1,721,292 research outputs found
Numerical identification procedure between a micro-Cauchy model and a macro-second gradient model for planar pantographic structures
No full textIn order to design the microstructure of metamaterials showing high toughness in extension (property to beshared with muscles), it has been recently proposed (Dell’Isola et al. in Z Angew Math Phys 66(6):3473–3498,2015)toconsider pantographic structures. It is possible to model such structures at a suitably small length scale (resolving in detailthe interconnecting pivots/cylinders) using a standard Cauchy first gradient theory. However, the computational costs forsuch modelling choice are not allowing for the study of more complex mechanical systems including for instance manypantographic substructures. The microscopic model considered here is a quadratic isotropic Saint-Venant first gradientcontinuum including geometric nonlinearities and characterized by two Lam ́e parameters. The introduced macroscopictwo-dimensional model for pantographic sheets is characterized by a deformation energy quadratic both in the first andsecond gradient of placement. However, as underlined in Dell’Isola et al. (Proc R Soc Lond A 472(2185):20150790,2016),it is needed that the second gradient stiffness depends on the first gradient of placement if large deformations and largedisplacements configurations must be described. The numerical identification procedure presented in this paper consistsin fitting the macro-constitutive parameters using several numerical simulations performed with the micro-model. Theparameters obtained by the best fit identification in few deformation problems fit very well also in many others, showingthat the reduced proposed model is suitable to get an effective model at relevantly lower computational effort. The presentednumerical evidences suggest that a rigorous mathematical homogenization result most likely holds
Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives
No full textSince the first studies dedicated to the mechanics of deformable bodies (by Euler, D’Alembert, Lagrange) the principle of virtual work (or virtual velocities) has been used to provide firm guidance to the formulation of novel theories. Gabrio Piola dedicated his scientific life to formulating a continuum theory in order to encompass a large class of deformation phenomena and was the first author to consider continua with non-local internal interactions and, as a particular case, higher-gradient continua. More recent followers of Piola (Mindlin, Sedov and then Richard Toupin) recognized the principle of virtual work (and its particular case, the principle of least action) as the (only!) firm foundation of continuum mechanics. Mindlin and Toupin managed to formulate a conceptual frame for continuum mechanics which is able to effectively model the complex behaviour of so-called architectured, advanced, multiscale or microstructured (meta)materials. Other postulation schemes, in contrast, do not seem able to be equally efficient. The present work aims to provide a historical and theoretical overview of the subject. Some research perspectives concerning this theoretical approach are outlined in the final section
Variational principles in numerical practice
Full text linkVariational principles represent a general framework for determining the mechanical state of a system, by identifying its motion as a minimum of a pertinent functional. Moreover, finite element methods are naturally based on variational principles and provide a very powerful tool for numerically solving many mechanical as well as other multi-physics problems. The purpose of the present note is to illustrate some recent applications with special reference to biomechanics and dissipation in quasi-brittle materials and piezo-electromechanical structures, in order to confirm the validation and to highlight the bright
prospects of this method
Identification of two-dimensional pantographic structure via a linear D4 orthotropic second gradient elastic model
Full text linkA linear elastic second gradient orthotropic two-dimensional solid that is invariant under (Formula presented.) rotation and for mirror transformation is considered. Such anisotropy is the most general for pantographic structures that are composed of two identical orthogonal families of fibers. It is well known in the literature that the corresponding strain energy depends on nine constitutive parameters: three parameters related to the first gradient part of the strain energy and six parameters related to the second gradient part of the strain energy. In this paper, analytical solutions for simple problems, which are here referred to the heavy sheet, to the nonconventional bending, and to the trapezoidal cases, are developed and presented. On the basis of such analytical solutions, gedanken experiments were developed in such a way that the whole set of the nine constitutive parameters is completely characterized in terms of the materials that the fibers are made of (i.e., of the Young’s modulus of the fiber materials), of their cross sections (i.e., of the area and of the moment of inertia of the fiber cross sections), and of the distance between the nearest pivots. On the basis of these considerations, a remarkable form of the strain energy is derived in terms of the displacement fields that closely resembles the strain energy of simple Euler beams. Numerical simulations confirm the validity of the presented results. Classic bone-shaped deformations are derived in standard bias numerical tests and the presence of a floppy mode is also made numerically evident in the present continuum model. Finally, we also show that the largeness of the boundary layer depends on the moment of inertia of the fibers
Experimental behavior of concrete with micro-particles under cyclic loading and effects due to frictional energy dissipation
No full textIn plane shear and bending for first gradient inextensible pantographic sheets. Numerical study of deformed shapes and global constraint reactions
No full textThe aim of the present paper is the analysis of a two-dimensional continuum with two families of inextensible fibers that are orthogonal in the initial configuration. In the first part of the work, a new formulation is presented, in which the problem is reduced to a standard nonlinear constrained minimization, while in the second part of the work several numerical investigations are presented considering different boundary conditions with respect to standard symmetric bias extensional tests. The conceptual framework can be recognized in the researches by Pipkin and Rivlin on inextensible nets. Furthermore, an implicit version of the Rivlin representation of the generic placement for a two-dimensional sheet with two families of inextensible fibers is provided by considering the angles of the fiber directors as degrees of the freedom of the formulation. In this way the first gradient formulation is given in terms of two angle fields only
Phytotherapy in the treatment of Benign Prostatic Hyperplasia (BPH): between evidence and empiricism
Full text linkThe treatment of Benign Prostatic Hyperplasia (BPH) has been
recently approved by different international guidelines like AUA, EAU, NICE, WHO consultation, etc, and drugs as the alpha-blockers and the 5-alpha-reductase inhibitors are widely indicated for this disease.Moreover, little space is given to the anti-cholinergics and recently to the phosphodiesterase type 5 inhibitors.In this field of application, the phytotherapics, in particularSerenoa repens, are less or not recommended, because they are not supported by adequate scientific evidence.However, the use of these molecules is widely diffuse all over the world, achieving the first choice of treatment in some Nations such as the Asians
A model for elastic flexoelectric materials including strain gradient effects
No full textA constitutive model for elastic flexoelectric materials under small deformation based on second gradient continuum theory
is developed, using a Toupin-like variational formulation to simultaneously obtain constitutive relations, balance equations and
boundary conditions. The model includes three different electromechanical ‘‘stresses’’: a higher-order stress, an extended
local electric force and a generalized Cauchy stress tensor. The constitutive equations of the model are obtained by postulating an internal energy density function which depends on both the strain and its gradient as well as the polarization. Finally, as
an application of the model, we derive the explicit analytical expressions of the polarization and displacement vector fields
for the problem of the polarization induced over a thin spherical shell subjected to hydrostatic loading conditions
Interfaces in micromorphic materials: Wave transmission and reflection with numerical simulations
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