  To insight the relationships between the self-organizing structures of cells,
such as the cell clusters, and the properties of biotissues is helpful in
revealing the function and designing biomaterial. Traditional random foam model
neglects several important details of the frameworks of cell clusters, in this
study we use a more complete model, cell adhesion model, to investigate the
mechanical and morphological properties of the two-dimensional (2D) dry foams
composed by cells. Supposing these structures are formed due to adhesion
between cells, the equilibrium formations result from the minimum of the free
energy. The equilibrium shape equations for high symmetrical structures without
the volume constraint are derived, and the analytical results of the
corresponding mechanical parameters, such as the Young's modulus, bulk modulus
and failure strength, are obtained. Numerical simulation method is applied to
study the complex shapes with the volume constraint and several stable
multicellular structures are obtained. Symmetry-breaking due to the volume
change is founded and typical periodic shapes and the corresponding phase
transformations are explored. Our study provides a potential method to connect
the microstructure with the macro-mechanical parameters of biotissues. The
results also are helpful to understand the physical mechanism of how the
structures of biotissues are formed.
