Riccardo De Pascalis - Academia.edu (original) (raw)
Papers by Riccardo De Pascalis
Extreme Mechanics Letters
applied mathematics, biomechanics, mechanics Keywords: viscoelastic, quasi-linear, Fung, strain e... more applied mathematics, biomechanics, mechanics Keywords: viscoelastic, quasi-linear, Fung, strain energy function, hyperelastic, biological soft tissue Author for correspondence:
The effective macroscopic response of nonlinear elastomeric inhomogeneous materials is of great i... more The effective macroscopic response of nonlinear elastomeric inhomogeneous materials is of great interest in many applications including nonlinear composite materials and soft biological tissues. The interest of the present work is associated with a microsphere composite material, which is modelled as a matrix-inclusion composite. The matrix phase is a homogeneous isotropic nonlinear rubber-like material and the inclusion phase is more complex, consisting of a distribution of sizes of stiff thin spherical shells filled with gas. Experimentally, such materials have been shown to undergo complex deformation under cyclic loading. Here, we consider microspheres embedded in an unbounded host material and assume that a hydrostatic pressure is applied in the 'far-field'. Taking into account a variety of effects including buckling of the spherical shells, large deformation of the host phase and evolving microstructure, we derive a model predicting the pressure-relative volume change load curves. Nonlinear constitutive behaviour of the matrix medium is accounted for by employing neo-Hookean and Mooney-Rivlin incompressible models. Moreover a nearly-incompressible solution is derived via asymptotic analysis for a spherical cavity embedded in un unbounded isotropic homogeneous hyperelastic medium loaded hydrostatically. The load-curve predictions reveal a strong dependence on the microstructure of the composite, including distribution of microspheres, the stiffness of the shells, and on the initial volume fraction of the inclusions, whereas there is only a modest dependence on the characteristic properties of the nonlinear elastic model used for the rubber host.
Bulletin of the American Physical Society, 2016
on soft compounds is still imperfectly understood, especially when the dry and wetted parts of th... more on soft compounds is still imperfectly understood, especially when the dry and wetted parts of the substrate have two different values of surface energies (contact angle different than 90 degrees). The problem is made very complex by geometrical nonlinearities arising from finite slope of the substrate and finite deformations, that must be absolutely considered, to distinguish at second order between Young law and Neuman equilibrium of surface tensions. We have developed a numerical, finite element, code that allows one to minimize surface and bulk energies, with finite deformations and asymmetry of the surface energies. The results are compared to a linear theory based on Green function theory [1,2] and Fredholm integrals, and with recent experiments using X-ray visualization [3]. The non-linear numerics reproduce very well the observed profiles, while the linear approach gives helpful analytical approximates. [
This paper offers a reappraisal of Fung's model for quasi-linear viscoelasticity. It is shown tha... more This paper offers a reappraisal of Fung's model for quasi-linear viscoelasticity. It is shown that a number of negative features exhibited in other works, commonly attributed to the Fung approach, are merely a consequence of the way it has been applied. The approach outlined herein is shown to yield improved behaviour and offers a straightforward scheme for solving a wide range of models. Results from the new model are contrasted with those in the literature for the case of uniaxial elongation of a bar: for an imposed stretch of an incompressible bar and for an imposed load. In the latter case, a numerical solution to a Volterra integral equation is required to obtain the results. This is achieved by a high-order discretization scheme. Finally, the stretch of a compressible viscoelastic bar is determined for two distinct materials: Horgan-Murphy and Gent.
Inverse methods A general boundary value problem of elastostatics for a body B consists in findin... more Inverse methods A general boundary value problem of elastostatics for a body B consists in finding a motion x = χ(X) that satisfies a(X, t) = 0 for all particles X of B r and for all times t. Recalling equation (1.24), this means that the motion must satisfy the equilibrium equation DivT R + ρ r b r = 0, (3.1) everywhere in B r , and the boundary conditions of surface tractions (1.22) and place, brought to you by CORE View metadata, citation and similar papers at core.ac.uk
The effective dynamic properties of specific periodic structures involving rubber-like materials ... more The effective dynamic properties of specific periodic structures involving rubber-like materials can be adjusted by pre-strain, thus facilitating the design of custom acoustic filters. While nonlinear viscoelastic behaviour is one of the main features of soft solids, it has been rarely incorporated in the study of such phononic media. Here, we study the dynamic response of nonlinear viscoelastic solids within a ‘small-on-large’ acoustoelasticity framework, that is we consider the propagation of small amplitude waves superimposed on a large static deformation. Incompressible soft solids whose behaviour is described by the Fung–Simo quasi-linear viscoelasticy theory (QLV) are considered. We derive the incremental equations using stress-like memory variables governed by linear evolution equations. Thus, we show that wave dispersion is governed by a strain-dependent generalised Maxwell rheology. Illustrations cover the propagation of plane waves under homogeneous tensile strain in a QLV...
