2002
Journal article
Unknown
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) 37 (2002): 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) 37 (2002): 515–525.
See at: CNR ExploRA
2002
Journal article
Unknown
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 67 (2002): 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 67 (2002): 187–204.
See at: CNR ExploRA
2006
Other
Unknown
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
See at: CNR ExploRA
2001
Report
Unknown
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 caseSource: ISTI Technical reports, 2001
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 caseSource: ISTI Technical reports, 2001
See at: CNR ExploRA
2002
Other
Unknown
See at: CNR ExploRA
2009
Other
Unknown
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 ExploRA
2012
Report
Unknown
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.Source: Project report, NOSA-ITACA, 2012
Padovani C., Lucchesi M.
Tools for the modelling and assessment of the structural behaviour of masonry nuilfings of historical interest - Project Report.Source: Project report, NOSA-ITACA, 2012
See at: CNR ExploRA
2013
Report
Unknown
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.Source: Project report, NOSA-ITACA, 2013
Padovani C., Lucchesi M.
Tools for the modelling and assessment of the structural behaviour of masonry buildings of historical interest - Project Report.Source: Project report, NOSA-ITACA, 2013
See at: CNR ExploRA
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.
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.
See at:
cab.unime.it 
| CNR ExploRA
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 48 (2013): 487–489. doi:10.1007/s11012-012-9690-7
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 48 (2013): 487–489. doi:10.1007/s11012-012-9690-7
DOI: 10.1007/s11012-012-9690-7
Metrics:
See at:
Meccanica | link.springer.com | CNR ExploRA
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 22 (2017): 1606–1618. doi:10.1177/1081286515571786
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 22 (2017): 1606–1618. doi:10.1177/1081286515571786
DOI: 10.1177/1081286515571786
Metrics:
See at:
ISTI Repository 
| Mathematics and Mechanics of Solids | mms.sagepub.com | CNR ExploRA
2000
Other
Unknown
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.
See at: CNR ExploRA
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 58 (2000): 257–268. doi:10.1023/A:1007615519220
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 58 (2000): 257–268. doi:10.1023/A:1007615519220
DOI: 10.1023/a:1007615519220
Metrics:
See at:
Journal of Elasticity | CNR ExploRA | 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 37 (2000): 7787–7807. doi:10.1016/S0020-7683(99)00307-8
DOI: 10.1016/s0020-7683(99)00307-8
Metrics:
Padovani C.
An abstract is not available.Source: International journal of solids and structures 37 (2000): 7787–7807. doi:10.1016/S0020-7683(99)00307-8
DOI: 10.1016/s0020-7683(99)00307-8
Metrics:
See at:
International Journal of Solids and Structures | www.scopus.com | CNR ExploRA | www.scopus.com
1999
Report
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 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.Source: ISTI Technical reports, pp.1–23, 1999
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.Source: ISTI Technical reports, pp.1–23, 1999
See at: CNR ExploRA
1999
Other
Unknown
See at: CNR ExploRA
1999
Conference article
Unknown
Su una classe di materiali elastici non lineari
Padovani C.
An abstract is not available.Source: XIV Convegno Nazionale dell'Associazione Italiana di Meccanica Teorica ed Applicata, Como, Italy, 6-9 October 1999
Padovani C.
An abstract is not available.Source: XIV Convegno Nazionale dell'Associazione Italiana di Meccanica Teorica ed Applicata, Como, Italy, 6-9 October 1999
See at: CNR ExploRA
1994
Other
Unknown
See at: CNR ExploRA
1995
Other
Unknown
Some explicit solutions for non-linear elastic solids
Bennati S., Padovani C.
The present work deals with some equilibrium problems for solids made of elastic materials of bounded tensile strength and for which explicit solutions are achieved. The preliminary considerations Section presents the constitutive equation adopted and describes its main properties, also with regard to the possible uniqueness of the solution to boundary problems. Four distinct equilibrium problems are then considered, the first three of which are characterised by specific symmetry conditions, polar, spherical and cylindrical, respectively
Bennati S., Padovani C.
The present work deals with some equilibrium problems for solids made of elastic materials of bounded tensile strength and for which explicit solutions are achieved. The preliminary considerations Section presents the constitutive equation adopted and describes its main properties, also with regard to the possible uniqueness of the solution to boundary problems. Four distinct equilibrium problems are then considered, the first three of which are characterised by specific symmetry conditions, polar, spherical and cylindrical, respectively
See at: CNR ExploRA
1995
Other
Unknown
Masonry-like solids in the presence of thermal expansion: an explicit solution
Padovani C.
In this paper the constitutive equation of masonry-like materials is generalised in order to account for thermal dilatation. Subsequently, the explicit solution to the equilibrium problem if of a circular ring subjected I0 two uniform radial pressures pi and pg, acting respectively on the inner and outer boundary and a temperature distribution depending linearly on the radius, is calculated
Padovani C.
In this paper the constitutive equation of masonry-like materials is generalised in order to account for thermal dilatation. Subsequently, the explicit solution to the equilibrium problem if of a circular ring subjected I0 two uniform radial pressures pi and pg, acting respectively on the inner and outer boundary and a temperature distribution depending linearly on the radius, is calculated
See at: CNR ExploRA