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

DOI10.1007/s00033-014-0403-zzbMath1317.74064OpenAlexW2092158844WikidataQ58226131 ScholiaQ58226131MaRDI QIDQ2342163

Angela Madeo, Ivan Giorgio, Ugo A. Andreaus

Publication date: 11 May 2015

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-014-0403-z

zbMATH Keywords

mechanical loadingcontinuum mixture modelporo-elasticitygrowth/resorption processesmechanical-biological coupling

Mathematics Subject Classification ID

Biomechanical solid mechanics (74L15)

Related Items (29)

Homogenization à la Piola produces second gradient continuum models for linear pantographic lattices ⋮ On the whole spectrum of Timoshenko beams. II: Further applications ⋮ On the whole spectrum of Timoshenko beams. I: A theoretical revisitation ⋮ On the contribution of Angelo Luongo to mechanics: in honor of his 60th birthday ⋮ Some general remarks on hyperplasticity modelling and its extension to partially saturated soils ⋮ A strain gradient variational approach to damage: a comparison with damage gradient models and numerical results ⋮ The influence of different loads on the remodeling process of a bone and bioresorbable material mixture with voids ⋮ Granular micromechanics based micromorphic model predicts frequency band gaps ⋮ A poroplastic model of structural reorganisation in porous media of biomechanical interest ⋮ Modeling of a non-local stimulus for bone remodeling process under cyclic load: Application to a dental implant using a bioresorbable porous material ⋮ An analytical assessment of finite element and isogeometric analyses of the whole spectrum of Timoshenko beams ⋮ In-depth gaze at the astonishing mechanical behavior of bone: A review for designing bio-inspired hierarchical metamaterials ⋮ Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof ⋮ Symmetric forms for hyperbolic‐parabolic systems of multi‐gradient fluids ⋮ Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence ⋮ The mechanical role of the periodontal ligament for developing mathematical models in orthodontics ⋮ Bias extension test for pantographic sheets: numerical simulations based on second gradient shear energies ⋮ Numerical investigation of a particle system compared with first and second gradient continua: Deformation and fracture phenomena* ⋮ On the well posedness of static boundary value problem within the linear dilatational strain gradient elasticity ⋮ Linear theory for the mechanics of third-gradient continua reinforced with fibers resistance to flexure ⋮ A novel coupled system of non-local integro-differential equations modelling Young's modulus evolution, nutrients' supply and consumption during bone fracture healing ⋮ A novel mathematical model for growth of capillaries and nutrient supply with application to prediction of osteophyte onset ⋮ A model for bone mechanics and remodeling including cell populations dynamics ⋮ Two-dimensional strain gradient damage modeling: a variational approach ⋮ New description of gradual substitution of graft by bone tissue including biomechanical and structural effects, nutrients supply and consumption ⋮ Numerical investigations of ultrasound wave propagating in long bones using a poroelastic model ⋮ A mathematical model for bone cell population dynamics of fracture healing considering the effect of energy dissipation ⋮ Phase field approach for void dynamics with interface stresses at the nanoscale ⋮ Green-Naghdi rate of the Kirchhoff stress and deformation rate: the elasticity tensor

Cites Work

• Unnamed Item
• Unnamed Item
• The effect of fluid streams in porous media on acoustic compression wave propagation, transmission, and reflection
• Thermomechanics of shells undergoing phase transition
• On the derivation of thermomechanical balance equations for continuous systems with a nonmaterial interface
• Modelling bioactivity and degradation of bioactive glass based tissue engineering scaffolds
• Complementary energy approach to contact problems based on consistent augmented Lagrangian formulation
• Boundary conditions at fluid-permeable interfaces in porous media: a variational approach
• Variational formulation of pre-stressed solid-fluid mixture theory, with an application to wave phenomena
• Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network
• Linear elastic materials with voids
• A phenomenological approach to phase transition in classical field theory
• On some mixed finite element methods for plane membrane problems
• Continuum modelling of piezoelectromechanical truss beams: An application to vibration damping
• Damping of bending waves in truss beams by electrical transmission lines with PZT actuators
• Dynamics of solids with microperiodic nonconnected fluid inclusions
• Saint-Venant's problem for porous linear elastic materials
• Perturbation methods for bifurcation analysis from multiple nonresonant complex eigenvalues
• A micro-structured continuum modelling compacting fluid-saturated grounds: The effects of pore-size scale parameter
• Growth and balance.
• Stress rate formulation for elastoplastic models with internal variables based on augmented Lagrangian regularisation
• Thermomechanics of volumetric growth in uniform bodies
• A variational approach for the deformation of a saturated porous solid: A second-gradient theory extending Terzaghi's effective stress principle
• The nonlinear theory of elastic shells with phase transitions
• On a model of layered piezoelectric beams including transverse stress effect
• Multiple timescales analysis for 1:2 and 1:3 resonant Hopf bifurcations
• Modelling of bone adaptation based on an optimal response hypothesis
• An Eshelbian approach to the nonlinear mechanics of constrained solid-fluid mixtures
• On the reconstitution problem in the multiple time-scale method
• Control of sound radiation and transmission by a piezoelectric plate with an optimized resistive electrode
• Statistical damage theory of 2D lattices: energetics and physical foundations of damage parameter
• A continuum theory for granular materials
• Wave propagation in relaxed micromorphic continua: modeling metamaterials with frequency band-gaps
• Micro-macro numerical modelling of bone regeneration in tissue engineering
• A geometrically exact micromorphic model for elastic metallic foams accounting for affine microstructure. Modelling, existence of minimizers, identification of moduli and computational results
• The relaxed linear micromorphic continuum: Existence, uniqueness and continuous dependence in dynamics
• A mixture model with evolving mass densities for describing synthesis and resorption phenomena in bones reconstructed with bio-resorbable materials
• A microscale second gradient approximation of the damage parameter of quasi-brittle heterogeneous lattices
• A 2-D continuum model of a mixture of bone tissue and bio-resorbable material for simulating mass density redistribution under load slowly variable in time
• Linear plane wave propagation and normal transmission and reflection at discontinuity surfaces in second gradient 3D continua
• The determination of the elastic field of an ellipsoidal inclusion, and related problems
• A globally convergent numerical algorithm for damaging elasto-plasticity based on the Multiplier method
• The Cosserat couple modulus for continuous solids is zero viz the linearized Cauchy-stress tensor is symmetric
• Extended non-linear relations of elastic shells undergoing phase transitions
• A Variational Principle for Granular Materials
• What are the dominant thermomechanical processes in the basal sediment layer of large ice sheets?
• On Continuum Modelling the Interphase Layers in Certain Two-Phase Elastic Solids
• Piezoelectric Passive Distributed Controllers for Beam Flexural Vibrations
• A solid-fluid mixture model allowing for solid dilatation under external pressure.

This page was built for publication: Modeling of the interaction between bone tissue and resorbable biomaterial as linear elastic materials with voids