scholarly journals MODELING OF ANISOTROPIC GROWTH AND RESIDUAL STRESSES IN ARTERIAL WALLS

2016 ◽  
Vol 7 ◽  
pp. 85 ◽  
Author(s):  
Anna Zahn ◽  
Daniel Balzani
Keyword(s):  
Residual Stresses ◽  
Stress Reduction ◽  
Driving Force ◽  
Deformation Gradient ◽  
Biological Tissues ◽  
Opening Angle ◽  
Anisotropic Growth ◽  
Multiplicative Decomposition ◽  
Soft Biological Tissues ◽  
Arterial Walls

Based on the multiplicative decomposition of the deformation gradient, a local formulation for anisotropic growth in soft biological tissues is formulated by connecting the growth tensor to the main anisotropy directions. In combination with an anisotropic driving force, the model enables an effective stress reduction due to growth-induced residual stresses. A method for the imitation of opening angle experiments in numerically simulated arterial segments, visualizing the deformations related to residual stresses, is presented and illustrated in a numerical example.

scholarly journals The buckling of capillaries in solid tumours

2012 ◽  
Vol 468 (2148) ◽  
pp. 4123-4145 ◽  
Author(s):  
James MacLaurin ◽  
Jon Chapman ◽  
Gareth Wyn Jones ◽  
Tiina Roose
Keyword(s):  
Cell Proliferation ◽  
Stability Analysis ◽  
Diffusion Equation ◽  
Solid Mechanics ◽  
Deformation Gradient ◽  
Anisotropic Growth ◽  
Mechanical Instability ◽  
Multiplicative Decomposition ◽  
Solid Stress ◽  
Nonlinear Solid Mechanics

We develop a model of the buckling (both planar and axial) of capillaries in cancer tumours, using nonlinear solid mechanics. The compressive stress in the tumour interstitium is modelled as a consequence of the rapid proliferation of the tumour cells, using a multiplicative decomposition of the deformation gradient. In turn, the tumour cell proliferation is determined by the oxygen concentration (which is governed by the diffusion equation) and the solid stress. We apply a linear stability analysis to determine the onset of mechanical instability, and the Liapunov–Schmidt reduction to determine the postbuckling behaviour. We find that planar modes usually go unstable before axial modes, so that our model can explain the buckling of capillaries, but not as easily their tortuosity. We also find that the inclusion of anisotropic growth in our model can substantially affect the onset of buckling. Anisotropic growth also results in a feedback effect that substantially affects the magnitude of the buckle.

scholarly journals Mathematical Modelling of Residual-Stress Based Volumetric Growth in Soft Matter

2021 ◽  
Author(s):  
Ruoyu Huang ◽  
Raymond W. Ogden ◽  
Raimondo Penta
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Mathematical Modelling ◽  
Soft Matter ◽  
Direct Evidence ◽  
Deformation Gradient ◽  
Opening Angle ◽  
Spherically Symmetric ◽  
Volumetric Growth ◽  
Incompressibility Constraint

AbstractGrowth in nature is associated with the development of residual stresses and is in general heterogeneous and anisotropic at all scales. Residual stress in an unloaded configuration of a growing material provides direct evidence of the mechanical regulation of heterogeneity and anisotropy of growth. The present study explores a model of stress-mediated growth based on the unloaded configuration that considers either the residual stress or the deformation gradient relative to the unloaded configuration as a growth variable. This makes it possible to analyze stress-mediated growth without the need to invoke the existence of a fictitious stress-free grown configuration. Furthermore, applications based on the proposed theoretical framework relate directly to practical experimental scenarios involving the “opening-angle” in arteries as a measure of residual stress. An initial illustration of the theory is then provided by considering the growth of a spherically symmetric thick-walled shell subjected to the incompressibility constraint.

scholarly journals Computational model of damage-induced growth in soft biological tissues considering the mechanobiology of healing

2021 ◽  
Author(s):  
Meike Gierig ◽  
Peter Wriggers ◽  
Michele Marino
Keyword(s):  
Growth Factors ◽  
Matrix Metalloproteinases ◽  
Tissue Sample ◽  
Deformation Gradient ◽  
Biological Tissues ◽  
Tissue Response ◽  
Element Formulation ◽  
Growth And Remodeling ◽  
Soft Biological Tissues ◽  
Species Response

