Perspectives in Generalized Continua

Laudato, Marco; Ciallella, Alessandro

doi:10.1007/978-3-030-50464-9_1

Cited by 11 publications

(11 citation statements)

References 94 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The complexity of bone, both in its interior architecture and in its the functional adaptation, can be taken as a fount of inspiration for conceiving new mechanical metamaterials [214,[216][217][218][219][220][221][222][223]. This is why we (hopefully) try in this review paper to give a synoptic insight, from a mechanical point of view, of the amazing properties of the bone tissue.…”

Section: Discussionmentioning

confidence: 99%

In-depth gaze at the astonishing mechanical behavior of bone: A review for designing bio-inspired hierarchical metamaterials

Giorgio

Spagnuolo

Andreaus

et al. 2020

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

In this review paper, some relevant models, algorithms, and approaches conceived to describe the bone tissue mechanics and the remodeling process are showcased. Specifically, we briefly describe the hierarchical structure of the bone at different levels and underline the geometrical substructure characterizing the bone itself. The mechanical models adopted to describe the bone tissue at different levels of observation are introduced in their essential aspects. Furthermore, the modeling of the evolution, including the growth and resorption of bone, is treated by analyzing the main approaches employed, namely the mechanical feedback concept and the structural optimization perspective. In this regard, the most prominent ways to model the biomechanical stimulus are summarized. The modeling of the interaction with prostheses or grafts commonly used in reconstructive surgery is also recalled. The main aim of this survey consists thereby in providing the appropriate knowledge to mimic the deeply structured hierarchy of the bone tissue for synthesizing innovative and highly performing bio-inspired metamaterials.

show abstract

Section: Discussionmentioning

confidence: 99%

In-depth gaze at the astonishing mechanical behavior of bone: A review for designing bio-inspired hierarchical metamaterials

Giorgio

Spagnuolo

Andreaus

et al. 2020

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

show abstract

“…We can formulate Hooke’s law to define the stress tensor

as a linear combination of the volumetric and deviatoric strain tensors:

where K is the bulk modulus and G is the shear modulus. From Equation ( 1 ), it is possible then to recognize the two contributions to the stress, namely the hydrostatic:

and shear or deviatoric part:

This formulation can be generalized by using mechanical micromorphic [ 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 ], micropolar [ 57 , 58 , 59 , 60 ], higher-order [ 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 ], or peridynamic [ 71 , 72 , 73 , 74 ] models. As an opening move, the stiffnesses can be evaluated starting with the knowledge of the engineering parameters, Young’s modulus Y , and Poisson’s ratio

as follows:

since they are more str...…”

Section: Methodsmentioning

confidence: 99%

Bone Remodeling Process Based on Hydrostatic and Deviatoric Strain Mechano-Sensing

et al. 2022

Self Cite

View full text Add to dashboard Cite

A macroscopic continuum model intended to provide predictions for the remodeling process occurring in bone tissue is proposed. Specifically, we consider a formulation in which two characteristic stiffnesses, namely the bulk and shear moduli, evolve independently to adapt the hydrostatic and deviatoric response of the bone tissue to environmental changes. The formulation is deliberately simplified, aiming at constituting a preliminary step toward a more comprehensive modeling approach. The evolutive process for describing the functional adaptation of the two stiffnesses is proposed based on an energetic argument. Numerical experiments reveal that it is possible to model the bone remodeling process with a different evolution for more than one material parameter, as usually done. Moreover, the results motivate further investigations into the subject.

show abstract

“…The mathematical challenge that researchers in the field of Continuum Mechanics face today, therefore, is to design metamaterials that can be described within the framework of a generalized theory [86,87,90,[107][108][109]. These materials, as we shall see, are conceived in order to possess mechanical properties that are significantly more performing than those of the commonly called natural materials.…”

Section: Mathematics Designs the World: Metamaterials A Change Of Paradigmmentioning

confidence: 99%

The Study of the Genesis of Novel Mathematical and Mechanical Theories Provides an Inspiration for Future Original Research

Spagnuolo

Dell’Isola

Cazzani

2021

Advanced Structured Materials

View full text Add to dashboard Cite

In this introductory chapter we present the motivations that prompted the authors and editors to work on this volume. The fil rouge followed in the discussion presented below is based on the following consideration: the study of the genesis of mathematical and mechanical theories does not have a merely philological purpose, but can influence and even inspire the development of new original ideas. We present some examples that clarify our thesis: the development of the model of planetary motion and a historical-critical study of the development of Continuum Mechanics. Clearly understanding the main errors and misunderstandings that other than pure research logics have introduced in the scientific discussion is the only way to learn a serious and rigorous approach to Science. An idea that has guided us in the development of this chapter is that fragmentation of culture brings to inability to deal with complexity. The only way to study and, above all, understand the complexity of our world is through a unified vision of knowledge.

show abstract

Perspectives in Generalized Continua

Cited by 11 publications

References 94 publications

In-depth gaze at the astonishing mechanical behavior of bone: A review for designing bio-inspired hierarchical metamaterials

In-depth gaze at the astonishing mechanical behavior of bone: A review for designing bio-inspired hierarchical metamaterials

Bone Remodeling Process Based on Hydrostatic and Deviatoric Strain Mechano-Sensing

The Study of the Genesis of Novel Mathematical and Mechanical Theories Provides an Inspiration for Future Original Research

Contact Info

Product

Resources

About