scholarly journals Mathematical modeling and simulations for large-strain J-shaped diagrams of soft biological tissues

2018 ◽  
Author(s):  
K. Mitsuhashi ◽  
S. Ghosh ◽  
H. Koibuchi
Keyword(s):  
Degrees Of Freedom ◽  
Large Strain ◽  
Finsler Geometry ◽  
Biological Tissues ◽  
Strain Diagram ◽  
Stress Strain ◽  
Soft Biological Tissues ◽  
Stress Region ◽  
Animal Skin ◽  
2D And 3D

Herein, we study stress-strain diagrams of soft biological tissues such as animal skin, muscles and arteries by Finsler geometry (FG) modeling. The stress-strain diagram of these biological materials is always J-shaped and is composed of toe, heel, linear and failure regions. In the toe region, the stress is zero, and the length of this zero-stress region becomes very large (≃ 150%) in, for example, certain arteries. In this paper, we study long-toe diagrams using two-dimensional (2D) and 3D FG modeling techniques and Monte Carlo (MC) simulations. We find that except for the failure region, large-strain J-shaped diagrams are successfully reproduced by the FG models. This implies that the complex J-shaped curves originate from the interaction between the directional and positional degrees of freedom of polymeric molecules, as implemented in the FG model.

ON FIXED-STRESS AND FIXED-STRAIN SOLUTION SCHEMES FOR LARGE STRAIN POROELASTICITY APPLIED TO SOFT BIOLOGICAL TISSUES

2021 ◽  
Author(s):  
José Luís Medeiros Thiesen ◽  
Bruno Klahr ◽  
Thiago André Carniel ◽  
Eduardo Fancello
Keyword(s):  
Large Strain ◽  
Biological Tissues ◽  
Soft Biological Tissues

scholarly journals Mechanics of Biomacromolecular Networks Containing Folded Domains

2006 ◽  
Vol 128 (4) ◽  
pp. 509-518 ◽  
Author(s):  
H. Jerry Qi ◽  
Christine Ortiz ◽  
Mary C. Boyce
Keyword(s):  
Network Model ◽  
Single Molecule ◽  
Large Strain ◽  
Biological Membrane ◽  
Biological Materials ◽  
Biological Tissues ◽  
Force Extension ◽  
Stress Strain ◽  
Strain Behavior ◽  
Dimensional Network

The force-extension behavior of single modular biomacromolecules is known to exhibit a characteristic repeating pattern of a nonlinear rise in force with imposed displacement to a peak, followed by a significant force drop upon reaching the peak. This “saw-tooth” pattern is a result of stretch-induced unfolding of modules along the molecular chain and is speculated to play a governing role in the function of biological materials and structures. In this paper, constitutive models for the large strain deformation of networks of modular macromolecules are developed building directly from statistical mechanics based models of the single molecule force-extension behavior. The proposed two-dimensional network model has applicability to biological membrane skeletons and the three-dimensional network model emulates cytoskeletal networks, natural fibers, and soft biological tissues. Simulations of the uniaxial and multiaxial stress-strain behavior of these networks illustrate the macroscopic membrane and solid stretching conditions which activate unfolding in these microstructures. The models simultaneously track the evolution in underlying microstructural features with different macroscopic stretching conditions, including the evolution in molecular orientation and the forces acting on the constituent molecular chains and junctions. The effect of network pretension on the stress-strain behavior and the macroscopic stress and strain conditions which trigger unfolding are presented. The implications of the predicted stress-strain behaviors on a variety of biological materials are discussed.

Propagation of surface acoustic waves in the models of soft biological tissues

1992 ◽  
Vol 25 (7) ◽  
pp. 814
Author(s):  
Vladimir V. Shorokhov ◽  
Vadim N. Voronkov ◽  
Alexander N. Klishko
Keyword(s):  
Acoustic Waves ◽  
Surface Acoustic Waves ◽  
Biological Tissues ◽  
Soft Biological Tissues

A Two-Dimensional Linear Assumed Strain Triangular Element for Finite Deformation Analysis

2005 ◽  
Vol 73 (6) ◽  
pp. 970-976 ◽  
Author(s):  
Fernando G. Flores
Keyword(s):  
Finite Deformation ◽  
Degrees Of Freedom ◽  
Yield Function ◽  
Triangular Element ◽  
Deformation Analysis ◽  
Elastic Model ◽  
Stress Strain ◽  
Metric Tensor ◽  
Assumed Strain ◽  
Non Linear

An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then nonconforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. A hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong nonlinearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.

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