Mô hình hóa và mô phỏng trường pha của tổn thương xảy ra trong đốt sống người sau khi thực hiện cố định bằng vít

Braides A et al (1998) Approximation of free-discontinuity problems, vol 1694. Springer, Berlin

Braides A (2002) $$\Gamma $$-convergence for beginners. Oxford lecture series in mathematics and its applications, vol 22

Ambrosio L, Tortorelli VM (1990) Approximation of functional depending on jumps by elliptic functional via $$\Gamma $$-convergence. Commun Pure Appl Math 43(8):999–1036

Ambrosio L (1992) On the approximation of free discontinuity problems. Boll Un Mat Ital B 7:105–123

Francfort GA, Marigo J-J (1998) Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids 46(8):1319–1342

Bazant ZP (1982) Crack band model for fracture of geomaterials. pp 1137–1152, AA Balkema

Bažant ZP, Lin F-B (1988) Nonlocal smeared cracking model for concrete fracture. J Struct Eng 114(11):2493–2510

Bazant Z, Jirasek M (1994) Damage nonlocality due to microcrack interactions: statistical determination of crack influence function. Fracture and damage in Quasibrittle structures, pp 3–17

Gerard B, Pijaudier-Cabot G, Laborderie C (1998) Coupled diffusion-damage modelling and the implications on failure due to strain localisation. Int J Solids Struct 35(31–32):4107–4120

Geers M, De Borst R, Brekelmans W, Peerlings R (1998) Strain-based transient-gradient damage model for failure analyses. Comput Methods Appl Mech Eng 160(1–2):133–153

Bourdin B, Francfort GA, Marigo J-J (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48(4):797–826

Bourdin B, Francfort GA, Marigo J-J (2008) The variational approach to fracture. J Elast 91(1):5–148

Kuhn C, Müller R (2008) A phase field model for fracture. In: PAMM: proceedings in applied mathematics and mechanics. Wiley Online Library, vol 8, pp 10223–10224

Hakim V, Karma A (2009) Laws of crack motion and phase-field models of fracture. J Mech Phys Solids 57(2):342–368

Amor H, Marigo J-J, Maurini C (2009) Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments. J Mech Phys Solids 57(8):1209–1229

Nguyen TT, Yvonnet J, Zhu Q-Z, Bornert M, Chateau C (2015) A phase field method to simulate crack nucleation and propagation in strongly heterogeneous materials from direct imaging of their microstructure. Eng Fract Mech 139:18–39

Msekh MA, Sargado JM, Jamshidian M, Areias PM, Rabczuk T (2015) Abaqus implementation of phase-field model for brittle fracture. Comput Mater Sci 96:472–484

Jodlbauer D, Langer U, Wick T (2020) Parallel matrix-free higher-order finite element solvers for phase-field fracture problems. Math Comput Appl 25(3):40

Wu J-Y (2017) A unified phase-field theory for the mechanics of damage and quasi-brittle failure. J Mech Phys Solids 103:72–99

Miehe C, Hofacker M, Welschinger F (2010) A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng 199(45–48):2765–2778

Miehe C, Welschinger F, Hofacker M (2010) Thermodynamically consistent phase-field models of fracture: variational principles and multi-field FE implementations. Int J Numer Meth Eng 83(10):1273–1311

Tanné E, Li T, Bourdin B, Marigo J-J, Maurini C (2018) Crack nucleation in variational phase-field models of brittle fracture. J Mech Phys Solids 110:80–99

Bianchi D, Falcinelli C, Molinari L, Gizzi A, Di Martino A (2022) Osteolytic vs. osteoblastic metastatic lesion: Computational modeling of the mechanical behavior in the human vertebra after screws fixation procedure. J Clin Med 11(10):2850

Fritsch A, Hellmich C (2007) “universal’’ microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: micromechanics-based prediction of anisotropic elasticity. J Theor Biol 244(4):597–620

Bokov A et al (2016) Pedicle screw loosening prediction in patients with degenerative diseases of lumbar spine using bone density measured in hounsfield units. J Osteoporos Phys Act 4(1):1–4

Nguyen L, Stoter S, Baum T, Kirschke J, Ruess M, Yosibash Z, Schillinger D (2017) Phase-field boundary conditions for the voxel finite cell method: Surface-free stress analysis of ct-based bone structures. Int J Numer Methods Biomed Eng 33(12):e2880

Shen R, Waisman H, Yosibash Z, Dahan G (2019) A novel phase field method for modeling the fracture of long bones. Int J Numer Methods Biomed Eng 35(8):e3211

