem of linear homogeneous isotropic micropolar elastodynamics in which the displacement and rotation take the forms u ̲ = ( 0 , u θ , 0 ) , φ ̲ = ( φ r , 0 , φ z ) ((r,θ,z) are cylindrical coordinates; cf. [17]) is formulated in a pure stress language similar to that of [12]. In particular, it is shown how u ̲ and φ ̲ can be recovered from a solution of the associated pure stress initial-boundary value problem, and how a singular solution corresponding to harmonic vibrations of a concentrated...

Sufficient conditions for the validity of the Cauchy-Born rule close to SO ( n )

Sergio Conti, Georg Dolzmann, Bernd Kirchheim, Stefan Müller (2006)

Journal of the European Mathematical Society

The Cauchy–Born rule provides a crucial link between continuum theories of elasticity and the atomistic nature of matter. In its strongest form it says that application of affine displacement boundary conditions to a monatomic crystal will lead to an affine deformation of the whole crystal lattice. We give a general condition in arbitrary dimensions which ensures the validity of the Cauchy–Born rule for boundary deformations which are close to rigid motions. This generalizes results of Friesecke...

Sull’estensione di un teorema di Menabrea al caso di una microstruttura a deformazioni finite

Antonio Claudio Grioli (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In the present work an extension of a classical Menabrea’s theorem on a variational principle of the second potential energy is considered. Such extension deals with hyperelastic micropolar media without constraints.

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