Continuum Mechanics and Thermodynamics最新文献

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.

This paper describes the experiments carried out on a mediaeval masonry tower in the historic centre of Lucca and some finite element numerical simulations of the tower’s experimental response. The Guinigi Tower, one of the most iconic monuments in Lucca, has been continuously monitored by high-sensitivity seismic stations that recorded the structure’s response to the dynamic actions of the surrounding environment. The monitoring campaign results have been analysed to show the effectiveness of dynamic monitoring as a valuable source of information on the structural properties of the tower. The dynamic analyses of the tower and the surrounding palace subjected to some seismic events recorded during the experiments have highlighted the capabilities of experiment-based finite element modelling. The calibration of the finite element model and the numerical analysis have been carried out by resorting to procedures developed at ISTI-CNR and able to consider the nonlinear behaviour of masonry materials.

Using the possibilities of modern science and technology, it can be said that the presented mathematical model has been formulated without significant simplifications, and its (numerical) solution itself will be performed with high accuracy. The main purpose of the work was to create a tool supporting the calculation of the main problem of internal ballistics for barrel propellant systems in order to achieve digital solutions as close as possible to the results obtained using experimental ballistics methods. The scientific hypothesis of the work postulates that the physical model of internal ballistics formulated in Lagrange coordinates will allow to solve the main problem of internal ballistics of barrel systems in a digital way, obtaining such solution results that will satisfactorily reflect the solution results obtained using experimental ballistics methods. The results of digital simulations of physical phenomena of solutions to the main problem of internal ballistics of barrel weapons were compared with the results of experimental tests and the degree of agreement was determined.

This paper investigates the mechanical response and the mechanisms of failure of an ultra-high molecular weight polyethylene under service at cryogenic temperature. The service temperature (T_textrm{s}) being about ({50},^circ {text {C}}) below its glass transition temperature (T_textrm{g}), the study focuses on the experimental techniques to determine both the glass transition temperature (T_textrm{g}) and the ductile–brittle transition temperature (DBTT). (T_textrm{g}) was estimated by dynamic mechanical thermal analysis (DTMA) and contrasted with the glassy–rubbery transition defined by using the Young’s modulus issued from monotonic tensile tests on smooth specimens at room and low temperature and various cross-head speeds. Concerning the DBTT, two estimators of the transition, based on the fracture surface and the up-to-failure data, were studied. An operating diagram (temperature/cross-head speed) including the probability of ductile failure and both the rubbery and glassy domains is proposed. This diagram aims at finding an optimal compromise of the material response combining stiff versus soft with brittle versus ductile behaviour.

If a porous media is being damaged by excessive stress, the elastic matrix at every infinitesimal volume separates into a ‘solid’ and a ‘broken’ component. The ‘solid’ part is the one that is capable of transferring stress, whereas the ‘broken’ part is advecting passively and is not able to transfer the stress. In previous works, damage mechanics was addressed by introducing the damage parameter affecting the elastic properties of the material. In this work, we take a more microscopic point of view, by considering the transition from the ‘solid’ part, which can transfer mechanical stress, to the ‘broken’ part, which consists of microscopic solid particles and does not transfer mechanical stress. Based on this approach, we develop a thermodynamically consistent dynamical theory for porous media including the transfer between the ‘broken’ and ‘solid’ components, by using a variational principle recently proposed in thermodynamics. This setting allows us to derive an explicit formula for the breaking rate, i.e., the transition from the ‘solid’ to the ‘broken’ phase, dependent on the Gibbs’ free energy of each phase. Using that expression, we derive a reduced variational model for material breaking under one-dimensional deformations. We show that the material is destroyed in finite time, and that the number of ‘solid’ strands vanishing at the singularity follows a power law. We also discuss connections with existing experiments on material breaking and extensions to multi-phase porous media.

