scholarly journals Structural hierarchy confers error tolerance in biological materials

2019 ◽  
Vol 116 (8) ◽  
pp. 2875-2880 ◽  
Author(s):  
Jonathan A. Michel ◽  
Peter J. Yunker
Keyword(s):  
Lattice Structure ◽  
Hierarchical Structures ◽  
Biological Materials ◽  
Hierarchical Level ◽  
Length Scales ◽  
Structural Hierarchy ◽  
Material Stiffness ◽  
Multiple Length Scales ◽  
Model Independent ◽  
Distinct Features

Structural hierarchy, in which materials possess distinct features on multiple length scales, is ubiquitous in nature. Diverse biological materials, such as bone, cellulose, and muscle, have as many as 10 hierarchical levels. Structural hierarchy confers many mechanical advantages, including improved toughness and economy of material. However, it also presents a problem: Each hierarchical level adds a new source of assembly errors and substantially increases the information required for proper assembly. This seems to conflict with the prevalence of naturally occurring hierarchical structures, suggesting that a common mechanical source of hierarchical robustness may exist. However, our ability to identify such a unifying phenomenon is limited by the lack of a general mechanical framework for structures exhibiting organization on disparate length scales. Here, we use simulations to substantiate a generalized model for the tensile stiffness of hierarchical filamentous networks with a nested, dilute triangular lattice structure. Following seminal work by Maxwell and others on criteria for stiff frames, we extend the concept of connectivity in network mechanics and find a similar dependence of material stiffness upon each hierarchical level. Using this model, we find that stiffness becomes less sensitive to errors in assembly with additional levels of hierarchy; although surprising, we show that this result is analytically predictable from first principles and thus potentially model independent. More broadly, this work helps account for the success of hierarchical, filamentous materials in biology and materials design and offers a heuristic for ensuring that desired material properties are achieved within the required tolerance.

Mechanistic Determination of In Situ Toughness of Bone Using a Nanoscratch Methodology

2009 ◽  
Author(s):  
Xiaodu Wang
Keyword(s):  
Mechanistic Model ◽  
Effective Means ◽  
Hierarchical Structures ◽  
Constitutive Relationship ◽  
Failure Behavior ◽  
Length Scales ◽  
Composites Materials ◽  
Multiple Length Scales ◽  
Relationship Of

Hierarchical structures at multiple length scales are characteristic in a class of natural (e.g., bone) and synthetic (e.g., nano-composites) materials that are quasi-brittle in nature but allow for appreciable plastic deformation (1, 2). Since the bulk mechanical properties of the materials are heavily dependent on their nano/microscopic structures, micro/nano mechanics approaches are often required to study their behaviors. However, lack of an effective means to exemplify the post-yield and failure behavior directly at micro/nanometer scales has significantly precluded understanding the constitutive relationship of these materials. A compelling example is that such paucity has significantly hindered establishment of physically sound constitutive relationships for bone tissues. Recent progresses in nanotechnology have allowed for estimation of the stiffness and hardness of bone tissues at submicron and nano length scales (3–5). However, no methods are currently available to assess the post-yield and failure behavior of bone tissues at nano/microscopic levels. Our pilot study (6) has shown that nanoscratch tests could be used in assessing the in situ energy dissipation during the post-yield deformation of bone tissues. To this end, the objective of the present study is to establish a mechanistic model for the nanoscratch methodology based on a assumption that the in situ toughness of bone tissues or the capacity to dissipate energy until failure can be estimated based on the removal energy of the tissue consumed during a nanoscratch test.

scholarly journals Fabrication and Compressive Behavior of a Micro-Lattice Composite by High Resolution DLP Stereolithography

Polymers ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 785
Author(s):  
Chow Shing Shin ◽  
Yu Chia Chang
Keyword(s):  
High Resolution ◽  
Lattice Structure ◽  
Low Cost ◽  
Hierarchical Structures ◽  
Dip Coating ◽  
Unit Cell ◽  
Digital Light Processing ◽  
Unit Cell Size ◽  
Wide Range ◽  
And Performance

Lattice structures are superior to stochastic foams in mechanical properties and are finding increasing applications. Their properties can be tailored in a wide range through adjusting the design and dimensions of the unit cell, changing the constituent materials as well as forming into hierarchical structures. In order to achieve more levels of hierarchy, the dimensions of the fundamental lattice have to be small enough. Although lattice size of several microns can be fabricated using the two-photon polymerization technique, sophisticated and costly equipment is required. To balance cost and performance, a low-cost high resolution micro-stereolithographic system has been developed in this work based on a commercial digital light processing (DLP) projector. Unit cell lengths as small as 100 μm have been successfully fabricated. Decreasing the unit cell size from 150 to 100 μm increased the compressive stiffness by 26%. Different pretreatments to facilitate the electroless plating of nickel on the lattice structure have been attempted. A pretreatment of dip coating in a graphene suspension is the most successful and increased the strength and stiffness by 5.3 and 3.6 times, respectively. Even a very light and incomplete nickel plating in the interior has increase the structural stiffness and strength by more than twofold.

