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Nonlinear Solid Mechanics: A Continuum Approach for Engineering Science
Introduction to Vectors and Tensors. Kinematics. The Concept of Stress. Balance Principles. Some Aspects of Objectivity. Hyperelastic Materials. Thermodynamics of Materials. Variational Principles.
A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models
In this paper we develop a new constitutive law for the description of the (passive) mechanical response of arterial tissue. The artery is modeled as a thick-walled nonlinearly elastic circular
Hyperelastic modelling of arterial layers with distributed collagen fibre orientations
TLDR
A structural continuum framework that is able to represent the dispersion of the collagen fibre orientation is developed and allows the development of a new hyperelastic free-energy function that is particularly suited for representing the anisotropic elastic properties of adventitial and intimal layers of arterial walls.
Determination of layer-specific mechanical properties of human coronary arteries with nonatherosclerotic intimal thickening and related constitutive modeling.
TLDR
The study showed the need to model nonstenotic human coronary arteries with nonatherosclerotic intimal thickening as a composite structure composed of three solid mechanically relevant layers with different mechanical properties.
Constitutive modelling of passive myocardium: a structurally based framework for material characterization
  • G. Holzapfel, R. Ogden
  • Computer Science, Biology
    Philosophical Transactions of the Royal Society A…
  • 13 September 2009
TLDR
This paper treats the left ventricular myocardium as a non-homogeneous, thick-walled, nonlinearly elastic and incompressible material and develops a general theoretical framework based on invariants associated with the three directions, then develops a structurally based model that accounts for the muscle fibre direction and the myocyte sheet structure.
Single lamellar mechanics of the human lumbar anulus fibrosus
TLDR
The single anulus lamella may be seen as the elementary structural unit of the anulus fibrosus, and exhibits marked anisotropy and distinct regional variation of tensile properties and fiber angles.
Determination of material models for arterial walls from uniaxial extension tests and histological structure.
  • G. Holzapfel
  • Mathematics, Medicine
    Journal of theoretical biology
  • 21 January 2006
TLDR
An approach is proposed that allows the determination of material models from uniaxial tests and histostructural data including fiber orientation of the tissue including Fung-type strain-energy functions providing strict local convexity and preferred fiber orientations.
Constitutive modelling of arteries
  • G. Holzapfel, R. Ogden
  • Materials Science
    Proceedings of the Royal Society A: Mathematical…
  • 8 June 2010
This review article is concerned with the mathematical modelling of the mechanical properties of the soft biological tissues that constitute the walls of arteries. Many important aspects of the
A structural model for the viscoelastic behavior of arterial walls: Continuum formulation and finite element analysis
In this paper we present a two-layer structural model suitable for predicting reliably the passive (unstimulated) time-dependent three-dimensional stress and deformation states of healthy young
Brain tissue deforms similarly to filled elastomers and follows consolidation theory
Slow, large deformations of human brain tissue—accompanying cranial vault deformation induced by positional plagiocephaly, occurring during hydrocephalus, and in the convolutional development—has
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