Elastic Characterization of Transversely Isotropic Soft Materials by Dynamic Shear and Asymmetric Indentation

The mechanical characterization of soft anisotropic materials is a fundamental challenge because of difficulties in applying mechanical loads to soft matter and the need to combine information from multiple tests. A method to characterize the linear elastic properties of transversely isotropic soft materials is proposed, based on the combination of dynamic shear testing (DST) and asymmetric indentation. The procedure was demonstrated by characterizing a nearly incompressible transversely isotropic soft material. A soft gel with controlled anisotropy was obtained by polymerizing a mixture of fibrinogen and thrombin solutions in a high field magnet (B = 11.7 T); fibrils in the resulting gel were predominantly aligned parallel to the magnetic field. Aligned fibrin gels were subject to dynamic (20–40 Hz) shear deformation in two orthogonal directions. The shear storage modulus was 1.08 ± 0. 42 kPa (mean ± std. dev.) for shear in a plane parallel to the dominant fiber direction, and 0.58 ± 0.21 kPa for shear in the plane of isotropy. Gels were indented by a rectangular tip of a large aspect ratio, aligned either parallel or perpendicular to the normal to the plane of transverse isotropy. Aligned fibrin gels appeared stiffer when indented with the long axis of a rectangular tip perpendicular to the dominant fiber direction. Three-dimensional numerical simulations of asymmetric indentation were used to determine the relationship between direction-dependent differences in indentation stiffness and material parameters. This approach enables the estimation of a complete set of parameters for an incompressible, transversely isotropic, linear elastic material.

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Probabilistic Analysis of Three-Dimensional Beams with Uncertain Damage

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.348-349.97 ◽

2007 ◽

Vol 348-349 ◽

pp. 97-100

Author(s):

Cristina Gentilini ◽

Lucio Nobile

Keyword(s):

Probabilistic Analysis ◽

Reliable Method ◽

Numerical Test ◽

Three Dimensional ◽

Elastic Response ◽

Frame Structures ◽

Linear Elastic ◽

Probabilistic Characterization ◽

Edge Cracks

This paper deals with a simple and reliable method for the probabilistic characterization of the linear elastic response of frame structures with edge cracks of uncertain depth and location in the three-dimensional setting. A numerical test evidences the performance of the approach.

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Recent developments in the evaluation of the 3D fundamental solution and its derivatives for transversely isotropic elastic materials

Electronic Journal of Boundary Elements ◽

10.14713/ejbe.v10i1.1116 ◽

2012 ◽

Vol 10 (1) ◽

Cited By ~ 1

Author(s):

V. Mantič ◽

L. Távara ◽

J.E. Ortiz ◽

F. París

Keyword(s):

Fundamental Solution ◽

Rotational Symmetry ◽

Three Dimensional ◽

Transversely Isotropic ◽

Real Variable ◽

Radius Vector ◽

Linear Elastic ◽

Plane Normal ◽

Starting Point ◽

Recent Developments

Explicit closed-form real-variable expressions of a fundamental solution and its derivatives for three-dimensional problems in transversely linear elastic isotropic solids are presented. The expressions of the fundamental solution in displacements Uik and its derivatives, originated by a unit point force, are valid for any combination of material properties and for any orientation of the radius vector between the source and field points. An ex- pression of Uik in terms of the Stroh eigenvalues on the oblique plane normal to the radius vector is used as starting point. Working from this expression of Uik, a new approach (based on the application of the rotational symmetry of the material) for deducing the first and second order derivative kernels, Uik,j and Uik,jl respectively, has been developed. The expressions of the fundamental solution and its derivatives do not suffer from the difficulties of some previous expressions, obtained by other authors in different ways, with complex valued functions appearing for some combinations of material parameters and/or with division by zero for the radius vector at the rotational symmetry axis. The expressions of Uik, Uik,j and Uik,jl are presented in a form suitable for an efficient computational implementation in BEM codes.

