Transversal isotropy based on a multiplicative decomposition of the deformation gradient within p-version finite elements

Al-Kinani Raad; Hartmann Stefan; Netz Torben

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Transversal isotropy based on a multiplicative decomposition of the deformation gradient within p-version finite elements

机译：基于p型有限元内变形梯度的乘法分解的横向各向同性

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In this article the multiplicative decomposition of the deformation gradient into one part constrained in the direction of the axis of anisotropy and one part describing the directional deformation is proposed. This leads to a clear division of the deformation and stress states in the direction of anisotropy and a remaining part. The decomposition is explained in detail and a constitutive model of hyper-elasticity is proposed for the case of transversal isotropy, where the behavior of the model is investigated with the aid of simple analytical examples. The model is also investigated for inhomogeneous deformation states using high-order finite elements based on hierarchical shape functions showing the sensitivity of the accuracy of the results in the case of anisotropic media. (C) 2014 WILEY-VCH Veriag GmbH & Co. KGaA, Weinheim

机译：在本文中，提出了将变形梯度的乘分解分解为约束在各向异性轴方向上的一部分和描述方向变形的一部分。这导致在各向异性方向上的变形和应力状态以及其余部分的清晰划分。详细解释了分解过程，并针对横向各向同性的情况提出了超弹性本构模型，其中借助简单的分析示例研究了模型的行为。还使用基于分层形状函数的高阶有限元对模型进行了非均匀变形状态研究，显示了在各向异性介质情况下结果准确性的敏感性。（C）2014 WILEY-VCH Veriag GmbH＆Co.KGaA，魏因海姆

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《Zeitschrift fur Angewandte Mathematik und Mechanik》 |2015年第7期|共20页
作者
Al-Kinani Raad; Hartmann Stefan; Netz Torben;
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正文语种 eng
中图分类应用数学;力学;
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Anisotropy; transversal isotropy; hyper-elasticity; hierarchical shape functions; high-order finite elements;

机译：各向异性;横观各向同性;超弹性;分层形状函数;高阶有限元;

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1. 非对称格林函数的指数梯度横向各向同性基体涂层系统 [J] . F. Akbari, A. Khojasteh, M. Rahimian 中南大学学报（英文版） . 2018,第001期
2. Transversal isotropy based on a multiplicative decomposition of the deformation gradient within p-version finite elements (vol 95, pg 742, 2015) [J] . Al-Kinani Raad, Hartmann Stefan, Netz Torben Zeitschrift fur Angewandte Mathematik und Mechanik . 2015,第7期

机译：横向各向同性基于p型有限元内变形梯度的乘积分解（vol 95，pg 742，2015）
3. FINITE DEFORMATION THERMOELASTICITY OF THICK-WALLED CYLINDRICAL VESSELS BASED ON THE MULTIPLICATIVE DECOMPOSITION OF DEFORMATION GRADIENT [J] . H. Darijani Journal of thermal stresses . 2012,第10a12期

机译：基于变形梯度乘积分解的厚壁圆筒的有限变形热弹性
4. Kinematics and kinetics description of thermoelastic finite deformation from multiplicative decomposition of deformation gradient viewpoint [J] . Darijani H., Kargarnovin M.H. Mechanics research communications . 2010,第6期

机译：从变形梯度观点的乘分解看热弹性有限变形的运动学和动力学描述
5. Constitutive Model Based on the Multiplicative Decomposition of Deformation Gradient in Arbitrary Orthogonal Coordinate System [C] . Wan Chao Sun, Shan Lu International conference on manufacturing engineering and automation . 2012

机译：正交坐标系中变形梯度乘积分解的本构模型
6. Posteriori Error Analysis for the P-version of the Finite Element Method. [D] . Yang, Xiaofeng. 2014

机译：有限元方法P版本的后验误差分析。
7. Optical Acquisition and Polar Decomposition of the Full-Field Deformation Gradient Tensor Within a Fracture Callus [O] . Wangdo Kim, Sean S. Kohles -1

机译：裂缝愈伤组织内全场变形梯度张量的光学获取和极性分解
8. Subloading surface Cam-clay model with anisotropic rotational hardening for finite strains based on multiplicative decomposition of plastic deformation gradient tensor [O] . Yutaka Chida, Yuki Yamakawa, Koichi Hashiguchi, 2013

机译：具有各向异性旋转硬化的升压表面CAM-CLAY模型，用于塑性变形梯度张量乘法分解的有限菌株
9. Implementation of a C1 Triangular Element Based on the p-Version of the Finite Element Method [R] . Wang, D. W., Katz, I. N., Szabo, B. A. 1984

机译：基于p-型有限元法的C1三角单元的实现

Transversal isotropy based on a multiplicative decomposition of the deformation gradient within p-version finite elements

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