Micropolar beam-like structures under large deformation

Results from experimental torsion and bending tests show the existence of a size effect, which conventional continuum models are unable to describe. Therefore, the incorporation of the micropolar media into numerical approaches for the analysis of materials with a complex microstructure looks necessary. So far, most studies utilize Cosserat continuum theory with 3D finite solid elements, even though, it covers only few beam elements developed within a linear strain–displacement relationship, and therefore only works in a small deformation regime. In this study, the authors aim to develop a size-dependent 3D continuum beam element based on the absolute nodal coordinate formulation (ANCF) with microstructure inclusions. Comparing analytical solutions within the Cosserat continuum model and models based on the proposed and already existing 3D micropolar solid elements, one can see a good correlation between them, with a faster convergence rate for the developed ANCF beam element. That allows exploiting the developed beam element within the non-linear deformation range, which is usually bypassed because of high computational costs, thus, accounting fully for differences between two media descriptions.publishedVersionPeer reviewe

О величине зазора в распределительном узле аксиально-поршневых гидромашин

Тез. докл. Междунар. науч.-техн. конф. (науч. чтения, посвящ. П. О. Сухому), Гомель, 4-6 июля. 2002 г

Modeling of the Achilles Subtendons and Their Interactions in a Framework of the Absolute Nodal Coordinate Formulation

Experimental results have revealed the sophisticated Achilles tendon (AT) structure, including its material properties and complex geometry. The latter incorporates a twisted design and composite construction consisting of three subtendons. Each of them has a nonstandard cross-section. All these factors make the AT deformation analysis computationally demanding. Generally, 3D finite solid elements are used to develop models for AT because they can discretize almost any shape, providing reliable results. However, they also require dense discretization in all three dimensions, leading to a high computational cost. One way to reduce degrees of freedom is the utilization of finite beam elements, requiring only line discretization over the length of subtendons. However, using the material models known from continuum mechanics is challenging because these elements do not usually have 3D elasticity in their descriptions. Furthermore, the contact is defined at the beam axis instead of using a more general surface-to-surface formulation. This work studies the continuum beam elements based on the absolute nodal coordinate formulation (ANCF) for AT modeling. ANCF beam elements require discretization only in one direction, making the model less computationally expensive. Recent work demonstrates that these elements can describe various cross-sections and materials models, thus allowing the approximation of AT complexity. In this study, the tendon model is reproduced by the ANCF continuum beam elements using the isotropic incompressible model to present material features.peerReviewe

Approximation of pre-twisted Achilles sub-tendons with continuum-based beam elements

Achilles sub-tendons are materially and geometrically challenging structures that can nearly undergo around 15% elongation from their pre-twisted initial states during physical activities. Sub-tendons’ cross-sectional shapes are subject-specific, varying from simple to complicated. Therefore, the Achilles sub-tendons are often described by three-dimensional elements that lead to a remarkable number of degrees of freedom. On the other hand, the continuum-based beam elements in the framework of the absolute nodal coordinate formulation have already been shown to be a reliable and efficient replacement for the three-dimensional continuum elements in some special problems. So far, that element type has been applied only to structures with a simple cross-section geometry. To computationally efficiently describe a pre-twisted Achilles sub-tendon with a complicated cross-section shape, this study will develop a continuum-based beam element based on the absolute nodal coordinate formulation with an arbitrary cross-section description. To demonstrate the applicability of the developed beam element to the Achilles sub-tendons, 16 numerical examples are considered. During these numerical tests, the implemented cross-section descriptions agreed well with the reference solutions and led to faster convergence rates in comparison with the solutions provided by commercial finite element codes. Furthermore, it is demonstrated that in the cases of very complicated cross-sectional forms, the commercial software ANSYS provides inflated values for the elongation deformation in comparison with ABAQUS (about 6.2%) and ANCF (about 9.4%). Additionally, the numerical results reveal a possibility to model the whole sub-tendons via coarse discretization with high accuracy under uniaxial loading. This demonstrates the huge potential for use in biomechanics and also in multibody applications, where the arbitrary cross-section of beam-like structures needs to be taken into account.peerReviewe

Comparison of the Absolute Nodal Coordinate and Geometrically Exact Formulations for Beams

The modeling of flexibility in multibody systems has received increase scrutiny in recent years. The use of finite element techniques is becoming more prevalent, although the formulation of structural elements must be modified to accommodate the large displacements and rotations that characterize multibody systems. Two formulations have emerged that have the potential of handling all the complexities found in these systems: the absolute nodal coordinate formulation and the geometrically exact formulation. Both approaches have been used to formulate naturally curved and twisted beams, plate, and shells. After a brief review of the two formulations, this paper presents a detailed comparison between these two approaches; a simple planar beam problem is examined using both kinematic and static solution procedures. In the kinematic solution, the exact nodal displacements are prescribed and the predicted displacement and strain fields inside the element are compared for the two methods. The accuracies of the predicted strain fields are found to differ: The predictions of the geometrically exact formulation are more accurate than those of the absolute nodal coordinate formulation. For the static solution, the principle of virtual work is used to determine the solution of the problem. For the geometrically exact formulation, the predictions of the static solution are more accurate than those obtained from the kinematic solution; in contrast, the same order of accuracy is obtained for the two solution procedures when using the absolute nodal coordinate formulation. It appears that the kinematic description of structural problems offered by the absolute nodal coordinate formulation leads to inherently lower accuracy predictions than those provided by the geometrically exact formulation. These observations provide a rational for explaining why the absolute nodal coordinate formulation computationally intensive