Reliable and Efficient Modeling by Adaptive Methods for Structural Mechanics and Its Industrial Applications

Nowadays, the use of adaptive methods is commonly recognized as a critical issue to achieve reliability and efficiency in the numerical modeling for computational structural mechanics. The purpose of this contribution is to present some recent achievements to perform adaptive computing in the situations where, relative to the size of studied structures, very small space or/and time scales are implied by localized phenomena such as cracks or high frequency elastic waves. An adaptive approach is developed in order to build numerical models, which not only give appropriate description of those phenomena occurring on small scales but also take into account the global behaviour of the studied structure on large scales. The following aspects related to dynamic and non-linear adaptive computing are especially considered: 1) A posteriori error estimation based on a residual method, especially its goal-oriented feature in order to optimize meshes with respect to localized phenomena that occur on a very small space-time scale; 2) Numerical and physical criteria that allow to perform optimal mesh or shell/3D model adaptions; 3) Influence on the waves propagation of different kinds of interfaces introduced by the adaptive modeling: interfaces of cracks, interfaces between refined and unrefined meshes or between 3D and shell modeling zones. As industrial applications of our approach, two examples are presented: The first one deals with the propagation of pyrotechnic shock waves such as the one observed in the launcher Ariane V during its stages separation; The second one considers highly localized dynamic or/and non linear phenomena triggered by the propagation of brittle or ductile cracks in large size shell-like structures.