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Variational-based energy-momentum schemes of higher-order for elastic fiber-reinforced continua

机译:弹性纤维增强连续体基于变分的高阶能量动量方案

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This paper contributes to the improvement of recently published higher-order accurate energy momentum schemes for an anisotropic hyperelastic material formulation based on the concept of structural tensors. These Galerkin-based energy momentum schemes are developed by means of time finite elements with the focus on improving numerical stability and robustness in the presence of stiffness and large rotations. They show advantages over conventional time stepping schemes in combination with anisotropic materials formulated with polyconvex strain energy density functions. In this paper, higher-order energy momentum schemes are developed by using a differential variational principle in order to remedy the drawbacks of these Galerkin-based schemes, namely a variationally inconsistent time approximation of the strains in the higher-order case, no coordinate free superimposed stress tensor and an unseparated time approximation of the fibers and the matrix material. These new structure preserving time integrators preserve all conservation laws of a free flying hyperelastic anisotropic continuum, namely the total linear and the total angular momentum conservation as well as the total energy conservation. Numerical examples demonstrate dynamic behavior of anisotropic continua, discrete conservation properties of flying continua and the effect of higher-order accuracy subject to transient loads. (C) 2017 Elsevier B.V. All rights reserved.
机译:本文为改进基于结构张量概念的各向异性超弹性材料配方的最近发布的高阶精确能量动量方案做出了贡献。这些基于Galerkin的能量动量方案是通过时间有限元开发的,重点是在存在刚度和大旋转的情况下提高数值稳定性和鲁棒性。它们显示了优于常规时间步长方案的优势,并结合了具有多凸应变能密度函数的各向异性材料。在本文中,通过使用微分变分原理开发了高阶能量动量方案,以弥补这些基于Galerkin方案的缺点,即在高阶情况下应变的时间变化不一致,没有坐标自由叠加的应力张量和纤维与基体材料的时间不可分离。这些新的结构保留时间积分器保留了自由飞行的超弹性各向异性连续体的所有守恒定律,即总线性和总角动量守恒以及总能量守恒。数值算例说明了各向异性连续体的动力学行为,飞行连续体的离散守恒特性以及瞬态载荷对高阶精度的影响。 (C)2017 Elsevier B.V.保留所有权利。

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