Mathematical modelling of uniaxial extension of a heterogeneous gas cell wall in bread dough: Stress fields and stress concentration analysis relating to the proving and baking steps

Abstract

A mathematical model was developed to increase the understanding of stress concentrations within a gas cell wall (GCW) in bread dough during baking. The GCW was composed of a single A-type wheat starch granule surrounded by various proportions of gluten typical of GCWs when about to rupture. Finite element simulations were carried out in 2D using linear viscoelasticity and visco-hyperelasticity. Strain orders of magnitude and rates relevant to dough during baking were applied as boundary conditions for two plausible sets of mechanical properties before and after protein coagulation and starch gelatinization (T < 50–60 °C and T > 70–80 °C). The average stress within the GCW was found to be strongly dependent on the starch fraction. Gluten-starch interactions influenced average stress values considerably when the starch fraction was greater than 11% v/v. The locations within the GCW where rupture was most likely to be initiated were identified by mapping maximal stress points using stress field and triaxiality analysis and the findings were discussed. • A mathematical model has been developed to better understand Gas Cell Wall rupture at the scale of bread dough constituents. • Stress fields in an extending GCW composed of a single starch granule and gluten were mapped. • Locations for rupture initiation in GCWs at strain and strain rates relevant to bread baking were identified. • The effects of gluten-starch proportion and gluten-starch interactions on stress concentration were discussed. • Gluten-starch proportion influenced average stress when the proportion was greater than 11%.