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A mixed variational framework for the design of energy-momentum integration schemes based on convex multi-variable electro-elastodynamics

机译:基于凸多变量电弹性动力学的能量动量集成方案设计的混合变分框架

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In Ortigosa et al. (2018), the authors presented a new family of time integrators for large deformation electromechanics. In that paper, definition of appropriate algorithmic expressions for the discrete derivatives of the internal energy and consideration of multi-variable convexity of the internal energy was made. These two ingredients were essential for the definition of a new energy-momentum (EM) time integrator in the context of large deformation electromechanics relying on materially stable (ellipticity compliant) constitutive models. In Betsch et al. (2018), the authors introduced a family of EM time integrators making use of mixed variational principles for large strain mechanics. In addition to the displacement field, the right Cauchy-Green deformation tensor, its co-factor and its Jacobian were introduced as unknown fields in the formulation. An elegant cascade system of kinematic constraints was introduced in this paper, crucial for the satisfaction of the required conservation properties of the new family of EM time integrators. The objective of the present paper is the introduction of new mixed variational principles for EM time integrators in electromechanics, hence bridging the gap between the previous work presented by the authors in Ortigosa et al. (2018) and Betsch et al. (2018), opening up the possibility to a variety of new Finite Element implementations. The following characteristics of the proposed EM time integrator make it very appealing: (i) the new family of time integrators can be shown to be thermodynamically consistent and second order accurate; (ii) piecewise discontinuous interpolation of the unknown fields (except displacements and electric potential) has been carried out, in order to yield a computational cost comparable to that of standard displacement-potential formulations. 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) 2019 Elsevier B.V. All rights reserved.
机译:在Ortigosa等。 (2018),作者介绍了用于大变形机电的新的时间积分器系列。在该论文中,为内部能量的离散导数定义了适当的算法表达式,并考虑了内部能量的多变量凸度。在依赖材料稳定(椭圆率)本构模型的大变形机电中,这两种成分对于定义新的能量动量(EM)时间积分器至关重要。在Betsch等人中。 (2018),作者介绍了一个EM时间积分器系列,它利用混合变分原理来处理大型应变力学。除了位移场外,在公式中还引入了正确的柯西-格林变形张量,其辅因子及其雅可比矩阵作为未知场。本文介绍了一种优雅的运动学限制级联系统,这对于满足新的EM时间积分器系列所需的守恒特性至关重要。本文的目的是为机电时间积分器引入新的混合变分原理,从而弥合了Ortigosa等人在作者之前所做的工作之间的差距。 (2018)和Betsch等人。 (2018),为各种新的有限元实现提供了可能性。拟议中的EM时间积分器的以下特性使其非常具有吸引力:(i)新的时间积分器系列可以证明在热力学上是一致的,并且是二阶精确的; (ii)已经进行了未知场的分段不连续插值(位移和电势除外),以产生与标准位移势公式相当的计算成本。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)2019 Elsevier B.V.保留所有权利。

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