Final Report Summary - MMMDT (Multi-scale Modelling of Mechanical Damage to Tomatoes)
The scientific aim of the project was to model the multi-scale mechanics of tomatoes to provide a tool for investigating internal damage to tomatoes caused by external forces during handling and processing. A technique called finite element modelling (FEM) was used. The outcome was a modelling method leading to better knowledge of how the mechanics of tomatoes can be correlated across the scales from single cells through fruit internal anatomy to the whole fruit, and how external forces cause damage to single cells internally.
Specific objective 1 was to characterise the anatomy of tomatoes for macro-scale modelling. Tomato fruits contain internal structures, namely exocarp, mesocarp, endocarp and locular gel tissues. The anatomy of the fruit is critical in FEM. The boundaries (and hence the thickness) of each tissue type were determined by scanning electron microscopy (SEM) and image analysis, using cell size as a discriminant. (The endocarp was treated as part of the mesocarp). For each tissue type, the shape, arrangement and size of the cells in each tissue were determined by SEM and the cell wall thickness in each tissue type was determined using transmission electron microscopy. Mean values of these parameters were used in FEM for subsequent creation of appropriate 3D elements for each type of tissue.
Specific objective 2 was to determine the multi-scale mechanical behaviour of tomatoes, their component tissues, and the cells within those tissues. FEM requires mechanical properties of the cells in each type of tissue and computer simulations of whole fruit compressions required validation against experimental data. For the former, viscoelastic-plastic characterization of single mesocarp cells was characterized by compression-holding tests using micromanipulation at a previously unachieved compression speed of 5 mm s -1. This minimized time-dependent effects during compression such as viscoelasticity and possible loss of water from the protoplast. The peak compression force at 15% deformation, instantaneous elastic modulus, equilibrium elastic modulus, yield stress, first relaxation time and second relaxation time of single tomato cells were calculated using the Hertz-Maxwell model. Other single cell data were taken from the literature. Whole fruit mechanical data were determined by compression of single fruits to rupture between parallel plates of a TA-Xi2 Texture Analyzer, also at 5 mm s -1. Force-deformation curves were recorded in real time. Although the data were not used in FEM, tissue mechanics were also determined by compression testing.
Specific objective 3 was to develop and validate multi-scale, finite element, mechanical models of tomatoes. A multiscale FE 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 elements representing small aggregates of cells. Assuming elastic-plastic constitutive behavior for the cuticle and the cell aggregate elements and water-like fluid in the locule, and using previously determined material parameters of the 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, as described below.
Specific objective 4 was to model internal mechanical damage to tomatoes caused by externally applied forces. As described above, a 3D virtual model was developed of compression of a whole tomato fruit to 10% deformation. In simulations of compressions, this included a 1/4 multiscale geometrical model of the fruit and the parallel plates of the Texture Analyzer. The simulations showed that the cuticle did not yield whilst the cells that did yield were mainly distributed inside the pericarp tissues and near the stem-blossom axis. The main deformation response was local to the contact area and there was a minor equatorial response. The internal damage volume increased from 0 to 6672 mm 3 when the deformation went from 0 to 10% with a corresponding external force of 0 to 6.5 N being applied. The relationship between internal damage volume and percentage deformation (or compression force) was fitted by a 4-parameter sigmoidal model to allow predictions of internal damage, which cannot be observed experimentally.
Specific objectives 1, 2, 3 and 4 were completed satisfactorily. FEM modelling of the mechanics of whole tomato fruits using internal anatomical data and single cell mechanical properties is a great advance, allowing as it has the prediction of internal damage caused by even low levels of compression. Although further work is needed, e.g. with non-axial compressions, the prospect is of a method to understand better how tomato fruits are damaged in handling and processing. This has potential to create important economic benefits for the ERA, and more broadly.
Specific objective 1 was to characterise the anatomy of tomatoes for macro-scale modelling. Tomato fruits contain internal structures, namely exocarp, mesocarp, endocarp and locular gel tissues. The anatomy of the fruit is critical in FEM. The boundaries (and hence the thickness) of each tissue type were determined by scanning electron microscopy (SEM) and image analysis, using cell size as a discriminant. (The endocarp was treated as part of the mesocarp). For each tissue type, the shape, arrangement and size of the cells in each tissue were determined by SEM and the cell wall thickness in each tissue type was determined using transmission electron microscopy. Mean values of these parameters were used in FEM for subsequent creation of appropriate 3D elements for each type of tissue.
Specific objective 2 was to determine the multi-scale mechanical behaviour of tomatoes, their component tissues, and the cells within those tissues. FEM requires mechanical properties of the cells in each type of tissue and computer simulations of whole fruit compressions required validation against experimental data. For the former, viscoelastic-plastic characterization of single mesocarp cells was characterized by compression-holding tests using micromanipulation at a previously unachieved compression speed of 5 mm s -1. This minimized time-dependent effects during compression such as viscoelasticity and possible loss of water from the protoplast. The peak compression force at 15% deformation, instantaneous elastic modulus, equilibrium elastic modulus, yield stress, first relaxation time and second relaxation time of single tomato cells were calculated using the Hertz-Maxwell model. Other single cell data were taken from the literature. Whole fruit mechanical data were determined by compression of single fruits to rupture between parallel plates of a TA-Xi2 Texture Analyzer, also at 5 mm s -1. Force-deformation curves were recorded in real time. Although the data were not used in FEM, tissue mechanics were also determined by compression testing.
Specific objective 3 was to develop and validate multi-scale, finite element, mechanical models of tomatoes. A multiscale FE 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 elements representing small aggregates of cells. Assuming elastic-plastic constitutive behavior for the cuticle and the cell aggregate elements and water-like fluid in the locule, and using previously determined material parameters of the 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, as described below.
Specific objective 4 was to model internal mechanical damage to tomatoes caused by externally applied forces. As described above, a 3D virtual model was developed of compression of a whole tomato fruit to 10% deformation. In simulations of compressions, this included a 1/4 multiscale geometrical model of the fruit and the parallel plates of the Texture Analyzer. The simulations showed that the cuticle did not yield whilst the cells that did yield were mainly distributed inside the pericarp tissues and near the stem-blossom axis. The main deformation response was local to the contact area and there was a minor equatorial response. The internal damage volume increased from 0 to 6672 mm 3 when the deformation went from 0 to 10% with a corresponding external force of 0 to 6.5 N being applied. The relationship between internal damage volume and percentage deformation (or compression force) was fitted by a 4-parameter sigmoidal model to allow predictions of internal damage, which cannot be observed experimentally.
Specific objectives 1, 2, 3 and 4 were completed satisfactorily. FEM modelling of the mechanics of whole tomato fruits using internal anatomical data and single cell mechanical properties is a great advance, allowing as it has the prediction of internal damage caused by even low levels of compression. Although further work is needed, e.g. with non-axial compressions, the prospect is of a method to understand better how tomato fruits are damaged in handling and processing. This has potential to create important economic benefits for the ERA, and more broadly.