Abstract The structure of steady shock waves in porous solids is a complex phenomenon involving in general the interplay of micro-inertia effects with the nonlinear elastic viscoplastic matrix response. Micro-inertia effects are due to the important acceleration of material particles in the vicinity of collapsing voids. By adopting the analytical approach recently developed for porous metals by Czarnota et al. [J. Mech. Phys. Solids 107 (2017)], we analyze the effects of matrix rate sensitivity, shock stress amplitude and micro-inertia on the structure of planar shock waves. We also analyze the relationship that links the strain rate within the shock to the jump of the stress across the shock. The fourth power law experimentally revealed for dense metals, Swegle & Grady [J. Appl. Phys. 58 (1985)] does not hold for heterogeneous materials. By considering the case of porous aluminum, we show that this relationship is characterized by two distinct regimes: (i) the first regime holds for weak shock intensities and is representative of the viscoplastic response of the dense matrix material, (ii) the second regime, that holds for shock of higher amplitude, is dominated by micro-inertia effects and is strongly influenced by the pore size. Micro-inertia effects appear to be quite beneficial since they are conducive to shock mitigation by attenuating the level of strain rate and of acceleration sustained by material particles.

中文翻译：

---

多孔金属中的稳态冲击波：粘度和微惯性效应

摘要 多孔固体中稳态冲击波的结构是一种复杂的现象，一般涉及微惯性效应与非线性弹性粘塑性基体响应的相互作用。微惯性效应是由于材料粒子在坍塌空隙附近的重要加速。通过采用 Czarnota 等人最近为多孔金属开发的分析方法。[J. 机械。物理。Solids 107 (2017)]，我们分析了基体速率敏感性、冲击应力幅度和微惯性对平面冲击波结构的影响。我们还分析了将冲击内的应变率与跨冲击的应力跳跃联系起来的关系。实验揭示了密集金属的第四次幂定律，Swegle 和 Grady [J. 应用程序 物理。58 (1985)] 不适用于异质材料。通过考虑多孔铝的情况，我们表明这种关系具有两个不同的状态：（i）第一个状态适用于弱冲击强度，代表致密基质材料的粘塑性响应，（ii）第二个状态，适用于更高振幅的冲击，受微惯性效应支配，并受孔径的强烈影响。微惯性效应似乎非常有益，因为它们通过减弱材料粒子所承受的应变率和加速度水平而有助于减轻冲击。(ii) 第二种机制，适用于更高振幅的冲击，主要受微惯性效应的影响，并受孔径的强烈影响。微惯性效应似乎非常有益，因为它们通过减弱材料粒子所承受的应变率和加速度水平而有助于减轻冲击。(ii) 第二种机制，适用于更高振幅的冲击，主要受微惯性效应的影响，并受孔径的强烈影响。微惯性效应似乎非常有益，因为它们通过减弱材料粒子所承受的应变率和加速度水平而有助于减轻冲击。