A novel coupled system of non-local integro-differential equations modelling Young's modulus evolution, nutrients' supply and consumption during bone fracture healing
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Publication:518953
DOI10.1007/s00033-016-0708-1zbMath1432.74153OpenAlexW2510254009WikidataQ115471504 ScholiaQ115471504MaRDI QIDQ518953
Publication date: 4 April 2017
Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00033-016-0708-1
Finite element methods applied to problems in solid mechanics (74S05) Biomechanical solid mechanics (74L15) PDEs in connection with mechanics of deformable solids (35Q74)
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Cites Work
- On the whole spectrum of Timoshenko beams. II: Further applications
- Buckling of an elastic hemispherical shell with an obstacle
- Three-dimensional instabilities of pantographic sheets with parabolic lattices: numerical investigations
- The influence of different loads on the remodeling process of a bone and bioresorbable material mixture with voids
- A variational approach for a nonlinear one-dimensional damage-elasto-plastic second-gradient continuum model
- Granular micromechanics based micromorphic model predicts frequency band gaps
- A method for the calculation of inter-element stresses in 3D
- Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models
- Numerical identification procedure between a micro-Cauchy model and a macro-second gradient model for planar pantographic structures
- Advanced methods of continuum mechanics for materials and structures
- An anisotropic flow law for incompressible polycrystalline materials
- Macroscopic description of microscopically strongly inhomogenous systems: a mathematical basis for the synthesis of higher gradients metamaterials
- Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof
- Continuum-mechanical, anisotropic flow model for polar ice masses, based on an anisotropic flow enhancement factor
- A simple non-linear model for internal friction in modified concrete
- Dynamic problems for metamaterials: review of existing models and ideas for further research
- Modeling of the interaction between bone tissue and resorbable biomaterial as linear elastic materials with voids
- Osteocytes as a record of bone formation dynamics: a mathematical model of osteocyte generation in bone matrix
- On the contribution of Angelo Luongo to mechanics: in honor of his 60th birthday
- A variational approach for a nonlinear 1-dimensional second gradient continuum damage model
- An isogeometric implicit \(G^1\) mixed finite element for Kirchhoff space rods
- A one-dimensional continuum with microstructure for single-wall carbon nanotubes bifurcation analysis
- A mixture model with evolving mass densities for describing synthesis and resorption phenomena in bones reconstructed with bio-resorbable materials
- Poroelastic materials reinforced by statistically oriented fibres--numerical implementation and application to articular cartilage
- Performance of a high-continuity finite element in three-dimensional elasticity
- Truss Modular Beams with Deformation Energy Depending on Higher Displacement Gradients
- Modeling of a non-local stimulus for bone remodeling process under cyclic load: Application to a dental implant using a bioresorbable porous material
- Isogeometric analysis of plane-curved beams
- Euromech 563 Cisterna di Latina 17–21 March 2014 Generalized continua and their applications to the design of composites and metamaterials: A review of presentations and discussions
- Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives
- At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola
