The continuum theory of mixtures is used to describe a medium consisting of a solid phase and fluid phase, both compressible and attributed distinct deformation, temperature, entropy, and internal energy fields. Continuum balance laws are presented, and constitutive equations consistent with thermodynamic restrictions are postulated. Jump conditions for shock waves are established. Evolution equations for transient, i.e., unsteady, shock wave propagation are newly derived for an ideal mixture consisting of an arbitrary number of nonlinear thermoelastic solids, whereby inviscid thermoelastic fluid behavior is attained for a given constituent under more restrictive constitutive assumptions. Detailed calculations of Hugoniot response and shock decay are specialized to the case of a two-phase mixture of a single solid and a single fluid, where physical properties pertinent to lung parenchymal tissue containing air are assigned. Local constitutive behaviors for this lung mixture model correspond to a compressible neo-Hookean solid phase and an ideal gas fluid phase. Predictions of the model offer new information on origins of soft tissue trauma, in the context of prior experimental observations, for dynamic impact or shock loading of the lung.

混合物的连续统理论用于描述由固相和液相组成的介质，它们都是可压缩的和归因于不同的变形、温度、熵和内部能量场。提出了连续平衡定律，并假设了与热力学限制一致的本构方程。建立冲击波的跳跃条件。对于由任意数量的非线性热弹性固体组成的理想混合物，新推导出瞬态（即非稳态）冲击波传播的演化方程，从而在更严格的本构假设下获得给定成分的无粘性热弹性流体行为。Hugoniot 响应和冲击衰减的详细计算专门针对单一固体和单一流体的两相混合物的情况，其中分配了与含有空气的肺实质组织相关的物理特性。该肺混合物模型的局部本构行为对应于可压缩的新胡克固相和理想的气相流体相。在先前的实验观察的背景下，该模型的预测提供了有关软组织创伤起源的新信息，用于肺部的动态冲击或冲击负荷。