Non-standard Timoshenko beam model for chiral metamaterial: Identification of stiffness parameters

Angelo, Michele De; Placidi, Luca; Nejadsadeghi, Nima; Misra, Anil

doi:10.1016/j.mechrescom.2019.103462

Cited by 47 publications

(22 citation statements)

References 24 publications

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“…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

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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.

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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

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“…The order of magnitude of ℓ is assumed to be 200 μm, i.e., the diameter of trabeculae that are the elements of which the microstructure is made of (see, for more details on lattice structures similar to the trabecular bone, [ 10 ]). The second gradient continuum model may be deduced using an homogenization technique that through a micro-macro identification permit to obtain an equivalent model that predicts at the macro scale the response of the material due to the microstructure existing at micro-scale (see e.g., [ 26 , 52 , 53 , 54 , 55 , 56 , 57 ]). In this context, some critical issues related to the rise of damage in the system constituted by bone tissue and bio-material can be taken into account (see e.g., [ 58 , 59 , 60 , 61 , 62 , 63 , 64 ]).…”

Section: The Model Employed To Describe Bone Remodelingmentioning

confidence: 99%

Bio-Inspired Design of a Porous Resorbable Scaffold for Bone Reconstruction: A Preliminary Study

2021

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The study and imitation of the biological and mechanical systems present in nature and living beings always have been sources of inspiration for improving existent technologies and establishing new ones. Pursuing this line of thought, we consider an artificial graft typical in the bone reconstruction surgery with the same microstructure of the bone living tissue and examine the interaction between these two phases, namely bone and the graft material. Specifically, a visco-poroelastic second gradient model is adopted for the bone-graft composite system to describe it at a macroscopic level of observation. The second gradient formulation is employed to consider possibly size effects and as a macroscopic source of interstitial fluid flow, which is usually regarded as a key factor in bone remodeling. With the help of the proposed formulation and via a simple example, we show that the model can be used as a graft design tool. As a matter of fact, an optimization of the characteristics of the implant can be carried out by numerical investigations. In this paper, we observe that the size of the graft considerably influences the interaction between bone tissue and artificial bio-resorbable material and the possibility that the bone tissue might substitute more or less partially the foreign graft for better bone healing.

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“…While a 1D system is helpful in understanding the underlying physics behind the observed phenomena, many engineering applications are concerned with higher dimensional systems. The GMA-based micromorphic model of degree 1 presented here can be systematically expanded to include two-dimensional and three-dimensional systems [41], or to model deflection in beams [61].…”

Section: Conclusion and Summary (Prognosis Toward Experimental Design)mentioning

confidence: 99%

On the statics and dynamics of granular-microstructured rods with higher order effects

Nejadsadeghi

Misra

2021

Mathematics and Mechanics of Solids

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Granular-microstructured rods show strong dependence of grain-scale interactions in their mechanical behavior, and therefore, their proper description requires theories beyond the classical theory of continuum mechanics. Recently, the authors have derived a micromorphic continuum theory of degree n based upon the granular micromechanics approach (GMA). Here, the GMA is further specialized for a one-dimensional material with granular microstructure that can be described as a micromorphic medium of degree 1. To this end, the constitutive relationships, governing equations of motion and variationally consistent boundary conditions are derived. Furthermore, the static and dynamic length scales are linked to the second-gradient stiffness and micro-scale mass density distribution, respectively. The behavior of a one-dimensional granular structure for different boundary conditions is studied in both static and dynamic problems. The effects of material constants and the size effects on the response of the material are also investigated through parametric studies. In the static problem, the size-dependency of the system is observed in the width of the emergent boundary layers for certain imposed boundary conditions. In the dynamic problem, microstructural effects are always present and are manifested as deviations in the natural frequencies of the system from their classical counterparts.

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Non-standard Timoshenko beam model for chiral metamaterial: Identification of stiffness parameters

Cited by 47 publications

References 24 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

Bio-Inspired Design of a Porous Resorbable Scaffold for Bone Reconstruction: A Preliminary Study

On the statics and dynamics of granular-microstructured rods with higher order effects

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