ANALOGY

Let us consider a simple bio system - tomato (arguably a fruit and a vegetable too!). However, before investigating the stress state in a tomato, let's take a quick look at the mechanism by which stress develops in a balloon.

A balloon filled with air exerts pressure on the internal surface of the skin resulting tensile stress in it. The behaviour is similar to a pressure vessel where the stress in the skin keep raises as the pressure intensifies and finally dissipate upon rupture of the skin (burst) as illustrated in the Figure. 2. Stresses do not redistribute or equilibrate following the balloon rupture, they can therefore be categorically classified as primary stresses and not as a secondary or residual stresses. However, now returning to the case in tomato, following few interesting questions arise to address,

• whether the phenomenon is same in the tomato?

• whether the pressure developed inside tomato is a primary loading?

• can the stresses developed in tomato skin (also termed as cuticle) be classified as secondary/residual stresses?

• do the cracks develop due to release of residual stress?

Figure 1. Stress State in Balloon and Laplace Law.

To answer the above questions, we need to look at the different growth stages and their corresponding physiological changes the tomato undergoes during its evolution from raw stage to ripened stage. The three common stages in tomato are illustrated in the Figure 2.

1. Raw tomato as unstressed cuticle/skin

2. Ripened tomato with stressed skin

3. Fissured tomato with stressed skin relieved by fracture

The fruit skin with evolving properties during harvest is shown to be highly responsive to the water content and ambient conditions. Cracks in the skin are generally developed when there is wide fluctuation in temperature and moisture which drastically changes the growth rate [6, 8]. The tomato in its raw stage has solid core with high strength and elastic skin without any pressure in it. During its ripening stage, the biomechanical properties of cuticle changes and starts experiencing the tensile stress due to inevitable growth of the core. Similar to but not quite like a balloon as the tomato is a composite material with its core as semi solid. The hydrostatic pressure developed inside fruit is termed as turgor pressure and is always balanced in cuticle in its uncracked state. Initiation of crack happens when there is an incompatible strain rate between the cuticle and the inner core. The incompatibility in strain rate is either due to a) sudden growth of the core or/and b) fluctuations in ambient weather [9]. Some authors also studied the effect of genetic differences on cracking but the physiological basis of these differences is still not clear [6, 8].

a) The incompatible growth of core is a consequence of rapid influx of solute (water) due to over watering at the time of ripening. Therefore, the stress development is attributed to the inability of skin to expand at the growth rate of core and its gradual evolution of elastic properties to endure the turgor pressure and expand appropriately.

b) In case of unexpected precipitation, the condition would be similar to case (a): the sudden influx of water from roots in saturated soil. In contrast, during summer, due to sudden raise in ambient temperature the skin loses its moisture and tries to contract and develops compressive thermal stress. It is worth noting here, the thermal stresses are always considered as residual stresses as they self-limit upon deformation or cracking.

Figure 2. Three stages of evolution of tomato, 1) Unstressed raw tomato, 2) Stressed ripened tomato and 3) Fissured tomato with stressed skin relieved by fracture

These requirements of strain compatibility in natural composite between the skin and core is what categorizes the stress developed in the tomato skin as secondary stress or residual stress. Once the crack is nucleated there will be no further increase in stress even with the increase in turgor pressure inside the tomato. However, both the stresses due to rapid influx of water and thermal stresses perhaps exceptional if they are found long-range and extreme form of splitting that penetrates deep into the pulp [10] is observed. Similar to structural integrity, fruit cracking is considered as a physical failure (physiological disorder) of the fruit that manifests as a fracture in the skin [10]. In horticultural science, it is considered as loss of marketable yield. Once the turgor pressure crosses beyond the critical stress intensity factor/fracture toughness of the cuticle, the residual stress in it relieved and is not considered as balanced residual stress anymore.