1,721,070 research outputs found
Multi-scale and multi-physics: towards next-generation engineering materials
No full textMulti-scale and multi-physics are two important thematics when thinking to how next-generation materials will be engineered, aimed at delivering exceptional performances. This special issue attempts at collecting a representative sample of the interdisciplinary efforts that the scientific community is making towards the understanding and exploitation of the complex behaviours that can arise from multi-scale and multi-physics interactions. This contribution aims at contextualising and giving a perspective on the current trends and ideas which drive these efforts
Kinematically triggered nonlinear vibrations of hencky-type pantographic sheets
No full textPantographic metamaterials are receiving increasing attention from the scientific community working in theoretical and numerical mechanics. Nevertheless, dynamic analysis of pantographic sheets in the large deformation regime is still a scarcely explored topic which deserves to be thoroughly investigated on its own. With the aim of contributing to filling this gap, we study kinematically triggered vibrations in pantographic sheets. More specifically, two tests are considered. At first, an initial nonzero velocity, i.e., an impulse, is applied to the pantographic sheet at a single fiber's end — such as in a dynamic pull test — which is left free to move afterwards. The second test addresses vibrations induced by a given accelerogram applied to a subset of nodes. In the spirit of Hencky's approach, the whole set of results is obtained by using a completely discrete mechanical model such that the fibers of the pantographic sheet are modeled as extensible Euler-Bernoulli beams, which are in turn discretized by means of rotational and extensional springs. The time integration scheme consists of a stepwise method based on the recently revisited scheme of Casciaro
Equilibrium paths of hencky pantographic beams in a three-point bending problem
No full textWe investigate the mechanical behavior of so-called pantographic beams undergoing large deformations. To this aim, an exact-kinematics Hencky pantographic beam model has been employed in a three-point bending test. Given the occurrence of local snap-through instabilities and limit points, said Hencky model has been solved by means of a step-by-step strategy based on Riks's arclength method. Such a method has been particularly adapted for the case of problems with prescribed displacements, as opposed to those with prescribed forces. Numerical simulations performed by varying the stiffness parameters are discussed, aimed at getting an insight into the different behaviors which can be exhibited by pantographic beams. Numerical simulations performed by varying the quantity of unit cells for fixed total length allow instead to understand whether the observed features are inherent to the pantographic beam structure or size-dependent. Therefore, beyond being interesting for possible future engineering exploitation, we believe this phenomenological evidence to be useful in guiding the formulation of conjectures regarding observed microscale local snap-through instability phenomena in the framework of a previously proposed macroscale continuum model for pantographic beams obtained by asymptotic homogenization
A new block-based approach for the analysis of damage in masonries undergoing large deformations
No full textA new block-based elasto-damage model for describing masonry structures has been recently proposed (Tran et al. in Mech Res Commun 118:103802, 2021), where the used constitutive elastic and damage behavioral laws were inspired from granular micromechanics. Preliminary results hinted at the realistic masonry deformation modes which could be obtained, as well as the importance of the damaging characteristic lengths featured in the model. The present work is an extension of that previous paper and presents a more detailed derivation of the model, along with a finer parametric study of the damaging characteristic lengths. Qualitative results hint at how those characteristic lengths allow to model interactions between normal and tangential deformations of the mortar, thus opening the way for future development and quantitative studies of the model
A partial report on the controversies about the Principle of Virtual Work: from Archytas of Tarentum to Lagrange, Piola, Mindlin and Toupin
No full textIn this chapter, we present a historical survey on the Principle of Virtual Work as the guiding principle for constructing mathematical models to describe and predict phenomena. In particular, we want to make the reader aware of the development of two main approaches toward the formulation of new models, the first using the Principle of Virtual Work, while the second using the balance of some quantities to be suitably chosen. This dualism, which was probably already present in Hellenistic times, has been nurtured in modern times by some of the most important scientists of the last centuries. We think it is worthwhile to study their work, not only to attempt a historically-founded authorship attribution of the underlying ideas, but especially so that their work can guide us while developing new theories. Our discussion, which begins from the available fragmentary sources dealing with Hellenistic Mechanics, focuses on the efforts by D'Alembert and Lagrange, which produced a modern comprehensive formulation of Classical Mechanics based on the Principle of Virtual Work. Referring to these historical instances, we advocate the effectiveness of using the Principle of Virtual Work, as opposed to balance laws, as a basic postulate in formulating new models, arguing that it allows using a minimal set of a priori and clear conjectures, avoiding the need for a posteriori ad hoc - hence often logically incompatible - assumptions based on "physical intuition". As a paradigmatic case, we present the formulation of N-th Gradient Continuum Mechanics developed in the pioneering - but not yet widely known - work of Piola, where a wise use of the Principle of Virtual Work leads to a theory that is more general than the one developed starting from Cauchy’s "tetrahedron argument", based on the Law of Balance
