Cosserat-Type Shells

Altenbach, Holm; Eremeyev, Victor A.

doi:10.1007/978-3-7091-1371-4_3

Cited by 27 publications

(18 citation statements)

References 155 publications

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“…The aim of the proposed model was to develop a suitable more general numerical tool capable of modelling the behaviour of deformable bodies, and to take into account higher gradient constituent relations. This approach seemed particularly promising considering the emerging role of micro structured continua, manufactured with computer-aided methods, as a technological resource [see [17][18][19][20][21][22][23][24][25][26][27][28][29], because the presence of a complex microstructure often leads to macroscopic behaviours that require generalized continua for their accurate modelling (see [30][31][32][33][34][35][36][37][38][39] for more details and [40] for a historical survey on the subject). Moreover, an algorithm based on the geometric centroid of the neighbours of a given particle is consistent with the idea of (locally) minimizing an elastic potential, as the centroid has the well-known properties of minimizing the sum of the squared distances from a set of given points in an Euclidean space.…”

Section: Introductionmentioning

confidence: 99%

Position-based dynamic of a particle system: a configurable algorithm to describe complex behaviour of continuum material starting from swarm robotics

Dell'Erba

2018

Continuum Mech. Thermodyn.

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In a previous work we considered a two-dimensional lattice of particles and calculated its time evolution by using an interaction law based on the spatial position of the particles themselves. The model reproduced the behaviour of deformable bodies both according to the standard Cauchy model and second gradient theory; this success led us to use this method in more complex cases. This work is intended as the natural evolution of the previous one in which we shall consider both energy aspects, coherence with the principle of Saint Venant and we start to manage a more general tool that can be adapted to different physical phenomena, supporting complex effects like lateral contraction, anisotropy or elastoplasticity.

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Section: Introductionmentioning

confidence: 99%

Position-based dynamic of a particle system: a configurable algorithm to describe complex behaviour of continuum material starting from swarm robotics

Dell'Erba

2018

Continuum Mech. Thermodyn.

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“…In order to improve the results of the classical theory of elasticity various theories of generalized continua have been developed [3][4][5]. The mechanics of generalized continua has long history of development.…”

Section: Introductionmentioning

confidence: 99%

“…to 1-D and 2-D media, the generalized models of shells, plates and roods are extensively discussed in the literature. Among the many articles on generalized theories of plates and shell that we mention here [4,5,16,26], for more information see the extensive review paper [14].…”

Section: Introductionmentioning

confidence: 99%

Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Zozulya

2017

Curved and Layered Structures

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New models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress and strain tensors, vectors of displacements and rotation and body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then in the same way as in the theory of elasticity, system of differential equations in term of displacements and boundary conditions for Fourier coefficients have been obtained. The Timoshenko's and EulerBernoulli theories are based on the classical hypothesis and 2-D equations of linear micropolar elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scale when taking into account micropolar couple stress and rotation effects.

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“…A comparison between these two models has been presented in the paper [11], in the case of plates. On the other hand, we should mention that the kinematic structure of the 6-parameter shell model is different from the kinematic structure of the so-called Cosserat surfaces, which are defined as material surfaces with one or more deformable directors attached to every point, see [35,7,56,57,4,6]. For instance, the kinematics of Cosserat surfaces with one deformable director is characterized also by 6 degrees of freedom (3 for the position of material points and 3 for the orientation and stretch of the material line element through the thickness), which differ essentially from the 6 degrees of freedom in the 6-parameter resultant shell model.…”

Section: Introductionmentioning

confidence: 99%

Existence of minimizers in the geometrically non-linear 6-parameter resultant shell theory with drilling rotations

Bîrsan

Neff

2013

Mathematics and Mechanics of Solids

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The paper is concerned with the geometrically non-linear theory of 6-parametric elastic shells with drilling degrees of freedom. This theory establishes a general model for shells, which is characterized by two independent kinematic fields: the translation vector and the rotation tensor. Thus, the kinematical structure of 6-parameter shells is identical to that of Cosserat shells. We show the existence of global minimizers for the geometrically non-linear 2D equations of elastic shells. The proof of the existence theorem is based on the direct methods of the calculus of variations using essentially the convexity of the energy in the strain and curvature measures. Since our result is valid for general anisotropic shells, we analyze separately the particular cases of isotropic shells, orthotropic shells, and composite shells.

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Cosserat-Type Shells

Cited by 27 publications

References 155 publications

Position-based dynamic of a particle system: a configurable algorithm to describe complex behaviour of continuum material starting from swarm robotics

Position-based dynamic of a particle system: a configurable algorithm to describe complex behaviour of continuum material starting from swarm robotics

Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Existence of minimizers in the geometrically non-linear 6-parameter resultant shell theory with drilling rotations

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