Mechanics Research Communications最新文献

This article presents a comprehensive investigation into electro-magneto-rheological (EMR) fluids that can exhibit reversible behavior changes when exposed to electrical and magnetic fields. The behavior of EMR fluids changes to a solid-like state under the influence of external fields prior to yielding. This research emphasizes the solid-like behavior of these smart materials when subjected to external fields. To establish a constitutive relation, the study makes use of Ericksen’s analysis in addition to classical continuum mechanics. The shear stress that results from the interaction with the external field is developed further using this relationship. The analytical results are validated with previously published research to ensure their validity and dependability. The findings of the study will also aid in the design and development of EMR fluid-based systems, enabling a range of practical applications.

Origami has been inspirating the development of novel engineering systems and structures. The traditional waterbomb folding pattern is one of the most widely employed pattern and its description from the unit-cell is related to multiple degrees of freedom (DoF) systems. This work investigates the nonlinear dynamics and chaos of a waterbomb origami through its unit-cell, considering different symmetry hypotheses that simplify its kinematics, resulting in 1-DoF and 2-DoF dynamical systems. The investigation starts with a kinematic analysis of the waterbomb folding pattern and afterward, a reduced-order dynamical model with lumped masses on vertices and torsional springs on creases is built. Symmetry assumptions are discussed, identifying the differences induced by either geometrical nonlinearities or external stimuli. Numerical simulations are carried out showing details of the system nonlinear dynamics, showing intricate situations such as chaos. The comparison among different symmetry conditions provides a qualitative picture of the system dynamics, showing significative differences and highlighting the importance of the origami mechanical behavior comprehension, its modeling and nonlinear dynamics for a proper design of origami-inspired systems.

Stability of the Λ-fractional equilibrium states of nematic liquid crystals is discussed. Applying bifurcation theory in the Λ-fractional space, branching analysis of the liquid crystals is performed and their constant initial direction ceases to exist at a critical value of the external (electromagnetic) field. Post-critical analysis is performed, defining the variable orientation of the crystals. The analysis is transferred into the initial space, defining the true variable orientation of the liquid crystal field.

Method of frequency dependent exact trial functions for thin plate vibration based on fundamental solutions of Voigt is suggested. Contrary to other methods, where one of the functions is chosen as the scale and specific boundary condition dependent, it employs only the frequency dependent functions for both space coordinates. Thus they are scale independent, so the same functions can be used for different boundary conditions and plate dimensions. General rule for the choice of exact trial functions is formulated. The boundary conditions are satisfied according to the Galerkin boundary method, which actually minimizes the energy residuals with respect to each weight function (fundamental solution).

The verification of method is performed on examples of rectangular plate with various boundary conditions. Several arbitrarily chosen sets of trial functions were employed in calculation of the same tasks, and it is shown that accuracy of the method is almost independent from the choice of them. Even the small number of trial functions provides the very accurate results for natural frequencies.

Tensegrity structures are attractive light-weight structures. In particular, spherical tensegrity structures are expected to be applied in various fields. This article proposes a simple method for modeling spherical tensegrities. Firstly, the nodal coordinates of the spherical tensegrity are systematically determined based on rotational symmetry and regular polyhedral configuration. This approach enables the systematic acquisition of the nodal coordinates of spherical tensegrities of all sizes by introducing a three-dimensional rotation matrix and the dihedral angle of the regular polyhedron. Secondly, the prestress ratio is determined iteratively. For the stability analysis of the spherical tensegrity, nonlinear analysis with prestress is required. For the analysis considering the prestress, a tangent stiffness matrix is applied in this study. The simple determination method enables the modeling of spherical tensegrities. The natural frequencies and mode shapes of the spherical tensegrity are identified by frequency analysis. A vibration experiment is conducted as a verification experiment. The natural frequencies from the analysis are compared to the resonance frequencies from the experiment. This comparison confirms the validity of the frequency analysis results, based on the two proposed methods.

A novel rate dependent but time independent plasticity constitutive framework is proposed by rendering the flow rule and the internal variables evolution equations, appropriate functions of the strain rate, while maintaining a rate independent yield surface. This new framework is applied to a full-fledged rate independent and Critical State Theory compatible constitutive model for sands, transforming it into a rate dependent to address the cases where rate dependence is the main interest in comparison with creep and relaxation of secondary importance and manifestation. A qualitative comparison is made with available rate dependent data for sands.

Large deformation anisotropic elastoplastic models have important application background and research value in engineering and materials fields. In this paper, a macroscopic phenomenological model of elastoplastic anisotropic deformation considering plastic spin is proposed. The model is based on the multiplication decomposition of deformation gradient. The free energy function is expressed as the isotropic function of the strain and the structural tensor on the intermediate configuration, which is a push-forward of initial configuration by using plastic deformation gradient. Advantageously, the non-equilibrium free energy function remains invariant under the superimposed rigid body rotation on the intermediate configuration, which is due to the non-uniqueness of the multiplicative decomposition of deformation gradient. However, the rate of superimposed rigid body rotation has effects on the model. The effects are discussed by considering three different spin assumptions. Numerical simulations show that the plastic spin has influence on the calculation results. Therefore, the plastic spin assumption should be carefully selected in the practical application of elastoplastic anisotropic model.

We discuss the classic rotary inertia notion and extend it for microstructured beams introducing new microinertia parameters as an additional dynamic response to microstructure changes. Slender structures made of beam- or platelet-lattice metamaterials may exhibit not only large translations and rotations but also general deformations of inner structure. Here we considered a few examples of beam-like structures and derive their inertia properties which include effective mass density, rotary inertia and microinertia. Extended dynamic characteristics related to enhanced kinematics may be crucial for description of origami-like structures or other beam-lattice metamaterials.