2002
Journal article
Restricted
Strong ellipticity of transversely isotropic elasticity tensors
Padovani C
The strong ellipticity of the elasticity tensor of a linearly hyperelastic, transversely isotropic material is investigated. The necessary and sufficient conditions for the elasticity tensor to be strongly elliptic are determined for the five constants characterizing it.Source: MECCANICA (DORDR., ONLINE), vol. 37 (issue 6), pp. 515-525
Padovani C
The strong ellipticity of the elasticity tensor of a linearly hyperelastic, transversely isotropic material is investigated. The necessary and sufficient conditions for the elasticity tensor to be strongly elliptic are determined for the five constants characterizing it.Source: MECCANICA (DORDR., ONLINE), vol. 37 (issue 6), pp. 515-525
2002
Journal article
Restricted
Relaxed energy for transversely isotropic two-phase materials
Padovani C, Silhavy M
The paper gives a simple derivation of the relaxed energy Wqc for the quadratic double-well material with equal elastic moduli and analyzes Wqc in the transversely isotropic case. We observe that the energy W is a sum of a degenerate quadratic quasiconvex function and a function that depends on the strain only through a scalar variable. For such a W, the relaxation reduces to a one-dimensional convexification. Wqc depends on a constant g defined by a three-dimensional maximum problem. It is shown that in the transversely isotropic case the problem reduces to a maximization of a fraction of two quadratic polynomials over [0,1]. The maximization reveals several regimes and explicit formulas are given in the case of a transversely isotropic, positive definite displacement of the wells.Source: JOURNAL OF ELASTICITY, vol. 67, pp. 187-204
Padovani C, Silhavy M
The paper gives a simple derivation of the relaxed energy Wqc for the quadratic double-well material with equal elastic moduli and analyzes Wqc in the transversely isotropic case. We observe that the energy W is a sum of a degenerate quadratic quasiconvex function and a function that depends on the strain only through a scalar variable. For such a W, the relaxation reduces to a one-dimensional convexification. Wqc depends on a constant g defined by a three-dimensional maximum problem. It is shown that in the transversely isotropic case the problem reduces to a maximization of a fraction of two quadratic polynomials over [0,1]. The maximization reveals several regimes and explicit formulas are given in the case of a transversely isotropic, positive definite displacement of the wells.Source: JOURNAL OF ELASTICITY, vol. 67, pp. 187-204
2004
Journal article
Restricted
A numerical method for the limit analysis of masonry structures
Degl'Innocenti S, Padovani C
The paper presents a numerical method for the limit analysis of structures made of a rigid no-tension material. Firstly, we formulate the constrained minimum problem resulting from the application of the kinematic theorem, which characterizes the collapse multiplier as the minimum of all kinematically admissible multipliers. Subsequently, by using the finite element method, we derive the corresponding discrete minimum problem in which the objective function is linear and the inequality constraints are linear as well as quadratic. The method is then applied to some examples for which the collapse multiplier and a collapse mechanism are explicitly known. Lastly, the solution to the minimum problem calculated via numerical codes for quadratic programming problems, is compared to the exact solution.Source: STRUCTURAL ENGINEERING AND MECHANICS, vol. 18 (issue 1), pp. 1-20
DOI: 10.12989/sem.2004.18.1.001
Metrics:
Degl'Innocenti S, Padovani C
The paper presents a numerical method for the limit analysis of structures made of a rigid no-tension material. Firstly, we formulate the constrained minimum problem resulting from the application of the kinematic theorem, which characterizes the collapse multiplier as the minimum of all kinematically admissible multipliers. Subsequently, by using the finite element method, we derive the corresponding discrete minimum problem in which the objective function is linear and the inequality constraints are linear as well as quadratic. The method is then applied to some examples for which the collapse multiplier and a collapse mechanism are explicitly known. Lastly, the solution to the minimum problem calculated via numerical codes for quadratic programming problems, is compared to the exact solution.Source: STRUCTURAL ENGINEERING AND MECHANICS, vol. 18 (issue 1), pp. 1-20
DOI: 10.12989/sem.2004.18.1.001
Metrics:
See at:
STRUCTURAL ENGINEERING AND MECHANICS 
| CNR IRIS | CNR IRIS | koreascience.or.kr | www.scopus.com
2003
Conference article
Restricted
Un metodo numerico per l'analisi limite di strutture in muratura
Degl'Innocenti S, Padovani C
In questo lavoro si presenta un metodo numerico per l'analisi limite di strutture costituite da un materiale rigido non resistente a trazione. In primo luogo si formula il problema di minimo vincolato derivante dall'applicazione del teorema cinematico, che caratterizza il moltiplicatore di collasso come il minimo dei moltiplicatori cinematicamente ammissibili. Successivamente, usando il metodo degli elementi finiti, si ricava il corrispondente problema di minimo discreto in cui la funzione obiettivo è lineare e i vincoli di uguaglianza sono sia lineari sia quadratici. Il metodo è quindi applicato ad alcuni esempi per i quali sono noti il moltiplicatore di collasso e un meccanismo di collasso. Finalmente la soluzione del problema di minimo calcolata con opportuni codici numerici per problemi di programmazione quadratica è confrontata con la soluzione esatta.