Maghami E, Moore JP, Josephson TO, Najafi AR (2022) Damage analysis of human cortical bone under compressive and tensile loadings. Comput Methods Biomech Biomed Engin 25(3):342–357

Sterba W, Kim D-G, Fyhrie DP, Yeni YN, Vaidya R (2007) Biomechanical analysis of differing pedicle screw insertion angles. Clin Biomech 22(4):385–391

Sansur CA, Caffes NM, Ibrahimi DM, Pratt NL, Lewis EM, Murgatroyd AA, Cunningham BW (2016) Biomechanical fixation properties of cortical versus transpedicular screws in the osteoporotic lumbar spine: an in vitro human cadaveric model. J Neurosurg Spine 25(4):467–476

Incorrect spinal stabilization intervention in a 70 years old female patient in lucca-italy. https://avvocaticollegati.it/2023/02/28/errato-intervento-alla-colonna-vertebrale/. Accessed: 01-12-2023

Ohba T, Ebata S, Oba H, Koyama K, Haro H (2019) Risk factors for clinically relevant loosening of percutaneous pedicle screws. Spine Surg Related Res 3(1):79–85

Inceoğlu S, Montgomery WH, Clair SS, McLain RF (2011) Pedicle screw insertion angle and pullout strength: comparison of 2 proposed strategies. J Neurosurg Spine 14(5):670–676

Molinari L, Falcinelli C, Gizzi A, Martino AD (2021) Biomechanical modeling of metal screw loadings on the human vertebra. Acta Mech Sin 37(2):307–320

Molinari L, Falcinelli C, Gizzi A, Di Martino A (2021) Effect of pedicle screw angles on the fracture risk of the human vertebra: a patient-specific computational model. J Mech Behav Biomed Mater 116:104359

Yosibash Z, Tal D, Trabelsi N (2010) Predicting the yield of the proximal femur using high-order finite-element analysis with inhomogeneous orthotropic material properties. Philos Trans R Soc A Math Phys Eng Sci 368(1920):2707–2723

Matsuura Y, Giambini H, Ogawa Y, Fang Z, Thoreson A, Yaszemski M, Lu L, An K (2014) Specimen-specific nonlinear finite element modeling to predict vertebrae fracture loads after vertebroplasty. Spine 39(22):E1291

Denaro V, Di Martino A (2019) Spinal metastases: diagnosis and management. Springer, Cham, pp 137–147

Costa M, Eltes P, Lazary A, Varga P, Viceconti M, Dall’Ara E (2019) Biomechanical assessment of vertebrae with lytic metastases with subject-specific finite element models. J Mech Behav Biomed Mater 98(4):268–290

Alnæs MS, Hake J, Kirby RC, Langtangen HP, Logg A, Wells GN (2011) The fenics manual. FEniCS Project, version October 31st, vol 36

Pongiman R (2014) HyperMesh introduction pre-processing for finite element analysis. Altair University, Troy

Geuzaine C, Remacle J-F (2009) Gmsh: A 3-D finite element mesh generator with built-in pre-and post-processing facilities. Int J Numer Meth Eng 79(11):1309–1331

Nalla RK, Kruzic JJ, Kinney JH, Ritchie RO (2004) Effect of aging on the toughness of human cortical bone: evaluation by r-curves. Bone 35(6):1240–1246

Fields AJ, Lee GL, Keaveny TM (2010) Mechanisms of initial endplate failure in the human vertebral body. J Biomech 43(16):3126–3131

Erdem I, Truumees E, van der Meulen MC (2013) Simulation of the behaviour of the L1 vertebra for different material properties and loading conditions. Comput Methods Biomech Biomed Eng 16(7):736–746

Song K, Wang Z, Lan J, Ma S (2021) Porous structure design and mechanical behavior analysis based on TPMS for customized root analogue implant. J Mech Behav Biomed Mater 115:104222

Aufa A, Hassan MZ, Ismail Z (2022) Recent advances in Ti-6Al-4V additively manufactured by selective laser melting for biomedical implants: prospect development. J Alloy Compd 896:163072

Bartsch K, Herzog D, Bossen B, Emmelmann C (2021) Material modeling of Ti-6Al-4V alloy processed by laser powder bed fusion for application in macro-scale process simulation. Mater Sci Eng, A 814:141237

Del Piero G, Lancioni G, March R (2007) A variational model for fracture mechanics: numerical experiments. J Mech Phys Solids 55(12):2513–2537