Fracture resistance of human cortical bone across multiple length-scales at physiological strain rates

Biomaterials ◽  
2014 ◽  
Vol 35 (21) ◽  
pp. 5472-5481 ◽  
Author(s):  
Elizabeth A. Zimmermann ◽  
Bernd Gludovatz ◽  
Eric Schaible ◽  
Björn Busse ◽  
Robert O. Ritchie
Keyword(s):  
Cortical Bone ◽  
Fracture Resistance ◽  
Strain Rates ◽  
Physiological Strain ◽  
Length Scales ◽  
Human Cortical Bone ◽  
Multiple Length Scales

Patterning of Soft Matter across Multiple Length Scales

2016 ◽  
Vol 26 (16) ◽  
pp. 2609-2616 ◽  
Author(s):  
Pim van der Asdonk ◽  
Hans C. Hendrikse ◽  
Marcos Fernandez-Castano Romera ◽  
Dion Voerman ◽  
Britta E. I. Ramakers ◽  
...  
Keyword(s):  
Soft Matter ◽  
Length Scales ◽  
Multiple Length Scales

Surface integrity analysis of machined Inconel 718 over multiple length scales

CIRP Annals ◽  
2012 ◽  
Vol 61 (1) ◽  
pp. 99-102 ◽  
Author(s):  
Rachid M'Saoubi ◽  
Tommy Larsson ◽  
José Outeiro ◽  
Yang Guo ◽  
Sergey Suslov ◽  
...  
Keyword(s):  
Surface Integrity ◽  
Inconel 718 ◽  
Length Scales ◽  
Multiple Length Scales ◽  
Integrity Analysis

An Energetic Approach to Modeling Cytoskeletal Architecture in Maturing Cardiomyocytes

2021 ◽  
Author(s):  
William F Sherman ◽  
Mira Asad ◽  
Anna Grosberg
Keyword(s):  
Cardiac Tissue ◽  
Length Scales ◽  
Functional Changes ◽  
Physical Constraints ◽  
Scale Parameters ◽  
Structure And Dynamics ◽  
Energetic Approach ◽  
Cytoskeletal Network ◽  
Multiple Length Scales ◽  
Potential Factors

Abstract Through a variety of mechanisms, a healthy heart is able to regulate its structure and dynamics across multiple length scales. Disruption of these mechanisms can have a cascad- ing effect, resulting in severe structural and/or functional changes that permeate across different length scales. Due to this hierarchical structure, there is interest in understand- ing how the components at the various scales coordinate and influence each other. However, much is unknown regarding how myofibril bundles are organized within a densely packed cell and the influence of the subcellular components on the architecture that is formed. To elucidate potential factors influencing cytoskeletal development, we proposed a compu- tational model that integrated interactions at both the cel- lular and subcelluar scale to predict the location of indi- vidual myofibril bundles that contributed to the formation of an energetically favorable cytoskeletal network. Our model was tested and validated using experimental metrics derived from analyzing single cell cardiomyocytes. We demonstrated that our model-generated networks were capable of repro- ducing the variation observed in experimental cells at different length scales as a result of the stochasticity inher- ent in the different interaction between the various cellu- lar components. Additionally, we showed that incorporat- ing length-scale parameters resulted in physical constraints that directed cytoskeletal architecture towards a structurally consistent motif. Understanding the mechanisms guiding the formation and organization of the cytoskeleton in individual cardiomyocytes can aid tissue engineers towards developing functional cardiac tissue.

scholarly journals ROBUSTNESS-STRENGTH PERFORMANCE OF HIERARCHICAL ALPHA-HELICAL PROTEIN FILAMENTS

2009 ◽  
Vol 01 (01) ◽  
pp. 85-112 ◽  
Author(s):  
ZHAO QIN ◽  
STEVEN CRANFORD ◽  
THEODOR ACKBAROW ◽  
MARKUS J BUEHLER
Keyword(s):  
De Novo ◽  
Hierarchical Structures ◽  
High Strength ◽  
Material Design ◽  
Building Blocks ◽  
Biological Materials ◽  
Strength Performance ◽  
Synthetic Materials ◽  
Helical Protein ◽  
Bioinspired Nanomaterials

An abundant trait of biological protein materials are hierarchical nanostructures, ranging through atomistic, molecular to macroscopic scales. By utilizing the recently developed Hierarchical Bell Model, here we show that the use of hierarchical structures leads to an extended physical dimension in the material design space that resolves the conflict between disparate material properties such as strength and robustness, a limitation faced by many synthetic materials. We report materiomics studies in which we combine a large number of alpha-helical elements in all possible hierarchical combinations and measure their performance in the strength-robustness space while keeping the total material use constant. We find that for a large number of constitutive elements, most random structural combinations of elements (> 98%) lead to either high strength or high robustness, reflecting the so-called banana-curve performance in which strength and robustness are mutually exclusive properties. This banana-curve type behavior is common to most engineered materials. In contrast, for few, very specific types of combinations of the elements in hierarchies (< 2%) it is possible to maintain high strength at high robustness levels. This behavior is reminiscent of naturally observed material performance in biological materials, suggesting that the existence of particular hierarchical structures facilitates a fundamental change of the material performance. The results suggest that biological materials may have developed under evolutionary pressure to yield materials with multiple objectives, such as high strength and high robustness, a trait that can be achieved by utilization of hierarchical structures. Our results indicate that both the formation of hierarchies and the assembly of specific hierarchical structures play a crucial role in achieving these mechanical traits. Our findings may enable the development of self-assembled de novo bioinspired nanomaterials based on peptide and protein building blocks.

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