1,721,053 research outputs found
Multi-scale modelling of rubber-like materials and soft tissues: An appraisal
Full text linkWe survey, in a partial way, multi-scale approaches for the modelling of rubber-like and soft tissues and compare them with classical macroscopic phenomenological models. Our aim is to show how it is possible to obtain practical mathematical models for the mechanical behaviour of these materials incorporating mesoscopic (network scale) information. Multi-scale approaches are crucial for the theoretical comprehension and prediction of the complex mechanical response of these materials. Moreover, such models are fundamental in the perspective of the design, through manipulation at the micro- and nano-scales, of new polymeric and bioinspired materials with exceptional macroscopic properties
“The Software THERMICO for the Numerical Simulation of Asphalt Concrete Pavement Temperature”
No full textPREPRINT N. 2008/01 DIPARTIMENTO DI MATEMATICA, UNIVERSITÀ DEL SALENTO, LECCE (2008
Some Remarks on the Weakly Nonlinear Theory of Isotropic Elasticity
No full textThird- and fourth-order weakly nonlinear theories of elasticity are widely used by applied mathematicians, physicists and acousticians. Although their introduction is traced back to a paper by Signorini dated 1930, some aspects related to the rigorous mathematical derivation of the strain energy for quasi-incompressible isotropic elastic solids are not satisfactorily clear. In this paper we address these aspects and use our results to discuss the incompressible limit of some fourth-order nonlinear constitutive parameters
The Gent model for rubber-like materials: an appraisal for an ingenious and simple idea
Full text linkWe review the main aspects of the celebrated Gent constitutive model for rubberlike materials. Emphasis is placed on the case of damageable materials describing possible damage and deformation localizatio
Revisiting the Love hypothesis for introducing dispersion of longitudinal waves in elastic rods
Full text linkWe re-examine the Love equation, which forms the first historical attempt at improving on the classical wave equation to encompass for dispersion of longitudinal waves in rods. Dispersion is introduced by accounting for lateral inertia through the Love hypothesis. Our aim is to provide a rigorous justification of the Love hypothesis, which may be generalized to other contexts. We show that the procedure by which the Love equation is traditionally derived is misleading: indeed, proper variational dealing of the Love hypothesis in a two -modal kinematics (the Mindlin-Herrmann system) leads to the Bishop-Love equation instead. The latter is not asymptotically equivalent to the Love equation, which is in fact a long wave low frequency approximation of the Pochhammer-Chree solution. However, the Love hypothesis may still be retrieved from the Mindlin-Herrmann system, by a slow -time perturbation process. In so doing, the linear KdV equation is retrieved. Besides, consistent approximation demands that a correction term be added to the classical Love hypothesis. Surprisingly, in the case of isotropic linear elasticity, this correction term produces no effect in the correction term of the Lagrangian, so that, to first order, the same Bishop-Love equation is the Euler-Lagrange equation corresponding to a family of Love -like hypotheses, all being different by the correction term. Besides, ill-posedness coming from non-standard (namely non static) natural boundary conditions is now amended
Spatial estimates for Kelvin-Voigt finite elasticity with nonlinear viscosity: Well behaved solutions in space
No full textWe provide some spatial estimates for the nonlinear partial differential equation governing anti-plane motions in a nonlinear viscoelastic theory of Kelvin-Voigt type when the viscosity is a function of the strain rate. The spatial estimates we prove are an alternative of Phragmen-Lindelöf type. These estimates are possible when a precise balance between the elastic and viscoelastic nonlinearities holds
“The Relevance of Nonlinear Stacking Interactions in Simple Models of Double-Stranded DNA”
No full textSingle molecule DNA experiments provide interesting data that allow a better understanding
of the mechanical interactions between the strands and the nucleotides of this molecule. In
some sense, these experiments complement the classical ones about DNA thermal
denaturation. It is well known that the original Peyrard–Bishop (PB) model by means of a
harmonic stacking potential and a nonlinear substrate potential has been able to predict the
existence of a critical temperature of full denaturation of the molecule. In the present paper,
driven by the findings of single molecule experiments, we substitute the original harmonic
intra-strand stacking potential with a Duffing type potential. By elementary and analytical
arguments, we show that with this choice it is possible to obtain a sharp transition in the
classical domain wall solution of the PB model and the compactification of the classical
solitary wave solutions of other models for the dynamics of DNA. We discuss why these
solutions may improve our knowledge of the DNA dynamics in several directions
Generalised Mooney–Rivlin models for brain tissue: A theoretical perspective
No full textA vivid research on brain tissue has proven that in simple shear tests the relation
between the shear stress and shear strain is linear for strains in a range which
is significative in the physiological and pathological regime. Since Mooney-
Rivlin materials satisfy this peculiar property when subjected to simple shear
deformations, the celebrated mathematical model introduced first by Mooney,
and then developed by Rivlin, has been often used to describe the mechanical
behaviour of brain tissue. Recently, it has been shown that a most general strain
energy density for incompressible isotropic elastic materials exhibiting a linear
relationship between shear stress and shear strain in simple shear deformation
consists of the sum of the Mooney-Rivlin model and an arbitrary function of
the difference of the first two principal invariants of the deformation tensor.
For this reason, a strain energy function of this form is called a generalised
Mooney-Rivlin model. In this note we design theoretically a procedure aiming
at the determination of the generalised Mooney-Rivlin model which fits best the
experimental data
Implicit nonlinear elastic bodies with density dependent material moduli and its linearization
No full textWe develop an implicit constitutive relation to describe the response of a compressible elastic solid, based on physical considerations, that captures all the characteristics exhibited by the popular Blatz–Ko model, but in addition presents some interesting novel features. The fact that the Cauchy stress appears linearly in the implicit constitutive relation between the stress and the left Cauchy–Green strain with the material moduli depending nonlinearly on the deformation gradient, allows us to capture several characteristic features of the response of rubber-like elastic solids. Interestingly, in the nonlinear implicit model that we develop, we find that it is possible to have the normal stress components of the stress influence the shearing motion at second order, when considering weakly nonlinear waves, that only occurs at third order within the case of the classical nonlinear Cauchy elasticity theory. Linearization of the constitutive relation under the assumption of small displacement gradient reduces the constitutive relation to one whose material moduli can depend on the trace of the linearized strain and hence the density in virtue of the balance of mass, such a feature is not possible within the context of the Blatz–Ko constitutive relation, or for that matter any Cauchy elastic body, as linearization leads to the classical linearized elastic constitutive relation that has constant material moduli
Antonio Signorini and the proto-history of the non-linear theory of elasticity
No full textAntonio Signorini's contribution to the constitutive theory of non-linear elasticity is reconstructed and analyzed. Some uninformed opinions suggesting he had a minor role, lacking of significant results, are discussed and refuted. It is shown that Signorini should be rightly credited for being among the first scholars aware of the central problem of non-linear elasticity: the determination of the general form of the elastic potential
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