The growth of an elastic film adhered to a confining substrate might lead to the formation of del... more The growth of an elastic film adhered to a confining substrate might lead to the formation of delimitation blisters. Many results have been derived when the substrate is flat. The equilibrium shapes, beyond small deformations, are determined by the interplay between the sheet elastic energy and the adhesive potential due to capillarity. Here, we study a non-trivial generalization to this problem and consider the adhesion of a growing elastic loop to a confining circular substrate. The fundamental equations, i.e., the Euler Elastica equation, the boundary conditions and the transversality condition, are derived from a variational procedure. In contrast to the planar case, the curvature of the delimiting wall appears in the transversality condition, thus acting as a further source of adhesion. We provide the analytic solution to the problem under study in terms of elliptic integrals and perform the numerical and the asymptotic analysis of the characteristic lengths of the blister. Fin...
ThèseTh`Thèse de doctorat Spécialité: Mécanique Ecole Doctorale: Sciences Mécaniques, Acoustique ... more ThèseTh`Thèse de doctorat Spécialité: Mécanique Ecole Doctorale: Sciences Mécaniques, Acoustique et Electronique de Paris présentée par RICCARDO DE PASCALIS La méthode semi-inverse en mécanique des solides: Fondements théoriques et applications nouvelles Thèse dirigée par Michel DESTRADE et Giuseppe SACCOMANDI Soutenance prévue le 7 décembre 2010 devant le jury composé de:
The effective macroscopic response of nonlinear elastomeric inhomogeneous materials is of great i... more The effective macroscopic response of nonlinear elastomeric inhomogeneous materials is of great interest in many applications including nonlinear composite materials and soft biological tissues. The interest of the present work is associated with a microsphere composite material, which is modelled as a matrix-inclusion composite. The matrix phase is a homogeneous isotropic nonlinear rubber-like material and the inclusion phase is more complex, consisting of a distribution of sizes of stiff thin spherical shells filled with gas. Experimentally, such materials have been shown to undergo complex deformation under cyclic loading. Here, we consider microspheres embedded in an unbounded host material and assume that a hydrostatic pressure is applied in the "far-field". Taking into account a variety of effects including buckling of the spherical shells, large deformation of the host phase and evolving microstructure, we derive a model predicting the pressure-relative volume chang...
La biomecanique des tissus mous est devenue un sujet de recherche important dans nombreux domaine... more La biomecanique des tissus mous est devenue un sujet de recherche important dans nombreux domaines de l’ingenierie, comme la bio-medecine. Les tissus mous peuvent subir des deformations importantes (dans les regimes physiologiques et pathologiques) et qui presentent clairement un comportement mecanique nonlineaire. Dans ce contexte, l’etude des deformations en s’appuyant sur des methodes de calcul numerique, comme les elements finis, peut s’averer compliquee. En effet, il est difficile de connaitre avec certitude les equations constitutives adequates et les logiciels commerciaux sont souvent insuffisants pour la resolution des equations nonlineaires correspondantes. La methode semi-inverse est un des rares outils existants donnant des solutions exactes dans la theorie mathematique de la mecanique des milieux continus, qui malheureusement, a toujours ete employee de facon heuristique et detachee d’une methodologie generale. Cette These, qui se developpe en six chapitres, etudie diver...
The growth of an elastic film adhered to a confining substrate might lead to the formation of del... more The growth of an elastic film adhered to a confining substrate might lead to the formation of delimitation blisters. Many results have been derived when the substrate is flat. The equilibrium shapes, beyond small deformations, are determined by the interplay between the sheet elastic energy and the adhesive potential due to capillarity. Here, we study a non-trivial generalization to this problem and consider the adhesion of a growing elastic loop to a confining circular substrate. The fundamental equations, i.e., the Euler Elastica equation, the boundary conditions and the transversality condition, are derived from a variational procedure. In contrast to the planar case, the curvature of the delimiting wall appears in the transversality condition, thus acting as a further source of adhesion. We provide the analytic solution to the problem under study in terms of elliptic integrals and perform the numerical and the asymptotic analysis of the characteristic lengths of the blister. Fin...
The quasi-linear model of viscoelasticity is a constitutive law widely used to investigate the ti... more The quasi-linear model of viscoelasticity is a constitutive law widely used to investigate the time dependent behaviour of soft tissues and bio-materials. For this model, we study the shearing motion and discuss the existence of kink-type wave solutions. In particular, we derive a nonlinear second-order ordinary differential equation which allows to widen the class of solutions given by Samsonov (1995). When the stress relaxation function is a Prony series, kink-wave solutions can exist for strongly elliptic strain energy functions, except for the Mooney–Rivlin model. We provide numerical simulations for the Yeoh model.
