Cosserat弹性中的零拉格朗日量

Geometrically nonlinear Cosserat elasticity in the plane: applications to chirality

Modelling two-dimensional chiral materials is a challenging problem in continuum mechanics because three-dimensional theories reduced to isotropic two-dimensional problems become non-chiral. Various approaches have been suggested to overcome this problem. We propose a new approach to this problem by formulating an intrinsically two-dimensional model which does not require references to a higher dimensional one. We are able to model planar chiral materials starting from a geometrically non-linear Cosserat type elasticity theory. Our results are in agreement with previously derived equations of …

The stationary Weyl equation and Cosserat elasticity

The paper deals with the Weyl equation which is the massless Dirac equation. We study the Weyl equation in the stationary setting, i.e. when the spinor field oscillates harmonically in time. We suggest a new geometric interpretation of the stationary Weyl equation, one which does not require the use of spinors, Pauli matrices or covariant differentiation. We think of our 3-dimensional space as an elastic continuum and assume that material points of this continuum can experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of…

Modelling the neutrino in terms of Cosserat elasticity

The paper deals with the Weyl equation which is the massless Dirac equation. We study the Weyl equation in the stationary setting, i.e. when the the spinor field oscillates harmonically in time. We suggest a new geometric interpretation of the stationary Weyl equation, one which does not require the use of spinors, Pauli matrices or covariant differentiation. We think of our 3-dimensional space as an elastic continuum and assume that material points of this continuum can experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotation…

有限Cosserat微极弹性中SO(3)旋转场的保结构离散化

A structure-preserving discretisation of SO(3)-rotation fields for finite Cosserat micropolar elasticity

提出几何保结构插值法（Γ-SPIN），通过测地线单元插值Cosserat旋转张量并降低其正则性以缓解闭锁，在耦合模量趋于无穷时稳定收敛到偶应力极限。

Modeling the electron with Cosserat elasticity

We suggest an alternative mathematical model for the electron in dimension 1+2. We think of our (1+2)-dimensional spacetime as an elastic continuum whose material points can experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis which gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory we choose a coframe and a density. We then add an extra (third) spatial dimension…

Cosserat 微极和双曲应力弹性模型在有限变形下的铁磁性研究

Cosserat micropolar and couple-stress elasticity models of flexomagnetism at finite deformations

本文提出基于Cosserat微极理论及其衍生双曲应力理论的几何非线性（有限）连续模型，用于研究铁磁性在有限变形下的行为，通过引入微极模型的微裂纹张量与磁化矢量的耦合，利用Lifshitz不变量实现磁-力学相互作用，提出新的铁磁性作用泛函并推导对应的控制方程，通过纳米梁几何的数值结果验证模型的物理合理性和计算可行性。

微极型线性理论中的零拉格朗日量及弹性理论的其他若干推广

Null Lagrangians in linear theories of micropolar type and few other generalizations of elasticity

该研究在微极介质、准晶等广义弹性线性理论中，利用H. Rund充分条件推导零拉格朗日量族，发现部分情形下存在非零零拉格朗日量且储存能可分解，同时明确其在类柯西对称条件下退化为零的规律。

非线性弹性应变极限Cosserat模型的广义多尺度有限元方法

Generalized multiscale finite element method for a nonlinear elastic strain-limiting Cosserat model

本文针对非线性弹性应变极限Cosserat模型，利用广义多尺度有限元方法（GMsFEM）结合Picard迭代处理非线性，通过二维实验验证了离线与在线自适应策略的收敛性、效率和鲁棒性。

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

The rotation ${\rm polar}(F) \in {\rm SO}(3)$ arises as the unique orthogonal factor of the right polar decomposition $F = {\rm polar}(F) \cdot U$ of a given invertible matrix $F \in {\rm GL}^+(3)$. In the context of nonlinear elasticity Grioli (1940) discovered a geometric variational characterization of ${\rm polar}(F)$ as a unique energy-minimizing rotation. In preceding works, we have analyzed a generalization of Grioli's variational approach with weights (material parameters) $μ> 0$ and $μ_c \geq 0$ (Grioli: $μ= μ_c$). The energy subject to minimization coincides with the Cosserat shear-s…

The constitutive tensor of linear elasticity: its decompositions, Cauchy relations, null Lagrangians, and wave propagation

In linear anisotropic elasticity, the elastic properties of a medium are described by the fourth rank elasticity tensor C. The decomposition of C into a partially symmetric tensor M and a partially antisymmetric tensors N is often used in the literature. An alternative, less well-known decomposition, into the completely symmetric part S of C plus the reminder A, turns out to be irreducible under the 3-dimensional general linear group. We show that the SA-decomposition is unique, irreducible, and preserves the symmetries of the elasticity tensor. The MN-decomposition fails to have these desirab…

Rotational elasticity

We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis which gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory we choose the coframe and a density. We write down the general dynamic variational functional for our rotational theory of elasticity, assuming our material to be physically lin…

Blow up at finite time for wave equation in visco-elasticity: a new kind for one spatial variable Emden-Fowler type

For one spatial variable, a new kind of nonlinear wave equation for Emden-Fowler type is considered with boundary value null and initial values. Under certain conditions on the initial data and the exponent p, we exhibit that the visco-elastic term leads our problem to be dissipative and the global solutions still non-exist in L2 at given finite time.