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Advanced Modeling and Simulation in Engineering Sciences
Fig. 2 | Advanced Modeling and Simulation in Engineering Sciences

Fig. 2

From: Computational homogenization of transient chemo-mechanical processes based on a variational minimization principle

Fig. 2

Periodic boundary conditions associated with the minimization-based formulation of chemo-mechanics. The boundary of the RVE \({\mathcal {B}}_0\) is split into \({\mathcal {B}}_0^+\) and \({{\mathcal {B}}}_0^-\) with unit outward normals \({{\varvec{N}}}^+ = - {{\varvec{N}}}^- =: {{\varvec{N}}}\). At the respective material points \({{\varvec{X}}}^+\) and \({{\varvec{X}}}^-\) on these boundaries, the deformation map is considered to be periodic (\({\varvec{\varphi }}({{\varvec{X}}}^+) = {\varvec{\varphi }}({{\varvec{X}}}^-)\)) and the normal solvent-volume flux is considered to be anti-periodic ()

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