Buckling during drying of edible soft matter with cylindrical core–shell geometry

This paper investigates the large deformation during the drying of cylindrical core-shell geometries, having a stiff skin and a soft core of gel-like material, representing food materials like fruits or vegetables. This particular geometry is inspired by our earlier study on the drying of broccoli stalks. The MRI imaging of broccoli drying had shown non-affine large deformations, which were explained by the presence of an elastic skin. We solve this multiphysics problem with COMSOL, where the mass transfer of water is strongly coupled to the momentum equation and the energy equation. The core-shell geometry necessitates a multi-domain formalism, which we have developed in another recent study. Computer simulations show that the cylindrical core-shell system undergoes circumferential buckling if a critical buckling stress is imposed on the interface between core and shell. This critical stress depends on the ratio of shell thickness over total diameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>τ</mml:mi> <mml:mo>/</mml:mo> <mml:mi>D</mml:mi></mml:mrow> </mml:math> , and the ratio of elastic moduli of core and shell <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow> <mml:mrow><mml:mi>h</mml:mi></mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow> <mml:mrow><mml:mi>s</mml:mi></mml:mrow> </mml:msub> </mml:mrow> </mml:math> . The number of buckling modes is largely determined by the geometric ratio <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>τ</mml:mi> <mml:mo>/</mml:mo> <mml:mi>D</mml:mi></mml:mrow> </mml:math> , but it is also slightly dependent on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow> <mml:mrow><mml:mi>h</mml:mi></mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow> <mml:mrow><mml:mi>s</mml:mi></mml:mrow> </mml:msub> </mml:mrow> </mml:math> . For relatively thick shells we also observe vertical buckling, next to circumferential buckling. The vertical buckling first shows a barrelling instability, which later transitions to snap-back buckling. These modes of vertical buckling bear large similarities with those observed via MRI imaging during broccoli drying. As a final note, we have remarked that the presented model is a good starting point for modelling shape morphing of 4D printed foods, which is also governed by buckling instabilities as observed during our simulations.