Continuum Mechanics and Thermodynamics最新文献

In the paper, experimental and numerical results of the wear of a molybdenum disulfide coated on a titanium alloy disk are reported. The coating is in contact with a sapphire ball. The experiments are conducted for ambient temperatures varying from 20 to 350 (^circ )C. The results indicate that the wear profile becomes increasingly pronounced at the growth of the temperature up to 350 (^circ )C. A numerical model is proposed to describe the results of the experiment. The central assumption is the thermal steady state forming in the interface area. The resulting stress field serves as input for the simulation of wear. A good agreement can be observed between the experimental findings and the FE calculations.

In this study, a numerical framework based on the material point method is presented for the simulation of material extrusion (MEX)-based 3-D printing processes. The melt flow during material extrusion is assumed to be viscous flow including phase changes. To apply the free surface boundary conditions, the framework utilizes the level set method to track the free surface and the ghost fluid method for the application of the boundary conditions. For validation, three representative problems are first investigated to show the versatility of the model. Then, the numerical framework is adapted for the simulation of material extrusion (MEX) based 3-D printing processes. An in-depth parametric study is presented to show how printing parameters affect the overall extruded printing material.

We first study the plane strain problem associated with an incompressible liquid inclusion having an n-fold axis of symmetry which is embedded in an infinite isotropic elastic matrix subjected to uniform remote hydrostatic stresses. A closed-form solution is derived using Muskhelishvili’s complex variable formulation, a four-term conformal mapping function and the application of analytic continuation. The pair of analytic functions characterizing the elastic field in the matrix is completely determined in elementary closed-form. Explicit expressions are obtained and graphically illustrated for the internal uniform hydrostatic stresses within the liquid inclusion and the hoop stress along the liquid–solid interface on the matrix side. The closed-form solution for a linearly compressible liquid inclusion having an n-fold axis of symmetry is also obtained.

A three-dimensional model for the mechanics of elastic/hyperelastic materials reinforced with bidirectional fibers is presented in finite elastostatics. This includes the constitutive formulation of matrix–fiber composite system and the derivation of the corresponding Euler equilibrium equation. The responses of the matrix material and reinforcing fibers are characterized, respectively, via the Neo-Hookean model and quadratic strain energy potential of the Green–Lagrange type. These are further refined by the Mooney–Rivlin strain energy model and the high-order polynomial energy potential of fibers to incorporate the nonlinear behaviors of the matrix material and fibers. Within the framework of differential geometry and strain-gradient elasticity, the general kinematics of bidirectional fibers, including the three-dimensional bending of a fiber and twist between the two adjoining fibers, are formulated, and subsequently integrated into the model of continuum deformation. The admissible boundary conditions are also derived by virtue of variational principles and virtual work statement. In particular, a dimension reduction process is applied to the resulting three-dimensional model through which a compatible two-dimensional model describing both the in-plane and out-of-plane deformations of thin elastic films reinforced with fiber mesh is obtained. To this end, model implementation and comparison with the experimental results are performed, indicating that the proposed model successfully predicts key design considerations of fiber mesh reinforced composite films including stress–strain responses, deformation profiles, shear strain distributions and local structure (a unit fiber mesh) deformations. The proposed model is unique in that it is formulated within the framework of differential geometry of surface to accommodate the three-dimensional kinematics of the composite, yet the resulting equations are reframed in the orthonormal basis for enhanced practical unitality and mathematical tractability. Hence, the resulting model may also serve as an alternative Cosserat theory of plates and shells arising in two-dimensional nonlinear elasticity.

