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arXiv · 2006.13005

The linearized Kirchhoff theory for plates with incompatible prestrain

Yizhao Qin·Pengfei Yao
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Abstract

In this paper, we derive a linearized Kirchhoff model from three dimensional nonlinear elastic energy of plates with incompatible prestrain as its thickness $h$ tends to zero and its elastic energy scales like $h^{\beta}$ with $2<\beta<4.$ The incompatible prestrain is given as a Riemannian metric $G(x')$ in the three dimensional thin plate which only depends on mid-plate of the thin plates. The problem is studied rigorously by using a variational approach and establishing the $\Gamma-$ limit of the non-Euclidean version of the nonlinear elasticity functional when the gauss curvature of the mid-plate $(\Omega, g=G_{2\times2})$ is always positive, negative or zero.

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Yizhao Qin, Pengfei Yao. 2020-06-20. The linearized Kirchhoff theory for plates with incompatible prestrain. https://arxiv.org/abs/2006.13005

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