We develop a continuum mechanics model of blastocyst hatching. The blastocyst and the zona pellucida are modeled as concentric thick-walled initially spherical shells embedded in a viscous medium. Each shell is characterized by a nonlinear elastic–viscous–constitutive relation. The stiffer outer shell (the zona pellucida) contains an opening. The softer inner shell (the blastocyst) is subject to a continually increasing pressure, which can eventually drive the escape of the inner shell from the outer shell (“hatching”). The focus is on the continuum mechanics modeling framework and illustrating the sort of quantitative predictions that can be made. Numerical examples are presented for the predicted dependence of the evolution of the escape process on values of parameters characterizing the constitutive response of the shells, on the viscosity of the external medium and on the size of the opening in the zona pellucida.

我们开发了囊胚孵化的连续力学模型。将胚泡和透明带建模为嵌入粘性介质中的同心厚壁初始球形壳。每个壳的特征是非线性的弹性-粘滞-本构关系。较硬的外壳（透明带）包含一个开口。较软的内壳（胚泡）承受的压力不断增加，最终可能导致内壳从外壳中逸出（“阴影”）。重点是连续力学力学建模框架，并说明了可以进行的定量预测。给出了数值示例，说明了逃逸过程的演变对表征壳体本构响应的参数值的依赖关系，