Thermoforming of continuous fiber-reinforced plastics made of semi-crystalline thermoplastics has gained significant interest due to its potential for producing lightweight and high-strength components for various applications. Before thermoforming, a laminate is heated to a temperature beyond the melting point of the thermoplastic. During the subsequent forming process, the laminate is continuously cooled, which triggers non-isothermal crystallization in the semi-crystalline matrix material. In this context, the study of crystallization kinetics is crucial in identifying phase transition, analyzing exothermic latent heat during crystallization and determining inhomogeneous crystallinity distribution caused by uneven cooling in the laminate’s thickness direction. This contribution primarily deals with experimental investigations, modeling and finite element simulations for characterizing the crystallization kinetics in the matrix material, Polyamide 6 and investigating the aforementioned factors. To model the crystallization kinetics, an extended form of the Avrami model, known as the modified Nakamura–Ziabicki model, is adopted. The parameters for the modified Nakamura–Ziabicki model, which depend on the local cooling rates, are identified based on fitting the model to flash DSC (differential scanning calorimetry with high cooling rates) and standard DSC non-isothermal cooling experiments. Finally, the model is implemented into the commercial FE software COMSOL Multiphysics^® and the crystallinity evolution in the laminate is simulated for the process-relevant die and laminate temperatures and laminate thicknesses.

The rigid/plastic solutions are singular near certain surfaces. A special numerical method is required to solve such boundary value problems. The present paper develops such a method for two models of pressure-dependent plasticity. Both are based on the Mohr–Coulomb yield criterion. Stationary planar flows are considered. The numerical method is characteristics-based. Its distinguishing feature is employing the extended R–S method. The output of numerical solutions, in addition to stress and velocity fields, is the strain rate intensity factor, which controls the magnitude of the shear strain rate near the singular surface. The method applies to finding a solution for the flow of granular material through a wedge-shaped die. The accuracy of the solution is verified by comparison with an analytical solution for the flow through an infinite channel and an available numerical solution for pressure-independent material. An applied aspect of this study is that the strain rate intensity factor can be used in non-traditional constitutive equations for predicting the evolution of material properties near surfaces with high friction.

A new and explicit form of the multi-axial elastic potential for elastic soft materials is constructed by means of two invariants of the Hencky strain. The new elasticity model with this form can bypass coupling complexities and uncertainties usually involved in parameter identification. Namely, exact closed-form solutions of decoupled nature are obtainable for stress responses under multiple benchmark modes. Unlike usual solutions with numerous coupled parameters, such new solutions are independent of one another and, as such, data sets for multiple benchmark modes can be separately matched with mutually independent single-variable functions. A comparative study is presented between a few well-known models and the new model. Results show that predictions from the former agree well with uniaxial and biaxial data, as known in the literature, but would be at variance with data for the constrained stress response in the plane-strain extension. In contrast, predictions from the new model agree accurately with all data sets. Furthermore, exact solutions for the Poynting effect of freely twisted elastic thin-walled tube are obtained from the new model.

For the particular case of an elastic multibody system (MBS) that can be modeled using one-dimensional finite elements, the main methods offered by analytical mechanics in its classical form for analysis are presented in a unitary description. The aim of the work is to present in a unitary form the main methods offered by classical mechanics for the analysis of solid systems. There is also a review of the literature that uses and highlights these methods, which need to be reconsidered considering the progress of the industry and the complexity of the studied systems. Thus, the kinematics of a finite element is described for the calculation of the main quantities used in the modeling of multibody systems and in analytical mechanics. The main methods used in the research of MBS systems are presented and analyzed. Thus, Lagrange’s equations, Gibbs–Appell equations, Maggi’s formalism, Kane’s equations and Hamilton’s equations are studied in turn. This presentation is determined by the advantages that alternatives to Lagrange’s equations can offer, which currently represent the method most used by researchers.

The onset of self-excited oscillations in airways and blood vessels is a common phenomenon in the human body, connected to both normal and pathological conditions. A recent experimental investigation has shown that the onset of self-excited oscillations happens for values of the intramural pressure close to the contact critical pressure. The goal of this work is to analyse the dependence of the contact critical pressure on the vessel’s geometric parameters. The methodology is based on the implementation of an experimentally validated computational model of a collapsible tube. The results confirm the correlation between the contact critical pressure and the onset of self-excited oscillations in collapsible tubes. Moreover, a set of general equations to compute the contact critical pressure and the corresponding areas of collapsible tubes with arbitrary geometries has been derived.