Variational formulation of pre-stressed solid–fluid mixture theory, with an application to wave phenomena

Placidi, Luca; Dell’Isola, Francesco; Ianiro, Nicoletta; Sciarra, Giulio

doi:10.1016/j.euromechsol.2007.10.003

Cited by 93 publications

(79 citation statements)

References 55 publications

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“…Developed framework can also be used in other applications such as bone mechanics [20]. Moreover, utilizing variational approach as presented in dell'Isola and Placidi [9] and Placidi et al [30], the current formulation will be extended to represent the boundary conditions without utilizing fictitious regions.…”

Section: Final Remarksmentioning

confidence: 99%

Implementation of peridynamic beam and plate formulations in finite element framework

Yang

Öterkuş

Nguyen

et al. 2018

Continuum Mech. Thermodyn.

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Peridynamic (PD) theory is a new continuum mechanics formulation introduced to overcome the limitations of classical continuum mechanics such as predicting crack initiation and propagation, and capturing nonlocal effects. PD theory is based on integro-differential equations and these equations are generally difficult to be solved by using analytical techniques. Therefore, numerical approximations, especially with meshless method, have been widely used. Numerical solution of three-dimensional models is usually computationally expensive and structural idealization can be utilized to reduce the computational time significantly. In this study, two of such structural idealization types are considered, namely Timoshenko beam and Mindlin plate, and their peridynamic formulations are briefly explained. Moreover, the implementation of these formulations in finite element framework is presented. To demonstrate the capability of the present approach, several case studies are considered including beam and plate bending due to transverse loading, buckling analysis and propagation of an initial crack in a plate under bending loading.

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Section: Final Remarksmentioning

confidence: 99%

Implementation of peridynamic beam and plate formulations in finite element framework

Yang

Öterkuş

Nguyen

et al. 2018

Continuum Mech. Thermodyn.

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“…This means that the constitutive quantity or=ot has to be a function of the expression occurring in the bracket of product (61). where C r ðs m ; rÞ is positive coefficient characterising non-stationary processes of menisci transport in porous materials.…”

Section: Constitutive Relations For Quantities Describing Menisci Motionmentioning

confidence: 99%

“…The second gradient theory is used in mechanics as a thermodynamic model of continuous media to study capillarity in fluids [18,30,31] and other phenomena [2,19,30,47,[59][60][61]67] like damage [60] and plasticity [59] as well as in a micro-structural model for the dissipation phenomena in concrete [63].…”

Section: Introductionmentioning

confidence: 99%

Macroscopic description of capillary transport of liquid and gas in unsaturated porous materials

Cieszko

2016

Meccanica

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A new macroscopic description of capillary transport of liquid and gas in porous materials is presented within the framework of multiphase continuum mechanics. It is assumed that unsaturated porous material form a macroscopic continuum composed of three constituents: gas, mobile liquid and capillary liquid, while the skeleton is rigid with an isotropic pore space structure. The capillary liquid forms a thin layer on the internal contact surface with the skeleton, is immoveable and contains the whole capillary energy. The remaining part of the liquid, surrounded by the layer of the capillary liquid and menisci, forms the constituent called mobile liquid. Both liquids exchange mass, momentum and energy in the vicinity of menisci surfaces during their motion, which is described by an additional macroscopic velocity field. A macroscopic scalar quantity is introduced, parametrizing changes of saturations, which for quasi static and stationary processes is equal to the capillary pressure. This quantity extends the dimensionality of the description of mechanical processes taking place in unsaturated porous materials. For the three fluid constituents of the medium, balance equations of mass and linear momentum and evolution equations for saturations are formulated. The constitutive relations for quantities describing mechanical processes in such a medium are proposed based on the dissipation inequality of mechanical energy for the whole system. A new approach is proposed, similar to that used in rational thermodynamics, based on entropy inequality analysis and the Lagrange multipliers method.

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“…To accomplish this task, the linear theory of elastic materials with voids developed by Cowin and Nunziato [19] is herein employed to describe the mechanical behaviour of a mixture of bone tissue and bioresorbable material, where the change in void volume is induced by deformations (e.g. the results in [30,34,83,68,95,82,29,71,67,35,25] are useful to model complex porous materials). In the model presented here the mixture can be intended as a solid material with small distributed voids which contain nothing of mechanical or energetic significance.…”

Section: Introductionmentioning

confidence: 99%

Modeling of the interaction between bone tissue and resorbable biomaterial as linear elastic materials with voids

Andreaus

Giorgio

Madeo

2014

Z. Angew. Math. Phys.

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. Modeling of the interaction between bone tissue and resorbable biomaterial as linear elastic materials with voids. Zeitschrift für Angewandte Mathematik und Physik, Springer Verlag, 2015, 66 (1), pp.209-237. 10.1007 Modeling of the interaction between bone tissue and resorbable biomaterial as linear elastic materials with voids Ugo Andreaus, Ivan Giorgio and Angela Madeo Abstract. In this paper a continuum mixture model with evolving mass densities and porosity is proposed to describe the process of bone remodeling in presence of bio-resorbable materials as driven by externally applied loads. From a mechanical point of view, both bone tissue and biomaterial are modeled as linear-elastic media with voids in the sense of [19]. In the proposed continuum model the change of volume fraction related to the void volume is directly accounted for by considering porosity as an independent kinematical field. The bio-mechanical coupling is ensured by the introduction of a suitable stimulus which allows for discriminating between resorption (of both bone and biomaterial) and synthesis (of the sole natural bone) depending on the level of externally applied loads. The presence of a 'lazy zone' associated with intermediate deformation levels is also considered in which neither resorption nor synthesis occur. Some numerical solutions of the integro-differential equations associated with the proposed model are provided for the twodimensional case. Ranges of values of the parameters for which different percentages of biomaterial substitution occur are proposed, namely parameters characterizing initial and maximum values of mass densities of bone tissue and of the bioresorbable material.

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Variational formulation of pre-stressed solid–fluid mixture theory, with an application to wave phenomena

Cited by 93 publications

References 55 publications

Implementation of peridynamic beam and plate formulations in finite element framework

Implementation of peridynamic beam and plate formulations in finite element framework

Macroscopic description of capillary transport of liquid and gas in unsaturated porous materials

Modeling of the interaction between bone tissue and resorbable biomaterial as linear elastic materials with voids

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