The stability of the equilibrium of two-phase elastic solids

Yeremeyev, V.A.; Freidin, A. B.; Sharipova, Leah L.

doi:10.1016/j.jappmathmech.2007.03.007

Cited by 62 publications

(48 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In contrast to the solution given in Eremeyev and Pietraszkiewicz (2009), where the two-phase state is described by the horizontal line, here we have the decreasing part of the diagram. This is analogous to the loading diagram for the two-phase elastic sphere (Eremeyev and Zubov, 1991;Freidin et al, 2006;Yeremeyev et al, 2007). The decreasing part of the loading diagram indicates that there is an instability in the force-controlled loading.…”

Section: Stretchingsupporting

confidence: 57%

See 1 more Smart Citation

Thermomechanics of shells undergoing phase transition

Eremeyev

Pietraszkiewicz

2011

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

show abstract

Section: Stretchingsupporting

confidence: 57%

“…Note that non-uniqueness of solutions of the boundary-value problems for elastic bodies undergoing phase transformations is a standard situation, see e.g. Eremeyev and Zubov (1991), Freidin et al (2006), andYeremeyev et al (2007) for the 3D case.…”

Section: Stretchingmentioning

confidence: 99%

Thermomechanics of shells undergoing phase transition

Eremeyev

Pietraszkiewicz

2011

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

show abstract

“…It is worth noting that the phenomena of resorption or synthesis in bones and resorption in biomaterials due to the bio-mechanical evolution are similar to phase transitions studied in [43,44,45,46,47,81]. Moreover, the remodeling process presents some stability and bifurcation problems, especially when the applied load reaches a certain level in the presence of geometric or material nonlinearities.…”

Section: Introductionmentioning

confidence: 73%

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

Andreaus

Giorgio

Madeo

2014

Z. Angew. Math. Phys.

View full text Add to dashboard Cite

. 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.

show abstract

“…In could be relatively easy to use a metamaterial undergoing solid-solid phase transitions in the design of sound screen to stop undesired mechanical vibrations (the modeling of the phenomenon is presented e.g. in [213,65]. Damping effect needed to obtain energy adsorption from mechanical vibrations could consist in the induced phase transition, which in one direction should be endoenergetic.…”

Section: Sound and Vibration Control Via The Conception Of Frequency mentioning

confidence: 99%