Softening material models are known to trigger spurious localizations.This may be shown theoretically by the existence of solutions with zero dissipation when localization occurs and numerically with spurious mesh dependency and localization in a single layer of elements. We introduce in this paper a new way to avoid spurious localization. The idea is to enforce a Lipschitz regularity on the internal variables responsible for the material softening. The regularity constraint introduces the needed length scale in the material formulation. Moreover, we prove bounds on the domain affected by this constraint. A first one-dimensional finite element implementation is proposed for softening elasticity and softening plasticity.
翻译:已知的软化材料模型会引发虚假的本地化。 这可以从理论上从存在零分散的解决方案中看出。 当本地化发生时,从数字上看,在单层元素中存在虚假的网状依赖和本地化。 我们在本文件中引入了避免虚假本地化的新方法。 其理念是对造成材料软化的内部变量实施利普施奇茨常规化。 常规性制约在材料配制中引入了必要的长度尺度。 此外,我们证明受这一制约影响的领域存在界限。 为软化弹性和软化可塑性提出了第一个一维的元素实施。