scholarly journals Adaptive, Small-Rotation-Based, Corotational Technique for Analysis of 2D Nonlinear Elastic Frames

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Jaroon Rungamornrat ◽  
Saethapoom Sihanartkatakul ◽  
Pattawee Kanchanakitcharoen
Keyword(s):  
Elastic Material ◽  
Numerical Technique ◽  
Body Movement ◽  
Material Model ◽  
Material Behavior ◽  
Algebraic Equations ◽  
Nonlinear Elastic Material ◽  
Computational Performance ◽  
Nonlinear Elastic ◽  
Small Rotation

This paper presents an efficient and accurate numerical technique for analysis of two-dimensional frames accounted for both geometric nonlinearity and nonlinear elastic material behavior. An adaptive remeshing scheme is utilized to optimally discretize a structure into a set of elements where the total displacement can be decomposed into the rigid body movement and one possessing small rotations. This, therefore, allows the force-deformation relationship for the latter part to be established based on small-rotation-based kinematics. Nonlinear elastic material model is integrated into such relation via the prescribed nonlinear moment-curvature relationship. The global force-displacement relation for each element can be derived subsequently using corotational formulations. A final system of nonlinear algebraic equations along with its associated gradient matrix for the whole structure is obtained by a standard assembly procedure and then solved numerically by Newton-Raphson algorithm. A selected set of results is then reported to demonstrate and discuss the computational performance including the accuracy and convergence of the proposed technique.

scholarly journals Nonlinear-Elastic Orthotropic Material Modeling of an Epoxy-Based Polymer for Predicting the Material Behavior of Transversely Loaded Fiber-Reinforced Composites

2020 ◽  
Vol 4 (2) ◽  
pp. 46
Author(s):  
Caroline Lüders
Keyword(s):  
Elastic Material ◽  
Orthotropic Material ◽  
Material Model ◽  
Material Behavior ◽  
Fiber Reinforced Composites ◽  
Material Modeling ◽  
Reinforced Composites ◽  
The Matrix ◽  
Nonlinear Elastic ◽  
Loaded Fiber

Micromechanical analyses of transversely loaded fiber-reinforced composites are conducted to gain a better understanding of the damage behavior and to predict the composite behavior from known parameters of the fibers and the matrix. Currently, purely elastic material models for the epoxy-based polymeric matrix do not capture the nonlinearity and the tension/compression-asymmetry of the resin’s material behavior. In the present contribution, a purely elastic material model is presented that captures these effects. To this end, a nonlinear-elastic orthotropic material modeling is proposed. Using this matrix material model, finite element-based simulations are performed to predict the composite behavior under transverse tension, transverse compression and shear. Therefore, the composite’s cross-section is modeled by a representative volume element. To evaluate the matrix modeling approach, the simulation results are compared to experimental data and the prediction error is computed. Furthermore, the accuracy of the prediction is compared to that of selected literature models. Compared to both experimental and literature data, the proposed modeling approach gives a good prediction of the composite behavior under matrix-dominated load cases.

scholarly journals Sharp upper bounds on the maximum $M$-eigenvalue of fourth-order partially symmetric nonnegative tensors

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yuyan Yao ◽  
Gang Wang
Keyword(s):  
Fourth Order ◽  
Elastic Material ◽  
Quantum Physics ◽  
Upper Bounds ◽  
Nonlinear Elastic Material ◽  
Numerical Examples ◽  
Nonnegative Tensors ◽  
Material Analysis ◽  
Nonlinear Elastic ◽  
Partially Symmetric

<p style='text-indent:20px;'><inline-formula><tex-math id="M1">\begin{document}$ M $\end{document}</tex-math></inline-formula>-eigenvalues of partially symmetric nonnegative tensors play important roles in the nonlinear elastic material analysis and the entanglement problem of quantum physics. In this paper, we establish two upper bounds for the maximum <inline-formula><tex-math id="M2">\begin{document}$ M $\end{document}</tex-math></inline-formula>-eigenvalue of partially symmetric nonnegative tensors, which improve some existing results. Numerical examples are proposed to verify the efficiency of the obtained results.</p>

A note on the nonlinear mechanical behavior of planar random network structures subjected to in-plane compression

2011 ◽  
Vol 45 (25) ◽  
pp. 2697-2703 ◽  
Author(s):  
Pär E. Åslund ◽  
Per Isaksson
Keyword(s):  
Mechanical Behavior ◽  
Elastic Material ◽  
Random Network ◽  
Material Model ◽  
Element Model ◽  
Material Behavior ◽  
Fiber Networks ◽  
Damage Models ◽  
Plane Compression ◽  
Random Fiber Networks

The microstructural effect on the mechanical behavior of idealized two-dimensional random fiber networks subjected to in-plane compression is studied. A finite element model utilizing nonlinear beam elements assuming a linearly elastic material is developed. On a macroscopic level, random fiber networks often display an asymmetric material behavior when loaded in tension and compression. In mechanical models, this nonlinearity is traditionally described using continuum elastic-inelastic and/or damage models even though using a continuum approach risks overlooking microstructural effects. It is found that even though a linear elastic material model is used for the individual fibers, the network gives a nonlinear response in compression. The nonlinearity is found to be caused by buckling of individual fibers. This reversible nonlinear mechanism is limited in tensile loading and hence offers an alternative explanation to the global asymmetry of random fibernetworks.

Mixing of two co-directional Rayleigh surface waves in a nonlinear elastic material

2015 ◽  
Vol 137 (1) ◽  
pp. 281-292 ◽  
Author(s):  
Merlin B. Morlock ◽  
Jin-Yeon Kim ◽  
Laurence J. Jacobs ◽  
Jianmin Qu
Keyword(s):  
Surface Waves ◽  
Elastic Material ◽  
Nonlinear Elastic Material ◽  
Rayleigh Surface Waves ◽  
Nonlinear Elastic
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