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An energy-momentum time integration scheme based on a convex multi-variable framework for non-linear electro-elastodynamics

机译:基于凸多变量框架的非线性电弹性动力学能量动量时间积分方案

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This paper introduces a new one-step second order accurate energy-momentum (EM) preserving time integrator for reversible electro-elastodynamics. The new scheme is shown to be extremely useful for the long-term simulation of electroactive polymers (EAPs) undergoing massive strains and/or electric fields. The paper presents the following main novelties. (1) The formulation of a new energy-momentum time integrator scheme in the context of nonlinear electro-elastodynamics. (2) The consideration of well-posed ab initio convex multi-variable constitutive models. (3) Based on the use of alternative mixed variational principles, the paper introduces two different EM time integration strategies (one based on the Helmholtz's and the other based on the internal energy). (4) The new time integrator relies on the definition of four discrete derivatives of the internal/Helmholtz energies representing the algorithmic counterparts of the work conjugates of the right Cauchy-Green deformation tensor, its co-factor, its determinant and the Lagrangian electric displacement field. (6) Proof of thermodynamic consistency and of second order accuracy with respect to time of the resulting algorithm is included. Finally, a series of numerical examples are included in order to demonstrate the robustness and conservation properties of the proposed scheme, specifically in the case of long-term simulations. (C) 2018 Elsevier B.V. All rights reserved.
机译:本文介绍了一种用于可逆电弹性动力学的新型一步式二阶精确能量动量(EM)保持时间积分器。事实证明,该新方案对于长期模拟承受大量应变和/或电场的电活性聚合物(EAP)极为有用。本文介绍了以下主要新颖性。 (1)在非线性电弹性动力学的背景下制定新的能量动量时间积分器方案。 (2)考虑适当的从头算起的凸多变量本构模型。 (3)在使用替代混合变分原理的基础上,本文介绍了两种不同的EM时间积分策略(一种基于Helmholtz方法,另一种基于内部能量)。 (4)新的时间积分器依赖于内部/亥姆霍兹能量的四个离散导数的定义,这些离散导数代表右柯西-格林变形张量,其辅因子,其行列式和拉格朗日电位移的功共轭的算法对应物领域。 (6)包括所得算法的热力学一致性和相对于时间的二阶精度的证明。最后,包括一系列数值示例,以证明所提出方案的鲁棒性和保留特性,特别是在长期仿真的情况下。 (C)2018 Elsevier B.V.保留所有权利。

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