Luca Placidi

Bio: Luca Placidi is an academic researcher from Università telematica internazionale UniNettuno. The author has contributed to research in topics: Linear elasticity & Isotropy. The author has an hindex of 41, co-authored 99 publications receiving 4969 citations. Previous affiliations of Luca Placidi include Sapienza University of Rome & University of L'Aquila.

At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola

Abstract: Gabrio Piola’s scientific papers have been underestimated in mathematical physics literature. Indeed, a careful reading of them proves that they are original, deep and far-reaching. Actually, even ...

At the origins and in the vanguard of peri-dynamics, non-local and higher gradient continuum mechanics. An underestimated and still topical contribution of Gabrio Piola

Abstract: Gabrio Piola's scientific papers have been underestimated in the mathematical-physics literature. Indeed a careful reading of them proves that they are original, deep and far reaching. Actually -even if his contribution to mechanical sciences is not completely ignored- one can undoubtedly say that the greatest part of his novel contributions to mechanics, although having provided a great impetus and substantial influence on the work of many preminent mechanicians, is in fact generally ignored. It has to be remarked that authors [10] dedicated many efforts to the aim of unveiling the true value of Gabrio Piola as a scientist; however, some deep parts of his scientific results remain not yet sufficiently illustrated. Our aim is to prove that non-local and higher gradient continuum mechanics was conceived already in Piola's works and to try to explain the reasons of the unfortunate circumstance which caused the erasure of the memory of this aspect of Piola's contribution. Some relevant differential relationships obtained in Piola [Piola, 1845-6] are carefully discussed, as they are still nowadays too often ignored in the continuum mechanics literature and can be considered the starting point of Levi-Civita's theory of Connection for Riemannian manifolds.

Mechanical metamaterials: a state of the art:

Abstract: In this paper, we give a review of the state of the art in the study of mechanical metamaterials. The very attractive property of having a microstructure capable of determining exotic and specifica...

Pantographic metamaterials: an example of mathematically driven design and of its technological challenges

Abstract: In this paper, we account for the research efforts that have been started, for some among us, already since 2003, and aimed to the design of a class of exotic architectured, optimized (meta) materials. At the first stage of these efforts, as it often happens, the research was based on the results of mathematical investigations. The problem to be solved was stated as follows: determine the material (micro)structure governed by those equations that specify a desired behavior. Addressing this problem has led to the synthesis of second gradient materials. In the second stage, it has been necessary to develop numerical integration schemes and the corresponding codes for solving, in physically relevant cases, the chosen equations. Finally, it has been necessary to physically construct the theoretically synthesized microstructures. This has been possible by means of the recent developments in rapid prototyping technologies, which allow for the fabrication of some complex (micro)structures considered, up to now, to be simply some mathematical dreams. We show here a panorama of the results of our efforts (1) in designing pantographic metamaterials, (2) in exploiting the modern technology of rapid prototyping, and (3) in the mechanical testing of many real prototypes. Among the key findings that have been obtained, there are the following ones: pantographic metamaterials (1) undergo very large deformations while remaining in the elastic regime, (2) are very tough in resisting to damage phenomena, (3) exhibit robust macroscopic mechanical behavior with respect to minor changes in their microstructure and micromechanical properties, (4) have superior strength to weight ratio, (5) have predictable damage behavior, and (6) possess physical properties that are critically dictated by their geometry at the microlevel.

A unifying perspective: the relaxed linear micromorphic continuum

Abstract: We formulate a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force stresses and curvature contribution depending only on the micro-dislocation tensor. Our relaxed model is still able to fully describe rotation of the microstructure and to predict nonpolar size effects. It is intended for the homogenized description of highly heterogeneous, but nonpolar materials with microstructure liable to slip and fracture. In contrast to classical linear micromorphic models, our free energy is not uniformly pointwise positive definite in the control of the independent constitutive variables. The new relaxed micromorphic model supports well-posedness results for the dynamic and static case. There, decisive use is made of new coercive inequalities recently proved by Neff, Pauly and Witsch and by Bauer, Neff, Pauly and Starke. The new relaxed micromorphic formulation can be related to dislocation dynamics, gradient plasticity and seismic processes of earthquakes. It unifies and simplifies the understanding of the linear micromorphic models.

Introduction to the Finite Element Method

Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Electrodynamics Of Continuous Media

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