A multiscale FEA framework for bridging cell-wall to tissue-scale mechanical properties: the contributions of middle lamella interface and cell shape

Plant tissue represents cellular material with multiple structural hierarchies enabling a wide range of multifunctionalities and extraordinary mechanical properties. However, it is yet to be elucidated how subcellular-scale mechanical properties and cell-to-cell interactions by a middle lamella (ML) layer are translated to larger scale responses. In this study, we examined an onion epidermal cell wall profile as a representative multicellular material system and developed a novel framework for a multiscale finite element analysis (FEA) model that allows two-scale coupling in a commercial FEA package. The core of this multiscale approach is a 3D repetitive volume element (RVE), which is composed of four cell wall fragments from four adjacent cells attached by a distinct ML layer. We parameterized ML mechanical properties and cell shape anisotropy at RVE to investigate resulting mechanical responses, which were then scaled up to the tissue level. It was observed that, within the elastic limit, the RVE- and tissue-scale mechanical responses are barely affected by ML modulus value; however, they are moderately affected by cell shape factor. The detailed 3D feature of ML interface was found critical for creating anisotropic mechanical behavior and localized stress concentration at RVE scale. Based on the observed results, a soft nanoscopic ML layer with its specified 3D architecture was suggested as the key mediator for attributing multifunctionality in plant cellular material system. The reported computational model framework offers new insight into how different length scales may affect the material properties of multicellular materials exhibiting hierarchical multiscale structures.