Author

# Carlo Sansour

Other affiliations: University of Nottingham, University of Adelaide, University of Stuttgart ...read more

Bio: Carlo Sansour is an academic researcher from Intelligence and National Security Alliance. The author has contributed to research in topics: Finite strain theory & Finite element method. The author has an hindex of 22, co-authored 81 publications receiving 1584 citations. Previous affiliations of Carlo Sansour include University of Nottingham & University of Adelaide.

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TL;DR: In this paper, a non-linear shell theory, including transverse shear strains, with exact description of the kinematical fields is developed, and the strain measures are derived via the polar decomposition theorem allowing for an explicit use of a three parametric rotation tensor.

Abstract: A non-linear shell theory, including transverse shear strains, with exact description of the kinematical fields is developed. The strain measures are derived via the polar decomposition theorem allowing for an explicit use of a three parametric rotation tensor. Thus in-plane rotations, also called drilling degrees of freedom, are included in a natural way. Various alternatives of the theory are derived. For a special version of the theory, with altogether six kinematical fields, different mixed variational principles are given. A hybrid finite element formulation, which does not exhibit locking phenomena, is developed. Numerical examples of shell deformation at finite rotations, with excellent element performance, are presented. Comparison with results reported in the literature demonstrates the features of the theory as well as the proposed finite element formulation.

139 citations

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TL;DR: In this article, a nonlinear shell theory, including transverse strains perpendicular to the shell midsurface, as well as transverse shear strains, with exact description of the kinematical fields, is developed.

Abstract: A nonlinear shell theory, including transverse strains perpendicular to the shell midsurface, as well as transverse shear strains, with exact description of the kinematical fields, is developed. The strain measures are derived by considering theGreen strain tensor of the three-dimensional shell body. A quadratic displacement field over the shell thickness is considered. Altogether seven kinematical fields are incorporated in the formulation. The kinematics of the shell normal is described by means of a difference vector, avoiding the use of a rotation tensor and resulting in a configuration space, where the structure of a linear vector space is preserved. In the case of linear constitutive equations, a possible consistent reduction to six degrees of freedom is discussed. The finite element formulation is based on a hybrid variational principle. The accuracy of the theory and its wide range of applicability is demonstrated by several examples. Comparison with results based on shell theories formulated by means of a rotation tensor are included.

131 citations

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TL;DR: In this article, the authors compare three types of 4-node and 9-node finite elements for a recently formulated finite deformation shell theory with seven degrees of freedom, which allows for the applicability of three-dimensional constitutive laws and equipes the configuration space with the structure of a vector space.

Abstract: In this paper we discuss and compare three types of 4-node and 9-node finite elements for a recently formulated finite deformation shell theory with seven degrees of freedom. The shell theory takes thickness change into account and circumvents the use of a rotation tensor. It allows for the applicability of three-dimensional constitutive laws and equipes the configuration space with the structure of a vector space. The finite elements themselves are based either on a hybrid stress functional, on a hybrid strain functional, or on a nonlinear version of the enhanced strain concept. As independent variables either the normal and shear resultants, the strain tensor related to the deformation of the midsurface, or the incompatible enhanced strain field are taken as independent variables. The fields of equivalence of these different formulations, their limitations as well as possible improvements are discussed using different numerical examples.

130 citations

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TL;DR: In this paper, the multiplicative decomposition of the deformation gradient into its volumetric and isochoric parts and its implications in the case of anisotropy is discussed.

Abstract: This paper discusses the multiplicative decomposition of the deformation gradient into its volumetric and isochoric parts and its implications in the case of anisotropy. An analysis is carried out showing that the volumetric-isochoric split of the stored energy function can be justified and systematically derived on the basis of the physical assumption that the spherical part of the stress depends on the determinant of the deformation gradient without ad hoc introduction of the multiplicative split. The analysis shows that care must be exercised in the case of anisotropic material description in order not to violate certain physical requirements. Additive splits of the energy can be justified on the basis of certain physical observations and independent of the multiplicative decomposition of the deformation gradient. Specifically, it is shown that a spherical state of stress will cause even in the incompressible case, a change of shape. In fibre reinforced materials, the split of the stored energy function into a part related to the matrix and a part related to the fibre is considered, showing that the volumetric-isochoric split should be applied to the matrix part only.

116 citations

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TL;DR: In this paper, the Cosserat continuum is considered to be a two-dimensional surface and the structure of the configuration space is discussed and two possible definitions of it are given equipped once with a Killing metric and once with an Euclidean one.

Abstract: Relying on the concept of a Cosserat continuum, the reduction of the three-dimensional equations of a shell body to two-dimensions is carried out in a direct manner by considering the Cosserat continuum to be a two-dimensional surface. By that, a non-linear shell theory, including transverse shear strains, with exact description of the kinematical fields is derived. The strain measures are taken to be the first and the second Cosserat deformation tensors allowing for an explicit use of a three parametric rotation tensor. Thus, inplane rotations, also called drilling degrees of freedom, are included in a natural way. The structure of the configuration space is discussed and two possible definitions of it are given equipped once with a Killing metric and once with an Euclidean one. A partially mixed variational principle is proposed on the base of which an efficient hybrid finite-element formulation, which does not exhibit locking phenomena, is developed. Various numerical examples of shell deformations at finite rotations, with excellent element performance, are presented.

81 citations

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01 Aug 2014

TL;DR: In this article, a comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells is presented. But the authors do not consider the effect of boundary conditions on the large-amplitude vibrations of circular cylinders.