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Chemically Responsive Hydrogel Deformation Mechanics: A Review

Molecules ◽

10.3390/molecules24193521 ◽

2019 ◽

Vol 24 (19) ◽

pp. 3521 ◽

Cited By ~ 5

Author(s):

Eanna Fennell ◽

Jacques M. Huyghe

Keyword(s):

Numerical Models ◽

Three Dimensional ◽

Soft Materials ◽

Dimensional Network ◽

Health Products ◽

Deformation Mechanics ◽

Natural Tissue ◽

Responsive Hydrogels ◽

Geometric Surface

A hydrogel is a polymeric three-dimensional network structure. The applications of this material type are diversified over a broad range of fields. Their soft nature and similarity to natural tissue allows for their use in tissue engineering, medical devices, agriculture, and industrial health products. However, as the demand for such materials increases, the need to understand the material mechanics is paramount across all fields. As a result, many attempts to numerically model the swelling and drying of chemically responsive hydrogels have been published. Material characterization of the mechanical properties of a gel bead under osmotic loading is difficult. As a result, much of the literature has implemented variants of swelling theories. Therefore, this article focuses on reviewing the current literature and outlining the numerical models of swelling hydrogels as a result of exposure to chemical stimuli. Furthermore, the experimental techniques attempting to quantify bulk gel mechanics are summarized. Finally, an overview on the mechanisms governing the formation of geometric surface instabilities during transient swelling of soft materials is provided.

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On the Efficiency of Analyzing 3D Anisotropic, Transversely Isotropic, and Isotropic Bodies in BEM

Journal of Mechanics ◽

10.1017/s1727719100004688 ◽

2010 ◽

Vol 26 (4) ◽

pp. 483-491

Author(s):

Y. C. Shiah ◽

W. X. Sun

Keyword(s):

Closed Form ◽

Computational Efficiency ◽

Transverse Isotropy ◽

Three Dimensional ◽

Transversely Isotropic ◽

Fundamental Solutions ◽

Engineering Practice ◽

Closed Form Solutions ◽

Anisotropic Bodies ◽

Isotropic Bodies

ABSTRACTDue to a lack of closed-form solutions for three dimensional anisotropic bodies, the computational burden of evaluating the fundamental solutions in the boundary element method (BEM) has been a research focus over the years. In engineering practice, transversely isotropic material has gained popularity in the use of composites. As a degenerate case of the generally anisotropic material, transverse isotropy still needs to be treated separately to ease the computations. This paper aims to investigate the computational efficiency of the BEM implementations for 3D anisotropic, transversely isotropic, and isotropic bodies. For evaluating the fundamental solutions of 3D anisotropy, the explicit formulations reported in [1,2] are implemented. For treating transversely isotropic materials, numerous closed form solutions have been reported in the literature. For the present study, the formulations presented by Pan and Chou [3] are particularly employed. At the end, a numerical example is presented to compare the computational efficiency of the three cases and to demonstrate how the CPU time varies with the number of meshes.

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Invariant Theory for Dispersed Transverse Isotropy: An Efficient Means for Modeling Fiber Splay

Advances in Bioengineering ◽

10.1115/imece2004-61236 ◽

2004 ◽

Author(s):

D. R. Einstein ◽

A. D. Freed ◽

I. Vesley

Keyword(s):

Invariant Theory ◽

Soft Tissues ◽

Structural Model ◽

Transverse Isotropy ◽

Three Dimensional ◽

Constitutive Law ◽

Fiber Direction ◽

Fiber Stress ◽

Element Analysis ◽

Model Modification

Microstructual studies suggest that in some tissues, collagen fibers are approximately normally distributed about a mean preferred fiber direction. Structural constitutive equations that account for this dispersion of fibers have been shown to capture the mechanical complexity of these tissues quite well. However, such descriptions are computationally cumbersome for two-dimensional fiber distributions, let alone for fully three dimensional fiber populations. We have developed a new constitutive law for such tissues, based on a novel invariant theory for dispersed transverse isotropy. The model is polyconvex and fits biaxial data for aortic valve tissue as accurately as the standard structural model. Modification of the fiber stress-strain law requires no re-formulation of the constitutive tangent matrix, making the model flexible for different types of soft-tissues. Most importantly, the model is computationally expedient in a finite element analysis.

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Soft matter research in India

Journal of Physics Condensed Matter ◽

10.1088/1361-648x/ac3d53 ◽

2021 ◽

Vol 34 (9) ◽

pp. 090402

Author(s):

Ranjini Bandyopadhyay ◽

Jürgen Horbach

Keyword(s):

Soft Matter ◽

Soft Materials ◽

Research Area ◽

Experimental Investigations ◽

Special Issue ◽

Complex Flow ◽

Research Papers ◽

The Past ◽

Biological Physics

Abstract Research on soft matter and biological physics has grown tremendously in India over the past decades. In this editorial, we summarize the twenty-three research papers that were contributed to the special issue on Soft matter research in India. The papers in this issue highlight recent exciting advances in this rapidly expanding research area and include theoretical studies and numerical simulations of soft and biological systems, the synthesis and characterization of novel, functional soft materials and experimental investigations of their complex flow behaviours.