Degl'Innocenti S, Padovani C
In questo lavoro si presenta un metodo numerico per l'analisi limite di strutture costituite da un materiale rigido non resistente a trazione. In primo luogo si formula il problema di minimo vincolato derivante dall'applicazione del teorema cinematico, che caratterizza il moltiplicatore di collasso come il minimo dei moltiplicatori cinematicamente ammissibili. Successivamente, usando il metodo degli elementi finiti, si ricava il corrispondente problema di minimo discreto in cui la funzione obiettivo è lineare e i vincoli di uguaglianza sono sia lineari sia quadratici. Il metodo è quindi applicato ad alcuni esempi per i quali sono noti il moltiplicatore di collasso e un meccanismo di collasso. Finalmente la soluzione del problema di minimo calcolata con opportuni codici numerici per problemi di programmazione quadratica è confrontata con la soluzione esatta.
2003
Other
Metadata Only Access
A numerical method for the limit analysis of masonry structures
Degl'Innocenti S, Padovani C
The paper presents a numerical method for the limit analysis of structures made of a rigid no-tension material. Firstly, we formulate the constrained minimum problem resulting from the application of the kinematic theorem, which characterizes the collapse multiplier as the minimum of all kinematically admissible multipliers. Subsequently, by using the finite element method, we derive the corresponding discrete minimum problem in which the objective function is linear and the inequality constraints are linear as well as quadratic. The method is then applied to some examples for which the collapse multiplier and a collapse mechanism are explicitly known. Lastly, the solution to the minimum problem calculated via numerical codes for quadratic programming problems, is compared to the exact solution.
Degl'Innocenti S, Padovani C
The paper presents a numerical method for the limit analysis of structures made of a rigid no-tension material. Firstly, we formulate the constrained minimum problem resulting from the application of the kinematic theorem, which characterizes the collapse multiplier as the minimum of all kinematically admissible multipliers. Subsequently, by using the finite element method, we derive the corresponding discrete minimum problem in which the objective function is linear and the inequality constraints are linear as well as quadratic. The method is then applied to some examples for which the collapse multiplier and a collapse mechanism are explicitly known. Lastly, the solution to the minimum problem calculated via numerical codes for quadratic programming problems, is compared to the exact solution.
See at:
CNR IRIS
2006
Other
Restricted
Introduzione al calcolo tensoriale
Padovani C
Appunti redatti in occasione del corso 'Algrabra per la Meccanica'tenuto alla Scuola di Dottorato in Ingegneria 'Leonardo Da Vinci' presso l'Universita' di Pisa, 2006
Padovani C
Appunti redatti in occasione del corso 'Algrabra per la Meccanica'tenuto alla Scuola di Dottorato in Ingegneria 'Leonardo Da Vinci' presso l'Universita' di Pisa, 2006
2001
Other
Open Access
Relaxed energy for transversely isotropic two-phase materials
Padovani C, Miroslav S
This paper gives a simple derivation of the relaxed energy Wqc for the quadratic double-well material with equal elastic moduli and analyzes Wqc in the transversal isotropic case
Padovani C, Miroslav S
This paper gives a simple derivation of the relaxed energy Wqc for the quadratic double-well material with equal elastic moduli and analyzes Wqc in the transversal isotropic case
2002
Other
Restricted
2009
Other
Metadata Only Access
Elementi di calcolo tensoriale
Padovani C
Lezioni del corso "Introduzione al calcolo tensoriale", Scuola di Dottorato in Ingegneria "Leonardo da Vinci", Universita' di Pisa, 2009.
Padovani C
Lezioni del corso "Introduzione al calcolo tensoriale", Scuola di Dottorato in Ingegneria "Leonardo da Vinci", Universita' di Pisa, 2009.
See at:
CNR IRIS
2012
Other
Restricted
NOSA-ITACA - Strumenti informatici per la modellazione e la verifica del comportamento strutturale di costruzioni antiche: il codice NOSA-ITACA
Padovani C, Lucchesi M
Tools for the modelling and assessment of the structural behaviour of masonry nuilfings of historical interest - Project Report.