Extreme Mechanics Letters
applied mathematics, biomechanics, mechanics Keywords: viscoelastic, quasi-linear, Fung, strain e... more applied mathematics, biomechanics, mechanics Keywords: viscoelastic, quasi-linear, Fung, strain energy function, hyperelastic, biological soft tissue Author for correspondence:
The effective macroscopic response of nonlinear elastomeric inhomogeneous materials is of great i... more The effective macroscopic response of nonlinear elastomeric inhomogeneous materials is of great interest in many applications including nonlinear composite materials and soft biological tissues. The interest of the present work is associated with a microsphere composite material, which is modelled as a matrix-inclusion composite. The matrix phase is a homogeneous isotropic nonlinear rubber-like material and the inclusion phase is more complex, consisting of a distribution of sizes of stiff thin spherical shells filled with gas. Experimentally, such materials have been shown to undergo complex deformation under cyclic loading. Here, we consider microspheres embedded in an unbounded host material and assume that a hydrostatic pressure is applied in the 'far-field'. Taking into account a variety of effects including buckling of the spherical shells, large deformation of the host phase and evolving microstructure, we derive a model predicting the pressure-relative volume change load curves. Nonlinear constitutive behaviour of the matrix medium is accounted for by employing neo-Hookean and Mooney-Rivlin incompressible models. Moreover a nearly-incompressible solution is derived via asymptotic analysis for a spherical cavity embedded in un unbounded isotropic homogeneous hyperelastic medium loaded hydrostatically. The load-curve predictions reveal a strong dependence on the microstructure of the composite, including distribution of microspheres, the stiffness of the shells, and on the initial volume fraction of the inclusions, whereas there is only a modest dependence on the characteristic properties of the nonlinear elastic model used for the rubber host.
Bulletin of the American Physical Society, 2016
on soft compounds is still imperfectly understood, especially when the dry and wetted parts of th... more on soft compounds is still imperfectly understood, especially when the dry and wetted parts of the substrate have two different values of surface energies (contact angle different than 90 degrees). The problem is made very complex by geometrical nonlinearities arising from finite slope of the substrate and finite deformations, that must be absolutely considered, to distinguish at second order between Young law and Neuman equilibrium of surface tensions. We have developed a numerical, finite element, code that allows one to minimize surface and bulk energies, with finite deformations and asymmetry of the surface energies. The results are compared to a linear theory based on Green function theory [1,2] and Fredholm integrals, and with recent experiments using X-ray visualization [3]. The non-linear numerics reproduce very well the observed profiles, while the linear approach gives helpful analytical approximates. [
This paper offers a reappraisal of Fung's model for quasi-linear viscoelasticity. It is shown tha... more This paper offers a reappraisal of Fung's model for quasi-linear viscoelasticity. It is shown that a number of negative features exhibited in other works, commonly attributed to the Fung approach, are merely a consequence of the way it has been applied. The approach outlined herein is shown to yield improved behaviour and offers a straightforward scheme for solving a wide range of models. Results from the new model are contrasted with those in the literature for the case of uniaxial elongation of a bar: for an imposed stretch of an incompressible bar and for an imposed load. In the latter case, a numerical solution to a Volterra integral equation is required to obtain the results. This is achieved by a high-order discretization scheme. Finally, the stretch of a compressible viscoelastic bar is determined for two distinct materials: Horgan-Murphy and Gent.
Inverse methods A general boundary value problem of elastostatics for a body B consists in findin... more Inverse methods A general boundary value problem of elastostatics for a body B consists in finding a motion x = χ(X) that satisfies a(X, t) = 0 for all particles X of B r and for all times t. Recalling equation (1.24), this means that the motion must satisfy the equilibrium equation DivT R + ρ r b r = 0, (3.1) everywhere in B r , and the boundary conditions of surface tractions (1.22) and place, brought to you by CORE View metadata, citation and similar papers at core.ac.uk
The effective dynamic properties of specific periodic structures involving rubber-like materials ... more The effective dynamic properties of specific periodic structures involving rubber-like materials can be adjusted by pre-strain, thus facilitating the design of custom acoustic filters. While nonlinear viscoelastic behaviour is one of the main features of soft solids, it has been rarely incorporated in the study of such phononic media. Here, we study the dynamic response of nonlinear viscoelastic solids within a ‘small-on-large’ acoustoelasticity framework, that is we consider the propagation of small amplitude waves superimposed on a large static deformation. Incompressible soft solids whose behaviour is described by the Fung–Simo quasi-linear viscoelasticy theory (QLV) are considered. We derive the incremental equations using stress-like memory variables governed by linear evolution equations. Thus, we show that wave dispersion is governed by a strain-dependent generalised Maxwell rheology. Illustrations cover the propagation of plane waves under homogeneous tensile strain in a QLV...