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Solutions for the Inclined Borehole in a Porothermoelastic Transversely Isotropic Medium

Journal of Applied Mechanics ◽

10.1115/1.1825433 ◽

2005 ◽

Vol 72 (1) ◽

pp. 102-114 ◽

Cited By ~ 73

Author(s):

Younane Abousleiman ◽

Shailesh Ekbote

Keyword(s):

Transverse Isotropy ◽

Three Dimensional ◽

Transversely Isotropic ◽

Systematic Analysis ◽

General Anisotropy ◽

Pressure Distributions ◽

In Situ Conditions ◽

Poroelastic Material ◽

Inclined Borehole

A porothermoelastic solution of the general problem of the inclined borehole in a transversely isotropic porous material is presented herein and compared with the isotropic porothermoelastic solution. The governing equations are outlined for the case of general anisotropy and specialized for a transversely isotropic poroelastic material under nonhydrostatic and nonisothermal in situ conditions. A superposition scheme is employed to obtain the analytical solutions within the isotropic and transversely isotropic poromechanics theory. The borehole generator is assumed to coincide with the material axis of symmetry, in the case of transverse isotropy, yet subjected to a three-dimensional state of stress. A systematic analysis has been carried out to evaluate the effect of the anisotropy of the poromechanical material parameters as well as the thermal material properties on stress and pore pressure distributions and the potential impact on the overall stability of deep wellbore drilling.

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Mechanical Spectroscopy: Some Applications On Structural Changes And Relaxation Dynamics In Soft Matter

Archives of Metallurgy and Materials ◽

10.1515/amm-2015-0351 ◽

2015 ◽

Vol 60 (3) ◽

pp. 2077-2084

Author(s):

Xuebang Wu ◽

Changsong Liu

Keyword(s):

Soft Matter ◽

Structural Changes ◽

Three Dimensional ◽

Low Frequency ◽

Soft Materials ◽

Large Temperature ◽

Relaxation Dynamics ◽

Mechanical Spectroscopy ◽

Frequency Scale ◽

Wide Range

Abstract The general trend in soft matter is to study systems of increasing complexity covering a wide range in time and frequency. Mechanical spectroscopy is a powerful tool for understanding the structure and relaxation dynamics of these materials over a large temperature range and frequency scale. In this work, we collect a few recent applications using low-frequency mechanical spectroscopy for elucidating the structural changes and relaxation dynamics in soft matter, largely based on the author’s group. We illustrate the potential of mechanical spectroscopy with three kinds of soft materials: colloids, polymers and granular systems. Examples include structural changes in colloids, segmental relaxations in amorphous polymers, and resonant dissipation of grain chains in three-dimensional media. The present work shows that mechanical spectroscopy has been applied as a necessary and complementary tool to study the dynamics of such complex systems.

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Mechanics of ultrasound elastography

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2016.0841 ◽

2017 ◽

Vol 473 (2199) ◽

pp. 20160841 ◽

Cited By ~ 28

Author(s):

Guo-Yang Li ◽

Yanping Cao

Keyword(s):

Soft Tissues ◽

Soft Materials ◽

Ultrasound Elastography ◽

Practical Applications ◽

Linear Elastic ◽

Non Invasive ◽

Anisotropic Elastic ◽

Non Destructive

Ultrasound elastography enables in vivo measurement of the mechanical properties of living soft tissues in a non-destructive and non-invasive manner and has attracted considerable interest for clinical use in recent years. Continuum mechanics plays an essential role in understanding and improving ultrasound-based elastography methods and is the main focus of this review. In particular, the mechanics theories involved in both static and dynamic elastography methods are surveyed. They may help understand the challenges in and opportunities for the practical applications of various ultrasound elastography methods to characterize the linear elastic, viscoelastic, anisotropic elastic and hyperelastic properties of both bulk and thin-walled soft materials, especially the in vivo characterization of biological soft tissues.

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