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

Abstract

. 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.

Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence

“…Another consideration is needed here: In the present work, we do not try to derive the used continuum model by means of a homogenization procedure. Of course this micro-macro procedure is needed, and following the ideas presented, for example, in [2,3,77], in [6][7][8]18,28,62,71,72] in [10] or in [48][49][50] will be the object of further investigations (see also [63] for a general overview on generalized continua).…”

Identification of higher-order elastic constants for grain assemblies based upon granular micromechanics

“…The micromorphic behavior of granular materials indicates the possibility of realizing materials with alternate synthesis pathways which show specific wave propagation behaviors that can be used for vibration control as an alternative to piezoelectric materials [Maurini et al 2004;2006;Porfiri et al 2005;Vidoli and dell'Isola 2001;dell'Isola and Vidoli 1998;Greco et al 2014] or for damage identification [Ferretti et al 2014;Andreaus and Baragatti 2011;. Alternatively, such materials can be applied to help optimize control procedures or for optimal biomaterial design in bone mechanics [Andreaus et al 2015b]. The identification process described herein can be used for extending the applicability of micromorphic models or their micropolar and second gradient simplifications to describe post-instability macroscale behavior, such as boundary and localization layers in microstructured media [Altenbach et al 2010;Placidi 2015;Yang et al 2011;Yang and Misra 2012].…”

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“…The micromorphic behavior of granular materials indicates the possibility of realizing materials with alternate synthesis pathways which show specific wave propagation behaviors that can be used for vibration control as an alternative to piezoelectric materials [Maurini et al 2004;2006;Porfiri et al 2005;Vidoli and dell'Isola 2001;dell'Isola and Vidoli 1998;Greco et al 2014] or for damage identification [Ferretti et al 2014;Andreaus and Baragatti 2011;. Alternatively, such materials can be applied to help optimize control procedures or for optimal biomaterial design in bone mechanics [Andreaus et al 2015b]. The identification process described herein can be used for extending the applicability of micromorphic models or their micropolar and second gradient simplifications to describe post-instability macroscale behavior, such as boundary and localization layers in microstructured media [Altenbach et al 2010;Placidi 2015;Yang et al 2011;Yang and Misra 2012].…”