Shock analysis and optimization of two-layered cellular materials subject to pulse loading

• Published in: International journal of impact engineering Vol. 57; pp. 55 - 69
• Main Authors: Goetz, John C., Matouš, Karel
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2013
• Subjects: Cellular; Cellular material; Design engineering; Energy conservation; Gain; Mathematical models; Method of characteristics; Optimization; Plasticity; Shock wave; Stress-strain relationships; Cellular material; Shock wave; Optimization; Plasticity
• ISSN: 0734-743X; 1879-3509
• DOI: 10.1016/j.ijimpeng.2013.01.001

We present the method of characteristics with mass, momentum, and energy conservation to solve the nonlinear wave equation with shock formation in a two layer one-dimensional rod made of cellular material. We show that the rigid-perfectly-plastic-locking model cannot predict shock formation at a material interface, so we propose an elastic–plastic-densifying model to describe the stress–strain behavior of the cellular materials. The conditions for shock formation at a material interface are provided. We conduct a two-layer analysis to gain insights into the behavior of two layer cellular systems and to determine which material properties are most important for design. Finally, we optimize the significant parameters to reduce the length of one and two layered cellular systems with impulse and mass constraints subject to pulse loading. The results reinforce the concept of sandwich structures and show that two layer systems can achieve a 30% reduction in length over single layer ones. ► We present the method of characteristics with mass, momentum, and energy conservation to solve the nonlinear wave equation. ► We show that the rigid-perfectly-plastic-locking model cannot predict shock formation at a material interface. ► We provide the conditions for shock formation at a material interface. ► We conduct parametric and sensitivity studies to gain insights into the behavior of two layer cellular systems. ► We optimize significant parameters to reduce the length of one and two layered cellular systems subject to pulse loading.