We consider a class of models motivated by previous numerical studies of wrinkling in highly stretched, thin rectangular elastomer sheets. The model used is characterized by a finite-strain hyperelastic membrane energy perturbed by small bending energy. Without bending energy, the stored-energy density is not rank-one convex for general spatial deformations but reduces to a polyconvex function when restricted to the plane, i.e., two-dimensional hyperelasticity. In addition, it grows unbounded as the local area ratio approaches zero. The small-bending component of the model is the same as that in the classical von Kármán model. Here we prove the existence of energy minima for a general class of such models.

Miniaturized electronics and components are becoming more common in precision-guided artillery-launched munitions and missiles. Due to the highly dynamic nature of projectile launch, and the demands for increased structural robustness, many miniaturized smart munitions resort to a potted design in order to achieve functionality and reliability requirements. In most of these applications, the potted electronics are inactive for most of their lifetime and may be stored without environmental (temperature and humidity) controls for up to 20 years. The uncontrolled environment for smart munitions however makes the thermal management task especially difficult due to the coefficient of thermal expansion (CTE) mismatch between the potting material and the electronic components. It has been previously observed that modeling a potted device, in support of its development through finite-element simulations, is a complex task due to the numerical-convergence issues, material properties and meshes, during simulations as well as resource limitations. In this paper, we will present a modeling/simulation methodology which can be used in the development of miniaturized potted smart munitions and the product qualification process. There are two basic tests that a potential new munition needs to satisfy: 1) a highly accelerated temperature-cycling life test (HALT), to emulate the un-controlled projectile storage environment and, 2) the extremely high-G acceleration during a projectile launch. In this paper, we will present, 1) the use of finite-element analysis to support design decisions to overcome the CTE differences between electronic components on the circuit board assembly and the potting material and, 2) the use of finite-element simulations to study and improve the survivability of the electronic components on the circuit board assembly during extremely high-G acceleration projectile launches.

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