This work presents a new finite element variational formulation for the numerical treatment of diffusional phase transformations using the discontinuous Galerkin method (DGM). Steep concentration and property gradients near phase boundaries require particular focus on a sound numerical treatment. There are different ways to tackle this problem ranging from (i) the well-known phase field method (PFM) (Biner et al. in Programming phase-field modeling, Springer, Berlin, 2017, Emmerich in The diffuse interface approach in materials science: thermodynamic concepts and applications of phase-field models, Springer, Berlin, 2003), where the interface is described continuously to (ii) methods that allow sharp transitions at phase boundaries, such as reactive diffusion models (Svoboda and Fischer in Comput Mater Sci 127:136–140, 2017, 78:39–46, 2013, Svoboda et al. in Comput Mater Sci 95:309–315, 2014). Phase transformation problems with continuous property changes can be implemented using the continuous Galerkin method (GM). Sharp interface models, however, lead to stability problems with the GM. A method that is able to treat the features of sharp interface models is the discontinuous Galerkin method. This method is well understood for regular diffusion problems (Cockburn in ZAMM J Appl Math Mech 83(11):731–754, 2003). As will be shown, it is also particularly well suited to model phase transformations. We discuss the thermodynamic background by review of a multi-phase, binary system. A new DGM formulation for the phase transformation problem with sharp interfaces is then introduced. Finally, the derived method is used in a 2D microstructural evolution simulation that features a binary, three-phase system that also takes the vacancy mechanism of solid body diffusion into account.

The post-elastic mechanical behavior of cortical bone, which is represented by extensive microcracking once the elastic regime is exceeded, has been characterized by a nonlinear constitutive relationship for osteonal microcracking. The relationship/model is based on the formalism of Statistical Mechanics, allowing the degree of irreversibility to be calculated using the increase in entropy associated with the progression of microcracking. Specific tensile and bending tests were conducted to compare theoretical predictions of constitutive relationships to empirical curves. In addition, the tests were utilized to determine the model’s parameters, whose values were used to explicitly calculate the entropy increase. A large sample was used: 51 cortical bone coupons (dog-bone-shaped specimens) were extracted from the 4th ribs of numerous individuals and subjected to uniaxial tensile testing. Additionally, fifteen complete 4th ribs were used for bending tests. Displacement and strain fields were measured for both types of tests using digital image correlation or video recordings of the tests. All experimental specimen data were successfully fitted to the model, and all constitutive parameter values were found to be correlated with anthropometric variables. Explicit entropy calculations indicate that microcracking is minimal for low strain and, initially, stress is nearly proportional to strain. After a certain point, significant microcracking occurs, and the relationship between stress and strain becomes invalid. Several significant associations between constitutive parameters and age have also been identified.

The main aim of the current study is to explore direction-dependent fracture initiation and propagation within an arbitrary anisotropic solid. In particular, the specific objective is to develop an anisotropic cohesive phase-field (PF) fracture model. In this model, weak and strong anisotropy is considered both in the strain energy and fracture energy. This is achieved by considering contributions to strain energy of fiber and matrix as in the case of fiber-reinforced composites (FRC) together with introducing anisotropy in fracture energy through higher-order structural tensors. Motivated from earlier works of Van den Bosch et al. (Eng Fract Mech 73:1220–1234, 2006), the PF fracture model is integrated with a coupled exponential cohesive zone law which considers both normal and tangential components of separation. Such a cohesive PF description has a strong micromechanical basis for fracture, requiring interface fracture toughness and ultimate traction in normal and tangential directions. (C^0) and (C^1) approximations are used for modeling the weak and strong anisotropy. Several numerical examples are presented to demonstrate the usefulness of the model developed herein. The obtained numerical results are validated with the experimental results from the literature. The anisotropic fracture resulting in either intergranular or transgranular failure of polycrystalline material is analyzed by adopting a coupled anisotropic phase field and cohesive zone approach.

We present a review of the recent workshop “Micropolar Continua and beyond” which held in March 28–31, 2023, at Technische University of Berlin, Germany.