An energy–momentum couple stress formula for variational-based macroscopic modelings of roving-matrix composites in dynamics
An energy–momentum couple stress formula for variational-based macroscopic modelings of roving-matrix composites in dynamics
复制标题
用于动力学中粗纱基体复合材料变分宏观建模的能量动量偶应力公式
DOI：
10.1016/j.cma.2021.114391
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发表时间：
2021
影响因子：
7.2
通讯作者：
Kalaimani I.
中科院分区：
文献类型：
--
作者：
Groß M;Dietzsch J;Kalaimani I.
例如，在动力系统中，在固化基体材料中采用纤维粗纱、通过定制纤维铺放 (TFP) 技术编织或制造的纤维增强材料对工程师来说具有重大意义。因此，目前在复合材料零件的设计过程中正在进行许多有限元模拟。但是，标准有限元公式没有考虑粗纱的尺寸以及方向相关的弯曲和扭转刚度。为了避免计算成本高昂的具有流动矩阵内部边界界面离散化的细观有限元模型，可以通过引入微极旋转自由度来导出宏观材料模型。微极旋转自由度允许对固化基质材料中的粗纱的方向相关刚度和惯性进行单独的本构描述。该连续统模型代表了具有扩展平衡定律集的扩展连续统公式。在其计算设置中，可以通过虚拟功率的混合原理结合能量动量拉应力和力偶应力公式来实现整套平衡定律的离散保存。保证的算法能量动量一致性允许基于平衡函数误差的细观模型对宏观材料常数进行一次性虚拟参数识别。因此，最近发布了具有独立微极旋转自由度的混合有限元公式，该公式能够通过考虑粗纱的弯曲和扭曲来模拟动力学问题。在这篇先前发表的论文中，本构定律至多是二次的，因此无需特殊的力偶应力近似即可进行能量动量时间积分。如果考虑粗纱弯曲和扭曲的非线性应变能函数，则需要一种新的特殊应力偶近似。因此，本文用一种新的应力偶近似完成了这种混合有限元公式，并通过单向粗纱的数值实验展示了其应用，这些实验是为虚拟参数识别而设计的。这些具有大平移、旋转和变形的全动态实例通过参数研究证明了具有 Kauderer 型粗纱曲率-扭转应变能函数的粗纱的弯曲和扭转刚度。独立于边界条件满足完整的离散平衡定律集，以便允许即将进行的虚拟参数识别。
In dynamical systems, fiber-reinforced materials with fiber rovings in a cured matrix material, woven or manufactured by the technology of tailored fiber placement (TFP), for instance, have gained great significance for engineers. Therefore, many finite element simulations are currently in progress during the design of composite parts. But, standard finite element formulations do not take into accountdimensionsand the direction-dependentflexureand twist stiffnessof the rovings. In order to avoid computationally costly mesoscopic finite element models with a discretization of roving-matrix interior boundary interfaces, a macroscopic material model can be derived by introducingmicropolar rotation degrees of freedom. Micropolar rotation degrees of freedom allow for a separate constitutive description of the direction-dependent stiffness and inertia of the rovings in the cured matrix material. This continuum model represents an extended continuum formulation with an extended set of balance laws. In its computational setting, the discrete preservation of the complete set of balance laws can be realized by a mixed principle of virtual power in connection with energy–momentum tension stress and couple stress formulas. The guaranteed algorithmic energy–momentum consistency then allows an one-off virtual parameter identification of the macroscopic material constants with the mesoscopic model based on the error of the balance functions. Therefore, a mixed finite element formulation with independent micropolar rotation degrees of freedom is recently published, which are able to simulate dynamical problems by taking into account flexure and twist of the rovings. In this previously published paper, the constitutive laws are at most quadratic such that energy–momentum time integrations are possible without a special couple stress approximation. If a nonlinear strain energy function for flexure and twist of the rovings is considered, a new special couple stress approximation is necessary. Therefore, the present paper completes this mixed finite element formulation with a new couple stress approximation and shows its application by means of that numerical experiments with unidirectional rovings, which are designed for the virtual parameter identification. These fully dynamical examples with large translations, rotations and deformations demonstrate the flexure and twist stiffness of the rovings with roving curvature–twist strain energy functions of Kauderer-type by parameter studies. The complete set of discrete balance laws are satisfied independent of boundary conditions in order to allow the upcoming virtual parameter identification.
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DOI：
--
发表时间：
2002
期刊：
影响因子：
--
作者：
X. Meng;T. Laursen
通讯作者：
T. Laursen
有限弹塑性应变下的各向异性纤维基材料模型
DOI：
--
发表时间：
2005
期刊：
影响因子：
--
作者：
Sven Klinkel;C. Sansour;W. Wagner
通讯作者：
W. Wagner
气动膜中正交各向异性材料行为的有限元建模
DOI：
--
发表时间：
2001
期刊：
影响因子：
--
作者：
S. Reese;T. Raible;P. Wriggers
通讯作者：
P. Wriggers
DOI：
--
发表时间：
1949
期刊：
影响因子：
--
作者：
H. Kauderer
通讯作者：
H. Kauderer
DOI：
10.1002/nme.2579
发表时间：
2009-09-10
影响因子：
2.9
作者：
Geuzaine, Christophe;Remacle, Jean-Francois
通讯作者：
Remacle, Jean-Francois