Continuum Mechanics and Thermodynamics最新文献

The paper presents an analytical model to study the shear driven debonding of a composite cantilever beam subjected to a point load. The composite structure consists of two elastic beams connected by an interface layer, and the model uses cohesive zone models to simulate the degradation process at the joint. These cohesive zone models are characterized by non-continuous and linear softening in the relationship between shear stress and relative tangential displacement. The results are expressed using non-dimensional parameters, and the model yields quasi-static equilibrium paths that demonstrate snap-back responses in both force and displacement values. The significance of the research lies in its application to structural engineering, where composite materials are extensively used. The study emphasizes the critical role of the interface layer strength in maintaining the structural integrity of composites. The proposed model advances the understanding of debonding by introducing a constitutive relation for the interface that accounts for the step-wise change in mechanical properties. The governing equations for the cantilever beam are derived, considering the equilibrium of forces and moments, and the relative tangential displacement at the interface. The model delineates three stages of interface degradation: no relative slip, plastic deformation, and progressive debonding. The analytical solutions for each stage provide insights into the beam deflection, shear stress, and axial force distribution. This research contributes to the field by offering a more refined analytical approach to study debonding in composite beams, which is essential for improving the design and analysis of composite structures.

Orthodontic tooth movement is the fundamental phenomenon underlying the treatment of dental malocclusions. For orthodontic treatment to be efficient and effective, the amount of force applied to the teeth for every kind of movement should be appropriately dosed, because it is associated with the risk of side effects and the treatment time. However, our knowledge of the complex cascade of events that transforms a mechanical stimulus into an ordinated bone remodeling is incomplete. Predictive theoretical numerical models could be of invaluable help in understanding the bone response to orthodontic loading and in studying the effects of complex orthodontic force systems. However, either short-term or evolutive predictive models showed a large heterogeneity of material properties and governing equations. The present review provides an outline of the physical and biochemical basis of orthodontic tooth movement with a focus around the periodontal ligament interface. The use of a standardized method for designing predictive models is advocated, and perspectives for future studies are presented.

In this work, we investigate a dynamic internal dissipation mechanism in the context of cement-based materials by introducing a 1D-enhanced micromorphic beam model with a dynamic internal friction term. Here, we consider an inherent feature in concrete-like materials arising from the multi-scale structure, namely, microcracks. Thus, we assume that the internal dissipation of the energy depends on the overall relative sliding displacement of the opposite faces in the microcracks under the effects of an applied cyclic load whenever no significant phenomena related to damage occur at the macroscopic level. The dynamic friction term is based on a well-known model for dry friction in solids due to P. R. Dahl, where the friction force depends only on the sliding displacement and evolves in time, reproducing an elastoplastic behavior. The model proposed in this paper takes into account a mechanical energy interchange between both bending and shear distortion in the beam with the sliding occurring at the microcracks, a storage of mechanical energy because of the asperities inside the faces of the microcracks, and the dissipation of the energy that follows from the interaction between the bending and the microcracks. Numerical simulations of the kinematic descriptors and the dissipative cycles are also provided by using the Finite Element Method and the commercial software COMSOL Multiphysics^®.

This paper considers the problem of symmetrical three-point bending of a prismatic beam with an edge crack. The solution is obtained by the mixed finite element method within the simplified Toupin–Mindlin strain gradient elasticity theory. A mixed variational formulation of the boundary value problem for displacements–strains–stresses and their gradients is applied, simplifying the choice of approximating functions. The concept of energy balance is adopted to calculate the energy release rate with a virtual increase in crack length. The increment of the potential energy of an elastic body is determined by accounting for the strain and stress gradient contribution. Numerical calculations were performed using a quasi-uniform triangular mesh of the cross-type. The mesh refinement was applied in the vicinity of the crack tip, at the concentrated support, and the point of application of the transverse force, and uniform mesh partitioning was utilized in the rest of the beam. The fine-mesh analysis was carried out on the successively condensed meshes in the stress concentration domain for different values of the length scale parameter. The crack opening displacements and the distribution of strains and Cauchy stresses for various values of the length scale parameter are presented. An increase in this parameter increases the stiffness of the crack, which leads to a decrease in the crack opening displacements and a smooth closure of its faces at the crack tip. In addition, accounting for the scale parameter reduces the calculated values of strains and stresses near the crack tip. Based on the energy balance criterion, local fracture parameters such as the release rate of elastic energy at the crack tip and the stress intensity factor are determined for different values of the mesh step. The numerical calculations indicate the convergence of the obtained approximations. The main feature of solutions, which includes the strain gradient contribution, is the decrease in the values of the calculated parameters associated with the fracture energy compared to the classical elasticity theory.

