Calculation of the elasticplastic deformation of a solid body by multidimensional nodal method of characteristics

Описан многомерный узловой метод характеристик, предназначенный для численного расчета упругопластической деформации твердого тела в рамках модели Прандтля-Рейса с уравнением состояния небаротропного типа. В качестве критерия перехода из упругого в пластическое состояние применялось условие текучести Мизеса. Рассмотренный численный метод базируется на координатном расщеплении исходной системы уравнений на ряд одномерных подсистем с последующим их интегрированием с помощью одномерного узлового метода характеристик. Метод использован для расчета ряда одно- и двумерных модельных задач A multidimensional nodal method of characteristics is described. The method is designed to numerically calculate the elastoplastic deformation of a solid body within the Prandtl-Reis model with the non-barotropic state equation. The Mises flow condition was used as a criterion for the transition from an elastic to a plastic state. The considered numerical method is based on the coordinate splitting of the original system of equations into a number of one-dimensional subsystems. Then the resulting equations were integrated using a one-dimensional nodal method of characteristics. The proposed method allows calculating a number of one- and two-dimensional model problems. The results of calculations that employ the multidimensional node method of characteristics were compared with data calculated using the Godunov hybrid method in the framework of a model that did not take into account the contribution of potential elastic compression energy to the total energy of the medium. There are some discrepancies in the calculation results that occur at high speeds of interaction of the aluminum striker with the barrier, exceeding 500 m/s, which are associated with omission of the potential energy due to the elastic compression of the solid within the original Prandtl-Reis model