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An analysis of the boundary layer in the 1D surface Cauchy–Born model

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Figure

Figure 1. Displacements and displacement gradients of an atomistic solution and a surfaceCauchy–Born solution, relative to the bulk Cauchy–Born solution, for the 1D model problemdescribed in Sectionsat the finite element nodes (marked by diamonds) despite a
Figure 2. Visualisation of (2.7): the bond at the left-hand end of the graph is counted half inthe Cauchy–Born model, even though it does not exist in the atomistic model, hence it gives acontribution − 12φ(2y′(0)) to the surface energy.
Figure 3. Relative error in the W 1,2-seminorm of the 1D nonlinear SCB model for varyingstiffness parameter α and two types of finite element grids; cf
Figure 4. Relative error in the mean strain of the 1D nonlinear SCB model for varying stiffnesspresent why, in this experiment, the error is of a higher orderparameter α and two types of finite element grids; cf
+4

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