Abstract: Introduction. 1. Nonlinear theories of elasticity of plates and shells 2. Nonlinear theories of doubly curved shells for conventional and advanced materials 3. Introduction to nonlinear dynamics 4. Vibrations of rectangular plates 5. Vibrations of empty and fluid-filled circular cylindrical 6. Reduced order models: proper orthogonal decomposition and nonlinear normal modes 7. Comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells 8. Effect of boundary conditions on a large-amplitude vibrations of circular cylindrical shells 9. Vibrations of circular cylindrical panels with different boundary conditions 10. Nonlinear vibrations and stability of doubly-curved shallow-shells: isotropic and laminated materials 11. Meshless discretization of plates and shells of complex shapes by using the R-functions 12. Vibrations of circular plates and rotating disks 13. Nonlinear stability of circular cylindrical shells under static and dynamic axial loads 14. Nonlinear stability and vibrations of circular shells conveying flow 15. Nonlinear supersonic flutter of circular cylindrical shells with imperfections.

862 citations

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TL;DR: In this article, various formats of gradient elasticity and their performance in static and dynamic applications are discussed and an overview of length scale identification and quantification procedures is given, together with the variationally consistent boundary conditions.

Abstract: In this paper, we discuss various formats of gradient elasticity and their performance in static and dynamic applications. Gradient elasticity theories provide extensions of the classical equations of elasticity with additional higher-order spatial derivatives of strains, stresses and/or accelerations. We focus on the versatile class of gradient elasticity theories whereby the higher-order terms are the Laplacian of the corresponding lower-order terms. One of the challenges of formulating gradient elasticity theories is to keep the number of additional constitutive parameters to a minimum. We start with discussing the general Mindlin theory, that in its most general form has 903 constitutive elastic parameters but which were reduced by Mindlin to three independent material length scales. Further simplifications are often possible. In particular, the Aifantis theory has only one additional parameter in statics and opens up a whole new field of analytical and numerical solution procedures. We also address how this can be extended to dynamics. An overview of length scale identification and quantification procedures is given. Finite element implementations of the most commonly used versions of gradient elasticity are discussed together with the variationally consistent boundary conditions. Details are provided for particular formats of gradient elasticity that can be implemented with simple, linear finite element shape functions. New numerical results show the removal of singularities in statics and dynamics, as well as the size-dependent mechanical response predicted by gradient elasticity.

723 citations

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Mines ParisTech

^{1}TL;DR: In this paper, a unifying thermomechanical framework is presented that reconciles several classes of gradient elastoviscoplasticity and damage models proposed in the literature during the last 40 years.

Abstract: A unifying thermomechanical framework is presented that reconciles several classes of gradient elastoviscoplasticity and damage models proposed in the literature during the last 40 years . It is based on the introduction of the micromorphic counterpart ϕχ of a selected state or internal variable ϕ in a standard constitutive model. In addition to the classical balance of momentum equation, a balance of micromorphic momentum is derived that involves generalized stress tensors. The corresponding additional boundary conditions are also deduced from the procedure. The power of generalized forces is assumed to contribute to the energy balance equation. The free energy density function is then chosen to depend on a relative generalized strain, typically ϕ- ϕχ , and the microstrain gradient ∇ ϕχ . When applied to the deformation gradient itself, ϕ≡ F , the method yields the micromorphic theory of Eringen and Mindlin together with its extension to finite deformation elastoviscoplasticity by Forest and Sievert. If...

504 citations

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TL;DR: In this article, a review article is concerned with the mathematical modelling of the mechanical properties of the soft biological tissues that constitute the walls of arteries, focusing primarily on developments over the last decade based on the theory of deformation invariants, in particular invariants that capture structural aspects of the tissue, specifically the orientation of collagen fibres, the dispersion in the orientation, and the associated anisotropy of the material properties.

Abstract: 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 mechanical behaviour of arterial tissue can be treated on the basis of elasticity theory, and the focus of the article is therefore on the constitutive modelling of the anisotropic and highly nonlinear elastic properties of the artery wall. The discussion focuses primarily on developments over the last decade based on the theory of deformation invariants, in particular invariants that in part capture structural aspects of the tissue, specifically the orientation of collagen fibres, the dispersion in the orientation, and the associated anisotropy of the material properties. The main features of the relevant theory are summarized briefly and particular forms of the elastic strain-energy function are discussed and then applied to an artery considered as a thick-walled circular cylindrical tube in order to illustrate its extension–inflation behaviour. The wide range of applications of the constitutive modelling framework to artery walls in both health and disease and to the other fibrous soft tissues is discussed in detail. Since the main modelling effort in the literature has been on the passive response of arteries, this is also the concern of the major part of this article. A section is nevertheless devoted to reviewing the limited literature within the continuum mechanics framework on the active response of artery walls, i.e. the mechanical behaviour associated with the activation of smooth muscle, a very important but also very challenging topic that requires substantial further development. A final section provides a brief summary of the current state of arterial wall mechanical modelling and points to key areas that need further modelling effort in order to improve understanding of the biomechanics and mechanobiology of arteries and other soft tissues, from the molecular, to the cellular, tissue and organ levels.

474 citations

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TL;DR: In this article, a mesh-free method for thin shells with finite strains and arbitrary evolving cracks is described, and the C 1 displacement continuity requirement is met by the approximation, so no special treatments for fulfilling the Kirchhoff condition are necessary.

Abstract: A meshfree method for thin shells with finite strains and arbitrary evolving cracks is described. The C 1 displacement continuity requirement is met by the approximation, so no special treatments for fulfilling the Kirchhoff condition are necessary. Membrane locking is eliminated by the use of a cubic or quartic polynomial basis. The shell is tested for several elastic and elasto-plastic examples and shows good results. The shell is subsequently extended to modelling cracks. Since no discretization of the director field is needed, the incorporation of discontinuities is easy to implement and straightforward.

456 citations