Cellular aggregates play a significant role in the evolution of biological systems such as tumor growth, tissue spreading, wound healing, and biofilm formation. Analysis of such biological systems, in principle, includes examining the interplay of cell–cell interactions together with the cell–matrix interaction. These two interaction types mainly drive the dynamics of cellular aggregates which is intrinsically out of equilibrium. Here we propose a non-linear continuum mechanics formulation and the corresponding finite element simulation framework to model the physics of cellular aggregate formation. As an example, we focus in particular on the process of bacterial colony formation as recently studied by Kuan et al. (2021). Thereby we describe the aggregation process as an active phase separation phenomenon. We develop a Lagrangian continuum description of the problem which yields a substantial simplification to the formulations of the governing equations. Due to the presence of spatial Hessian and Laplacian operators, a gradient-enhanced approach is required to incorporate ${\mathcal{C}}^1$ continuity. In addition, a robust and efficient finite element formulation of the problem is provided. Taylor–Hood finite elements are utilized for the implementation to avoid instabilities related to the LBB condition. Finally, through a set of numerical examples, the influence of various parameters on the dynamics of the cellular aggregate formation is investigated. Our proposed methodology furnishes a general framework for the investigation of the rheology and non-equilibrium dynamics of cellular aggregates.

细胞聚集体在肿瘤生长、组织扩散、伤口愈合和生物膜形成等生物系统的进化中发挥着重要作用。原则上，对此类生物系统的分析包括检查细胞-细胞相互作用以及细胞-基质相互作用的相互作用。这两种相互作用类型主要驱动本质上不平衡的细胞聚集体的动力学。在这里，我们提出了一种非线性连续介质力学公式和相应的有限元模拟框架来模拟细胞聚集体形成的物理特性。例如，我们特别关注 Kuan 等人最近研究的细菌菌落形成过程。（2021 年）。因此，我们将聚集过程描述为主动相分离现象。我们开发了对该问题的拉格朗日连续统描述，这大大简化了控制方程的公式。由于空间 Hessian 和 Laplacian 算子的存在，需要梯度增强方法来结合${\mathcal{C}}^1$连续性。此外，还提供了该问题的稳健有效的有限元公式。Taylor-Hood 有限元用于实施以避免与 LBB 条件相关的不稳定性。最后，通过一组数值例子，研究了各种参数对细胞聚集体形成动力学的影响。我们提出的方法为研究细胞聚集体的流变学和非平衡动力学提供了一个通用框架。