In this paper, the bone tissue was modeled as a linear viscoelastic material saturated with interstitial fluid. We considered a specific case of harmonic loading and related the mechanical stimuli to the loading frequency. In this way, we could include the inertial effect in the model while not having to deal with the perturbation during each loading period. Two types of mechanical signals were considered: strain energy and dissipation energy. A parametric study revealed the dependency of the two signals on loading frequency and material property. The evolution of the apparent mass density supported the parametric study’s findings. Under the three different frequency loadings, the strain energy-stimulated samples experienced identical remodeling scenarios. The samples stimulated with dissipation energy, on the other hand, exhibited a strong frequency dependence. An additional study was performed to investigate the effect of long-term variations in the loading frequency on the remodeling process. This demonstrated the model’s capabilities in designing and evaluating load regimes for rehabilitation following a bone injury or bone reconstruction.

In this paper, the dynamic behavior of one degree-of-freedom oscillator subject to stick–slip and wear phenomena at the contact interface with a rigid substrate is investigated. The motion of the oscillator, induced by a harmonic excitation, depends on the tangential contact forces, exchanged with the rigid soil, which are modeled through piecewise nonlinear constitutive laws, accounting for stick–slip phenomena due to friction as well as wear due to abrasion, already developed by the authors in a previous work. The nonlinear ordinary differential equations governing the problem are derived, whose solution is numerically obtained via a typical Runge–Kutta-based algorithm. The main target of this study is to analyze and discuss the strong nonlinear behavior, descending from the presence of stick–slip and wear phenomena, thus investigating the effect of the different interface modeling. In this framework, the analysis is carried out considering the whole evolution of non-smooth contact laws, starting from the virgin interface.

This study examines a mixed initial-boundary value problem in thermoelastic materials with a double porosity structure, taking into account the effects of microtemperature. The existence of a solution is established by converting the problem into a Cauchy-type problem. Given the complexity of the equations, unknowns, and conditions, we apply contraction semigroup theory within a specific Hilbert space. We prove the existence of a solution using the Lax-Milgram theorem. Additionally, the uniqueness of the solution is demonstrated based on the Lumer-Phillips corollary, which corresponds to the Hille-Yosida theorem. In the final section, we show the continuous dependence of the solution on the mixed initial-boundary value problem for double porous thermoelasticity with microtemperature.

The paper analyzes the vibrational behavior of cylinders in the offset printing machine caused by a cylinder gap shock. Specifically, it assesses the stability of a system of two cylinders. The analysis of the proposed model is reduced to solving a set of Hill equations. The singularity of the obtained equations is the relationship between the natural frequencies of the system and modulation depth. Numerical simulations, along with the generalized Hill’s determinant method, were employed to determine the critical parameters of parametric resonance, thereby establishing the conditions necessary for the stability of periodic vibrations.

This study examines how heat travels as thermoelastic waves in a uniform, isotropic, and infinitely large solid material due to a constant line heat source. We leverage the theory of thermoelasticity with two phase lags to account for the time difference between temperature changes and the material’s stress response. By employing a potential function approach alongside Laplace and Hankel transforms, we can convert the governing equations into more manageable domains. This enables us to derive mathematical formulas for temperature, displacement, and stress distributions within the solid. Through a complex inversion process of the Laplace transforms, we obtain analytical formulas for these field distributions. These formulas, however, are only valid for short time periods and are most applicable in the initial stages of wave propagation. We then use these analytical formulas to visualize how temperature, displacement, and stress are distributed, revealing the influence of the heat source and phase lag parameters on these fields. This approach provides valuable insights into the characteristics of wave propagation, the heat source’s impact, and the time-dependent nature of the thermoelastic response. Furthermore, to demonstrate the method’s versatility and ability to connect with established theories, we incorporate specific examples from other thermoelasticity theories. This broadens our understanding of thermoelastic behavior under various conditions.

Mechanical metamaterials consist of specially engineered features designed to tailor and enhance the mechanical properties of their constituent materials. In this context, 2D pantographic fabrics have gained attention for their unique deformation behavior, providing remarkable resilience and damage tolerance. This study explores micro-metric metamaterials with 3D pantographic motifs, aiming to transfer these properties to small scales. 3D micro-metric structures were designed using 2D pantographic fabrics arranged in multiple layers, each featuring unit cells with quasi-perfect pivots. Relatively large specimens of 3D micro-metric pantographs, measuring 158 (upmu )m x 250 (upmu )m x 450 (upmu )m, were fabricated in various configurations using two-photon polymerization. These specimens were mechanically characterized through in-situ scanning electron microscopy microindentation under conditions of cyclic deformation. Structural failures were subsequently assessed via helium-ion microscopy. The 3D micro-metric pantographs exhibited complex mechanical properties, some aligning with those of 2D pantographic fabrics, while new properties, such as a dissipative response and softening, were identified. Nonetheless, the 3D micro-metric pantographs demonstrated great resilience against deformation and enhanced resistance to undesired out-of-plane motions, indicating their potential for novel applications in advanced engineering fields. Additionally, the findings can potentially lead to optimizing and enriching theoretical models describing the mechanical behavior of pantographic metamaterials.