Wave dispersion in non-linear pantographic beams
No full textIn this paper, amplitude-dependent dispersion relations for flexural and axial waves travelling along a pantographic beam in non-linear deformation regime are computed. The kinetic energy of the pantographic beam, including a gradient micro-inertia contribution, is derived by homogenization. In the limit of travelling waves with infinitesimal amplitude, well-known amplitude-independent wave dispersion relations for linear deformation regime are recovered. Our analysis concludes that exotic wave propagation is observed in pantographic beams and deserves further studies. </p
In-plane dynamic buckling of duoskelion beam-like structures: discrete modeling and numerical results
No full textIn this contribution, a previously introduced discrete model for studying the statics of duoskelion beam-like structures is extended to dynamics. The results of numerical simulations performed using such an extended model are reported to discuss the in-plane dynamic buckling of duoskelion structures under different loading and kinematic boundary conditions. The core instrument of the analysis is a discrete beam element, which, in addition to flexure, also accounts for extension and shearing deformations. Working in the setting of dynamics, inertial contributions are taken into account as well. A stepwise time integration scheme is employed to reconstruct the complete trajectory of the system, namely before and after buckling. It is concluded that the duoskelion structure exhibits exotic features compared with classical beam-like structures modeled at macro-scale by Euler–Bernoulli’s model
Two-dimensional strain gradient damage modeling: a variational approach
No full textIn this paper, we formulate a linear elastic second gradient isotropic two-dimensional continuum model accounting for irreversible damage. The failure is defined as the condition in which the damage parameter reaches 1, at least in one point of the domain. The quasi-static approximation is done, i.e., the kinetic energy is assumed to be negligible. In order to deal with dissipation, a damage dissipation term is considered in the deformation energy functional. The key goal of this paper is to apply a non-standard variational procedure to exploit the damage irreversibility argument. As a result, we derive not only the equilibrium equations but, notably, also the Karush–Kuhn–Tucker conditions. Finally, numerical simulations for exemplary problems are discussed as some constitutive parameters are varying, with the inclusion of a mesh-independence evidence. Element-free Galerkin method and moving least square shape functions have been employed
Three-point bending test of pantographic blocks: numerical and experimental investigation
No full textThe equilibrium forms of pantographic blocks in a three-point bending test are investigated via both experiments and numerical simulations. In the computational part, the corresponding minimization problem is solved with a deformation energy derived by homogenization within a class of admissible solutions. To evaluate the numerical simulations, series of measurements have been carried out with a suitable experimental setup guided by the acquired theoretical knowledge. The observed experimental issues have been resolved to give a robust comparison between the numerical and experimental results. Promising agreement between theoretical predictions and experimental results is demonstrated for the planar deformation of pantographic blocks
Nonlinear dynamics of origami metamaterials: energetic discrete approach accounting for bending and in-plane deformation of facets
No full textIn this paper, we start the analysis of the nonlinear dynamics of structural elements having an origami-type microstructure and micro-kinematics, also known as origami metamaterials. We use a finite-dimensional Lagrangian system to explore, via numerical simulations, the overall behaviour of an origami beam. This provides some significant hints about the structure of an effective homogenized continuum model for such a beam. We introduce a geometrically exact two-dimensional triangular discrete element, whose kinematics is given in terms of three-dimensional nodal displacements. Inertial terms are taken into account. Facets-which in this paper are quadrilateral-are modelled as the union of several triangles, each triangle deforming affinely in plane. Facet bending and sheet folding are taken into account by constraining through cylindrical hinges adjacent triangles and placing in-between torsional springs between them. In-plane and bending/folding strain energies are estimated from the elongation of the triangles' sides and from the relative rotations of adjacent triangles, respectively. The actual reconstruction of the equilibrium path is performed numerically through a stepwise time integration scheme that can handle large displacements
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