Soliton-like solutions based on geometrically nonlinear Cosserat micropolar elasticity

Abstract

The Cosserat model generalises an elastic material taking into account the possible microstructure of the elements of the material continuum. In particular, within the Cosserat model the structured material point is rigid and can only experience microrotation, which is also known as micropolar elasticity. We present the geometrically nonlinear theory taking into account all possible interaction terms between the elastic and microelastic structure. This is achieved by considering the irreducible pieces of the deformation gradient and of the dislocation curvature tensor. In addition we also consider the so-called Cosserat coupling term. In this setting we seek soliton type solutions assuming small elastic displacements, however, we allow the material points to experience full rotations which are not assumed to be small. By choosing a particular ansatz we are able to reduce the system of equations to a Sine-Gordon type equation which is known to have soliton solutions.

12 pages, 1 figure; minor revision, sine-Gordon-d'Alembert system discussed

References in corpus (1)

• A unifying perspective: the relaxed linear micromorphic continuum

Cited by in corpus (8)

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• Soliton solutions in geometrically nonlinear Cosserat micropolar elasticity with large deformations
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• Wave propagation in pantographic 2D lattices with internal discontinuities
• Geometrically nonlinear Cosserat elasticity in the plane: applications to chirality
• Characterization of the critical points for the free energy of a Cosserat problem
• Grioli's Theorem with weights and the relaxed-polar mechanism of optimal Cosserat rotations
• Existence theorem for geometrically nonlinear Cosserat micropolar model under uniform convexity requirements