The growth of an elastic film adhered to a confining substrate might lead to the formation of del... more The growth of an elastic film adhered to a confining substrate might lead to the formation of delimitation blisters. Many results have been derived when the substrate is flat. The equilibrium shapes, beyond small deformations, are determined by the interplay between the sheet elastic energy and the adhesive potential due to capillarity. Here, we study a non-trivial generalization to this problem and consider the adhesion of a growing elastic loop to a confining circular substrate. The fundamental equations, i.e., the Euler Elastica equation, the boundary conditions and the transversality condition, are derived from a variational procedure. In contrast to the planar case, the curvature of the delimiting wall appears in the transversality condition, thus acting as a further source of adhesion. We provide the analytic solution to the problem under study in terms of elliptic integrals and perform the numerical and the asymptotic analysis of the characteristic lengths of the blister. Fin...
ThèseTh`Thèse de doctorat Spécialité: Mécanique Ecole Doctorale: Sciences Mécaniques, Acoustique ... more ThèseTh`Thèse de doctorat Spécialité: Mécanique Ecole Doctorale: Sciences Mécaniques, Acoustique et Electronique de Paris présentée par RICCARDO DE PASCALIS La méthode semi-inverse en mécanique des solides: Fondements théoriques et applications nouvelles Thèse dirigée par Michel DESTRADE et Giuseppe SACCOMANDI Soutenance prévue le 7 décembre 2010 devant le jury composé de:
The effective macroscopic response of nonlinear elastomeric inhomogeneous materials is of great i... more The effective macroscopic response of nonlinear elastomeric inhomogeneous materials is of great interest in many applications including nonlinear composite materials and soft biological tissues. The interest of the present work is associated with a microsphere composite material, which is modelled as a matrix-inclusion composite. The matrix phase is a homogeneous isotropic nonlinear rubber-like material and the inclusion phase is more complex, consisting of a distribution of sizes of stiff thin spherical shells filled with gas. Experimentally, such materials have been shown to undergo complex deformation under cyclic loading. Here, we consider microspheres embedded in an unbounded host material and assume that a hydrostatic pressure is applied in the "far-field". Taking into account a variety of effects including buckling of the spherical shells, large deformation of the host phase and evolving microstructure, we derive a model predicting the pressure-relative volume chang...
La biomecanique des tissus mous est devenue un sujet de recherche important dans nombreux domaine... more La biomecanique des tissus mous est devenue un sujet de recherche important dans nombreux domaines de l’ingenierie, comme la bio-medecine. Les tissus mous peuvent subir des deformations importantes (dans les regimes physiologiques et pathologiques) et qui presentent clairement un comportement mecanique nonlineaire. Dans ce contexte, l’etude des deformations en s’appuyant sur des methodes de calcul numerique, comme les elements finis, peut s’averer compliquee. En effet, il est difficile de connaitre avec certitude les equations constitutives adequates et les logiciels commerciaux sont souvent insuffisants pour la resolution des equations nonlineaires correspondantes. La methode semi-inverse est un des rares outils existants donnant des solutions exactes dans la theorie mathematique de la mecanique des milieux continus, qui malheureusement, a toujours ete employee de facon heuristique et detachee d’une methodologie generale. Cette These, qui se developpe en six chapitres, etudie diver...
The growth of an elastic film adhered to a confining substrate might lead to the formation of del... more The growth of an elastic film adhered to a confining substrate might lead to the formation of delimitation blisters. Many results have been derived when the substrate is flat. The equilibrium shapes, beyond small deformations, are determined by the interplay between the sheet elastic energy and the adhesive potential due to capillarity. Here, we study a non-trivial generalization to this problem and consider the adhesion of a growing elastic loop to a confining circular substrate. The fundamental equations, i.e., the Euler Elastica equation, the boundary conditions and the transversality condition, are derived from a variational procedure. In contrast to the planar case, the curvature of the delimiting wall appears in the transversality condition, thus acting as a further source of adhesion. We provide the analytic solution to the problem under study in terms of elliptic integrals and perform the numerical and the asymptotic analysis of the characteristic lengths of the blister. Fin...
The quasi-linear model of viscoelasticity is a constitutive law widely used to investigate the ti... more The quasi-linear model of viscoelasticity is a constitutive law widely used to investigate the time dependent behaviour of soft tissues and bio-materials. For this model, we study the shearing motion and discuss the existence of kink-type wave solutions. In particular, we derive a nonlinear second-order ordinary differential equation which allows to widen the class of solutions given by Samsonov (1995). When the stress relaxation function is a Prony series, kink-wave solutions can exist for strongly elliptic strain energy functions, except for the Mooney–Rivlin model. We provide numerical simulations for the Yeoh model.