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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Implicit finite incompressible elastodynamics with linear finite elements: A stabilized method in rate form
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Implicit finite incompressible elastodynamics with linear finite elements: A stabilized method in rate form

机译：具有线性有限元的隐式有限不可压缩弹性力学：速率形式的稳定方法

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摘要

We propose a stabilization method for linear tetrahedral finite elements, suitable for the implicit time integration of the equations of nearly and fully incompressible nonlinear elastodynamics. In particular, we derive and discuss a generalized framework for stabilization and implicit time integration that can comprehensively be applied to the class of all isotropic hyperelastic models. In this sense the presented development can be considered an important extension and complement to the stabilization approach proposed by the authors in previous work, which was instead focused on explicit time integration and simple neo-Hookean models for nearly-incompressible elasticity. With the goal of computational efficiency, we also present a two-step block Gauss-Seidel strategy for the time update of displacements, velocities and pressures. Specifically, a mixed system of equations for the velocity and pressure is updated implicitly in a first stage, and the displacements are updated explicitly in a second stage. The proposed mixed formulation is then embedded in Newton-type strategies for the nonlinear solution of the equations of motion. Various implicit time integration strategies are considered, and, particularly, we focus on high-frequency dissipation time integrators, which are preferable in transient mechanics applications. An extensive set of numerical computations with linear tetrahedral elements is presented to demonstrate the performance of the proposed approach. (C) 2016 Elsevier B.V. All rights reserved.
机译：我们提出了一种线性四面体有限元的稳定化方法，适用于近似和完全不可压缩的非线性弹性动力学方程的隐式时间积分。特别是，我们推导并讨论了一个稳定化和隐式时间积分的通用框架，该框架可以全面应用于所有各向同性超弹性模型。从这个意义上说，提出的发展可以被认为是对作者在先前工作中提出的稳定化方法的重要扩展和补充，而稳定化方法则侧重于显式时间积分和用于几乎不可压缩弹性的简单新胡克模型。为了提高计算效率，我们还提出了一种两步式块高斯-塞德尔策略，用于时间，速度和压力的时间更新。具体而言，在第一阶段隐式更新速度和压力的混合方程组，并在第二阶段显式更新位移。然后将提出的混合公式嵌入到牛顿型策略中，以解决运动方程的非线性问题。考虑了各种隐式时间积分策略，尤其是，我们专注于高频耗散时间积分器，它们在瞬态力学应用中更可取。提出了一系列带有线性四面体元素的数值计算，以证明所提出方法的性能。 （C）2016 Elsevier B.V.保留所有权利。

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