Andreas Fischle

activity

20152017

collaborators

5 papers

math-ph2017

Grioli's Theorem with weights and the relaxed-polar mechanism of optimal Cosserat rotations

Andreas Fischle, Patrizio Neff

Let $F \in GL^{+} (3)$ and consider the right polar decomposition $F = R_{p} (F) \cdot U$ into an orthogonal factor $R_{p} (F) \in SO (3)$ and a symmetric, positive definite facto…

math-ph2016

Optimality of the relaxed polar factors by a characterization of the set of real square roots of real symmetric matrices

Lev Borisov, Andreas Fischle, Patrizio Neff

We consider the problem to determine the optimal rotations $R \in SO (n)$ which minimize $W : SO (n) \to R_{0}^{+}, W (R; D) := ∣∣ sym (R D - 1) ∣ ∣^{2}$ for a…

math-ph2016

The relaxed-polar mechanism of locally optimal Cosserat rotations for an idealized nanoindentation and comparison with 3D-EBSD experiments

Andreas Fischle, Patrizio Neff, Dierk Raabe

The rotation $polar (F) \in SO (3)$ arises as the unique orthogonal factor of the right polar decomposition $F = polar (F) \cdot U$ of a given invertible matrix $F \…

math-ph2015

The geometrically nonlinear Cosserat micropolar shear-stretch energy. Part II: Non-classical energy-minimizing microrotations in 3D and their computational validation

Andreas Fischle, Patrizio Neff

In any geometrically nonlinear, isotropic and quadratic Cosserat micropolar extended continuum model formulated in the deformation gradient field $F = \nabla φ : Ω \to G L^{+} (n)$ and th…

math.AP2015

The geometrically nonlinear Cosserat micropolar shear-stretch energy. Part I: A general parameter reduction formula and energy-minimizing microrotations in 2D

Andreas Fischle, Patrizio Neff

In any geometrically nonlinear quadratic Cosserat-micropolar extended continuum model formulated in the deformation gradient field $F := \nabla φ : Ω \to GL^{+} (n)$ and the mic…