Padovani C, Lucchesi M
Tools for the modelling and assessment of the structural behaviour of masonry nuilfings of historical interest - Project Report.
2013
Other
Restricted
NOSA-ITACA - Strumenti informatici per la modellazione e la verifica del comportamento strutturale di costruzioni antiche: il codice NOSA-ITACA
Padovani C, Lucchesi M
Tools for the modelling and assessment of the structural behaviour of masonry buildings of historical interest - Project Report.
Padovani C, Lucchesi M
Tools for the modelling and assessment of the structural behaviour of masonry buildings of historical interest - Project Report.
2012
Book
Restricted
Elementi di calcolo tensoriale
Padovani C
This is a collection of notes taken on the tensor calculus classes held at the Graduate School of Engineering "Leonardo da Vinci" at the University of Pisa from 2006 to 2011. The topics covered at lessons, aimed at providing the basic knowledge and tools necessary for the study of continuum mechanics, include fundamental results on tensor algebra and analysis. Chapter 1 provides a brief introduction to finite dimensional vector spaces. Then, Chapter 2 addresses the classical topics of tensor calculus, including symmetric and skew-symmetric tensors, the theorem of polar decomposition, fourth-order tensors, isotropic tensor functions and the differential calculus of tensor functions. The text is accompanied by numerous examples and exercises.Source: SIMAI E-LECTURE NOTES
Padovani C
This is a collection of notes taken on the tensor calculus classes held at the Graduate School of Engineering "Leonardo da Vinci" at the University of Pisa from 2006 to 2011. The topics covered at lessons, aimed at providing the basic knowledge and tools necessary for the study of continuum mechanics, include fundamental results on tensor algebra and analysis. Chapter 1 provides a brief introduction to finite dimensional vector spaces. Then, Chapter 2 addresses the classical topics of tensor calculus, including symmetric and skew-symmetric tensors, the theorem of polar decomposition, fourth-order tensors, isotropic tensor functions and the differential calculus of tensor functions. The text is accompanied by numerous examples and exercises.Source: SIMAI E-LECTURE NOTES
See at:
cab.unime.it | CNR IRIS | CNR IRIS
2013
Journal article
Restricted
Coaxiality of stress and strain in anisotropic no-tension materials
Padovani C., Silhavy M.
For an anisotropic no-tension material there exist at least two rotations such that stress and strain become coaxial. The same result holds for any hyperelastic material whose response is expressed in terms of the small strain tensor and whose stress function is a continuous positively homogeneous degree 1 function.Source: MECCANICA, vol. 48 (issue 2), pp. 487-489
DOI: 10.1007/s11012-012-9690-7
Metrics:
Padovani C., Silhavy M.
For an anisotropic no-tension material there exist at least two rotations such that stress and strain become coaxial. The same result holds for any hyperelastic material whose response is expressed in terms of the small strain tensor and whose stress function is a continuous positively homogeneous degree 1 function.Source: MECCANICA, vol. 48 (issue 2), pp. 487-489
DOI: 10.1007/s11012-012-9690-7
Metrics:
See at:
Meccanica | CNR IRIS | CNR IRIS | link.springer.com
2017
Journal article
Open Access
On the derivative of the stress-strain relation in a no-tension material
Padovani C, Silhavý M
The stress-strain relation of a no-tension material, used to model masonry structures, is determined by the nonlinear projection of the strain tensor onto the image of the convex cone of negative-semidefinite stresses under the fourth-order tensor of elastic compliances. We prove that the stress-strain relation is indefinitely differentiable on an open dense subset O of the set of all strains. The set O consists of four open connected regions determined by the rank k = 0, 1, 2, 3 of the resulting stress. Further, an equation for the derivative of the stress-strain relation is derived. This equation cannot be solved explicitly in the case of a material of general symmetry, but it is shown that for an isotropic material this leads to the derivative established earlier by Lucchesi et al. (Int J Solid Struct 1996; 33: 1961-1994 and Masonry constructions: Mechanical models and numerical applications. Berlin: Springer, 2008) by different means. For a material of general symmetry, when the tensor of elasticities does not have the representation known in the isotropic case, only general steps leading to the evaluation of the derivative are described.Source: MATHEMATICS AND MECHANICS OF SOLIDS, vol. 22 (issue 7), pp. 1606-1618
DOI: 10.1177/1081286515571786
Metrics:
Padovani C, Silhavý M
