A multiscale finite element model for mechanical response of tomato fruits

• A multiscale FE model was developed to simulate mechanical response of tomatoes.
• The macroscopic fruit could be linked to microscopic cell aggregates by the model.
• The model reproduced the force-deformation data of tomatoes within 10% deformation.
• The compression force mainly depended on the elastic modulus of the cells.
• The mechanics of cuticle at 5 mm/s was predicted by the multiscale FE model.

A multiscale finite element model, which included three parts: cuticle, pericarp frame and septal tissues, and a nearly incompressible surface-based fluid-filled locule, was developed to simulate the compressive mechanical response of a tomato fruit. In the model, the cuticle was bonded to the outer surface of a frame of pericarp tissue; the tissue frame was meshed into hexahedral tissue (cell aggregate) elements so that the macroscopic fruit could be linked to microscopic cell aggregates. The contact between the fruit and compression probe was defined as a hard contact pressure-overclosure relationship and followed a Coulomb friction model. Assuming elastic-plastic constitutive behavior for the cuticle and the cell aggregate elements and water-like fluid in the locule, the simulated compression force mainly depended on the elastic modulus of the cell aggregates. Increasing the modulus of the cell and cuticle resulted in coupling effects between the fruit tissue structure and the fluid inside the locule that gradually intensified with increasing percentage deformation. Using previously determined material parameters of pericarp cells and cuticle, the model was found to be remarkably capable of reproducing the macroscopic force-deformation behavior of a tomato fruit in compression up to 10% deformation. The model can be used to predict the mechanics of the cuticle if the mechanics of the pericarp are known, or vice versa. In this way, the elastic modulus, yield strength and Poisson’s ratio of Delyca tomato cuticle at 5 mm/s loading speed was eventually predicted to be 800 MPa, 50 MPa and 0.49 respectively. The multiscale modeling method might also be used for other fruits.