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We regret that in the expressions of the first kind Piola-Kirchhoff surface stress Ss and the Lagrangian description of the Young-Laplace equations (Eqs. 35–36), some terms associated with the “out-plane term” of surface gradient Fs and “out-plane term” of Ss were missing. In fact, Fs and Ss are “two-point” tensors, with base vectors both on the tangent planes J Y and Jy, and are not tensors in the 2-dimensional tangent plane J 0 Y only. The correct forms of Fs, Ss and the Lagrangian description of the Young-Laplace equations are given as follows. (1) If the displacement on the surface u is decomposed into u0s = uα0 Aα in the tangent plane J 0 Y and u0n = u0A3 along the normal direction of J 0 Y, then the surface gradient can be written as Fs = aα ⊗ A = i0 + u∇0s + d0αA3 ⊗ A, (c1)

Erratum to: A theory of hyperelasticity of multi-phase media with surface/interface energy effect