The stress-strain relation of a no-tension material, used to model masonry structures, is determined by the nonlinear projection of the strain tensor onto the image of the convex cone of negative-semidefinite stresses under the fourth-order tensor of elastic compliances. We prove that the stress-strain relation is indefinitely differentiable on an open dense subset O of the set of all strains. The set O consists of four open connected regions determined by the rank k = 0, 1, 2, 3 of the resulting stress. Further, an equation for the derivative of the stress-strain relation is derived. This equation cannot be solved explicitly in the case of a material of general symmetry, but it is shown that for an isotropic material this leads to the derivative established earlier by Lucchesi et al. (Int J Solid Struct 1996; 33: 1961-1994 and Masonry constructions: Mechanical models and numerical applications. Berlin: Springer, 2008) by different means. For a material of general symmetry, when the tensor of elasticities does not have the representation known in the isotropic case, only general steps leading to the evaluation of the derivative are described.Source: MATHEMATICS AND MECHANICS OF SOLIDS, vol. 22 (issue 7), pp. 1606-1618
DOI: 10.1177/1081286515571786
Metrics:
See at:
ISTI Repository 
| Mathematics and Mechanics of Solids | CNR IRIS | CNR IRIS | mms.sagepub.com
2000
Other
Open Access
Spectral decomposition and strong ellipticity of transversely isotropic elasticity tensors
Padovani C
In questo lavoro si determina la decomposizione spettrale del tensore di elasticità di un materiale iperelastico trasversalmente isotropo.La conoscenza degli autovalori del tensore di elasticità consente di determinare condizioni sulle cinque costanti che caratterizzano il tensore di elasticità, che sono necessarie e sufficienti affinché esso sia definito positivo. Successivamente vengono fornite condizioni necessarie e sufficienti sulle cinque costanti, affinchè il tensore di elasticità sia fortemente ellittico.
Padovani C
In questo lavoro si determina la decomposizione spettrale del tensore di elasticità di un materiale iperelastico trasversalmente isotropo.La conoscenza degli autovalori del tensore di elasticità consente di determinare condizioni sulle cinque costanti che caratterizzano il tensore di elasticità, che sono necessarie e sufficienti affinché esso sia definito positivo. Successivamente vengono fornite condizioni necessarie e sufficienti sulle cinque costanti, affinchè il tensore di elasticità sia fortemente ellittico.
2000
Journal article
Unknown
On the derivative of some tensor-valued functions
Padovani C
An explicit expression of the derivative of the square root of a tensor is provided, by using the expressions of the derivatives of the eigenvalues and eigenvectors of a symmetric tensor. Starting from this result, the derivatives of the right and left stretch tensor U, V and of the rotation R with respect to the deformation gradient F, are calculated. Expressions for the material time derivatives of U, V and R are also given.Source: JOURNAL OF ELASTICITY, vol. 58 (issue 3), pp. 257-268
DOI: 10.1023/a:1007615519220
Metrics:
Padovani C
An explicit expression of the derivative of the square root of a tensor is provided, by using the expressions of the derivatives of the eigenvalues and eigenvectors of a symmetric tensor. Starting from this result, the derivatives of the right and left stretch tensor U, V and of the rotation R with respect to the deformation gradient F, are calculated. Expressions for the material time derivatives of U, V and R are also given.Source: JOURNAL OF ELASTICITY, vol. 58 (issue 3), pp. 257-268
DOI: 10.1023/a:1007615519220
Metrics:
See at:
Journal of Elasticity | CNR IRIS | www.scopus.com
2000
Journal article
Closed Access
On a class of non-linear elastic materials
Padovani C
An abstract is not available.Source: INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, vol. 37 (issue 52), pp. 7787-7807
DOI: 10.1016/s0020-7683(99)00307-8
Metrics:
Padovani C
An abstract is not available.Source: INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, vol. 37 (issue 52), pp. 7787-7807
DOI: 10.1016/s0020-7683(99)00307-8
Metrics:
See at:
International Journal of Solids and Structures | CNR IRIS | www.scopus.com | www.scopus.com
1999
Other
Open Access
On the derivative of some tensor-valued functions
Padovani C
An explicit expression of the derivative of the square root of a tensor is provided by using the expressions of the derivatives of the eigenvalues and eigenvectors of the simmetric tensor. Starting from this result, the derivatives of the right and left stretch tensor U, V and of the rotation R with respect to the deformation gradient F, are calculated. Expressions for the material time derivatives of U, V and R are also given.
Padovani C
An explicit expression of the derivative of the square root of a tensor is provided by using the expressions of the derivatives of the eigenvalues and eigenvectors of the simmetric tensor. Starting from this result, the derivatives of the right and left stretch tensor U, V and of the rotation R with respect to the deformation gradient F, are calculated. Expressions for the material time derivatives of U, V and R are also given.
1999
Other
Open Access
1999
Conference article
Metadata Only Access
See at:
CNR IRIS