  We present a model for cell growth, division and packing under soft
constraints that arise from the deformability of the cells as well as of a
membrane that encloses them. Our treatment falls within the framework of
diffuse interface methods, under which each cell is represented by a scalar
phase field and the zero level set of the phase field represents the cell
membrane. One crucial element in the treatment is the definition of a free
energy density function that penalizes cell overlap, thus giving rise to a
simple model of cell-cell contact. In order to properly represent cell packing
and the associated free energy, we include a simplified representation of the
anisotropic mechanical response of the underlying cytoskeleton and cell
membrane through appropriate penalization of the cell shape change. Numerical
examples are presented to demonstrate the evolution of multi-cell clusters, and
the total free energy of the clusters as a consequence of growth, division and
packing.
