Applying the asymptotic expansion technique to the three-dimensional equations of non-linear elasticity, a non-linear asymptotic membrane theory considering large deflections and strains is obtained for thin hyperelastic plates. To this end, the displacement vector and stress tensor components are scaled via an appropriate thickness parameter such that the present approximation takes into account larger deflections compared with those of the von Karman plate theory. Later, for an arbitrary form of the strain energy function, the hierarchy of the field equations is obtained by expanding the displacement vector and the stress tensor in terms of powers of the square root of the thickness parameter.
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