Simple shear in nonlinear Cosserat elasticity: bifurcation and induced microstructure

Neff, Patrizio; Münch, Ingo
July 2009
Continuum Mechanics & Thermodynamics;Jul2009, Vol. 21 Issue 3, p195
Academic Journal
We discuss the simple shear problem for a geometrically exact Cosserat model. In contrast to linear Cosserat elasticity, where the unique solution is available in closed form we exhibit a multitude of solutions to the nonlinear problem, even if the two fields of deformations φ and microrotations $${\overline{R}}$$ remain homogeneous. This motivates a search for new conditions on the microrotations $${\overline{R}}$$ which single out a unique, physically reasonable, response. The influence of material parameters, notably the Cosserat couple modulus μ c and the internal length scale L c on the response is also studied. For small Cosserat couple modulus μ c > 0 we observe a pitchfork bifurcation of the homogeneous response and for vanishing internal length L c = 0 and zero Cosserat couple modulus μ c = 0 the Cosserat model may show highly oscillating “microstructure” solutions which are energetically better than the homogeneous response. Thus, the large scale nonlinear Cosserat limit is not necessarily a classical limit.


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