AbstractHealing in soft biological tissues is a chain of events on different time and length scales. This work presents a computational framework to capture and couple important mechanical, chemical and biological aspects of healing. A molecular-level damage in collagen, i.e., the interstrand delamination, is addressed as source of plastic deformation in tissues. This mechanism initiates a biochemical response and starts the chain of healing. In particular, damage is considered to be the stimulus for the production of matrix metalloproteinases and growth factors which in turn, respectively, degrade and produce collagen. Due to collagen turnover, the volume of the tissue changes, which can result either in normal or pathological healing. To capture the mechanisms on continuum scale, the deformation gradient is multiplicatively decomposed in inelastic and elastic deformation gradients. A recently proposed elasto-plastic formulation is, through a biochemical model, coupled with a growth and remodeling description based on homogenized constrained mixtures. After the discussion of the biological species response to the damage stimulus, the framework is implemented in a mixed nonlinear finite element formulation and a biaxial tension and an indentation tests are conducted on a prestretched flat tissue sample. The results illustrate that the model is able to describe the evolutions of growth factors and matrix metalloproteinases following damage and the subsequent growth and remodeling in the respect of equilibrium. The interplay between mechanical and chemo-biological events occurring during healing is captured, proving that the framework is a suitable basis for more detailed simulations of damage-induced tissue response.

Modeling residual stresses in arterial walls based on anisotropic growth

PAMM ◽  
2016 ◽  
Vol 16 (1) ◽  
pp. 115-116
Author(s):  
Anna Zahn ◽  
Daniel Balzani
Keyword(s):  
Residual Stresses ◽  
Anisotropic Growth ◽  
Arterial Walls

Failure Mechanisms of Particulate Two-Phase Composites

1998 ◽  
Vol 529 ◽  
Author(s):  
T. Antretter ◽  
E D. Fischer
Keyword(s):  
Residual Stresses ◽  
Crack Growth ◽  
Opening Angle ◽  
Geometrical Parameters ◽  
Two Phase ◽  
Absolute Size ◽  
The Matrix ◽  
Unit Cells ◽  
Angle Criterion ◽  
Probability Of Fracture

AbstractIn many composites consisting of hard and brittle inclusions embedded in a ductile matrix failure can be attributed to particle cleavage followed by ductile crack growth in the matrix. Both mechanisms are significantly sensitive towards the presence of residual stresses.On the one hand particle failure depends on the stress distribution inside the inclusion, which, in turn, is a function of various geometrical parameters such as the aspect ratio and the position relative to adjacent particles as well as the external load. On the other hand it has been observed that the absolute size of each particle plays a role as well and will, therefore, be taken into account in this work by means of the Weibull theory. Unit cells containing a number of quasi-randomly oriented elliptical inclusions serve as the basis for the finite element calculations. The numerical results are then correlated to the geometrical parameters defining the inclusions. The probability of fracture has been evaluated for a large number of inclusions and plotted versus the particle size. The parameters of the fitting curves to the resulting data points depend on the choice of the Weibull parameters.A crack tip opening angle criterion (CTOA) is used to describe crack growth in the matrix emanating from a broken particle. It turns out that the crack resistance of the matrix largely depends on the distance from an adjacent particle. Residual stresses due to quenching of the material tend to reduce the risk of particle cleavage but promote crack propagation in the matrix.

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

Spherical indentation load-relaxation of soft biological tissues

2006 ◽  
Vol 21 (8) ◽  
pp. 2003-2010 ◽  
Author(s):  
Jason M. Mattice ◽  
Anthony G. Lau ◽  
Michelle L. Oyen ◽  
Richard W. Kent
Keyword(s):  
Costal Cartilage ◽  
Kidney Tissue ◽  
Biological Tissues ◽  
Indentation Load ◽  
Spherical Indentation ◽  
Load Relaxation ◽  
Soft Biological Tissues ◽  
Long Time ◽  
Constant Displacement ◽  
Soft Biological Materials

Elastic-viscoelastic correspondence was used to generate displacement–time solutions for spherical indentation testing of soft biological materials with time-dependent mechanical behavior. Boltzmann hereditary integral operators were used to determine solutions for indentation load-relaxation following a constant displacement rate ramp. A “ramp correction factor” approach was used for routine analysis of experimental load-relaxation data. Experimental load-relaxation tests were performed on rubber, as well as kidney tissue and costal cartilage, two hydrated soft biological tissues with vastly different mechanical responses. The experimental data were fit to the spherical indentation ramp-relaxation solutions to obtain values of short- and long-time shear modulus and of material time constants. The method is used to demonstrate linearly viscoelastic responses in rubber, level-independent indentation results for costal cartilage, and age-independent indentation results for kidney parenchymal tissue.

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