Arroyo M, Ortiz M (2006) Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods. Int J Numer Meth Eng 65(13):2167–2202

Hofacker M, Miehe C (2013) A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns. Int J Numer Meth Eng 93(3):276–301

Miehe C, Schaenzel L-M, Ulmer H (2015) Phase field modeling of fracture in multi-physics problems. Part I. Balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids. Comput Methods Appl Mech Eng 294:449–485

Miehe C, Hofacker M, Schänzel L-M, Aldakheel F (2015) Phase field modeling of fracture in multi-physics problems. Part II. coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic-plastic solids. Comput Methods Appl Mech Eng 294:486–522

Nguyen T-T, Yvonnet J, Zhu Q-Z, Bornert M, Chateau C (2016) A phase-field method for computational modeling of interfacial damage interacting with crack propagation in realistic microstructures obtained by microtomography. Comput Methods Appl Mech Eng 312:567–595

Coleman BD, Noll W (1974) The thermodynamics of elastic materials with heat conduction and viscosity. In: The foundations of mechanics and thermodynamics. Springer, pp 145–156

Wambacq J, Ulloa J, Lombaert G, François S (2021) Interior-point methods for the phase-field approach to brittle and ductile fracture. Comput Methods Appl Mech Eng 375:113612

Ambati M, Gerasimov T, De Lorenzis L (2015) A review on phase-field models of brittle fracture and a new fast hybrid formulation. Comput Mech 55:383–405

Dreischarf M, Zander T, Shirazi-Adl A, Puttlitz C, Adam C, Chen C, Goel V, Kiapour A, Kim Y, Labus K et al (2014) Comparison of eight published static finite element models of the intact lumbar spine: predictive power of models improves when combined together. J Biomech 47(8):1757–1766

Matsukawa K, Yato Y, Imabayashi H, Hosogane N, Asazuma T, Nemoto K (2015) Biomechanical evaluation of the fixation strength of lumbar pedicle screws using cortical bone trajectory: a finite element study. J Neurosurg Spine 23(4):471–478

Gustafsson A, Wallin M, Isaksson H (2019) Age-related properties at the microscale affect crack propagation in cortical bone. J Biomech 95:109326

Hug L, Dahan G, Kollmannsberger S, Rank E, Yosibash Z (2022) Predicting fracture in the proximal humerus using phase field models. J Mech Behav Biomed Mater 134:105415

Chan KS, Chan CK, Nicolella DP (2009) Relating crack-tip deformation to mineralization and fracture resistance in human femur cortical bone. Bone 45(3):427–434

Koester K, Barth H, Ritchie R (2011) Effect of aging on the transverse toughness of human cortical bone: evaluation by R-curves. J Mech Behav Biomed Mater 4(7):1504–1513

Zhang X, Vignes C, Sloan SW, Sheng D (2017) Numerical evaluation of the phase-field model for brittle fracture with emphasis on the length scale. Comput Mech 59:737–752

Pham K, Amor H, Marigo J-J, Maurini C (2011) Gradient damage models and their use to approximate brittle fracture. Int J Damage Mech 20(4):618–652

Martínez-Pañeda E, Golahmar A, Niordson CF (2018) A phase field formulation for hydrogen assisted cracking. Comput Methods Appl Mech Eng 342:742–761

Préve D, Lenarda P, Maskery I, Paggi M (2023) A comprehensive characterization of fracture in unit cell open foams generated from triply periodic minimal surfaces. Eng Fract Mech 277:108949

Zysset PK, Guo XE, Hoffler CE, Moore KE, Goldstein SA (1999) Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. J Biomech 32(10):1005–1012

Gustafsson A, Wallin M, Khayyeri H, Isaksson H (2019) Crack propagation in cortical bone is affected by the characteristics of the cement line: a parameter study using an XFEM interface damage model. Biomech Model Mechanobiol 18(4):1247–1261

Gustafsson A, Isaksson H (2022) Phase field models of interface failure for bone application-evaluation of open-source implementations. Theor Appl Fract Mech 121:103432

Paggi M, Reinoso J (2017) Revisiting the problem of a crack impinging on an interface: a modeling framework for the interaction between the phase field approach for brittle fracture and the interface cohesive zone model. Comput Methods Appl Mech Eng 321:145–172

Kumar PAV, Dean A, Reinoso J, Lenarda P, Paggi M (2021) Phase field modeling of fracture in functionally graded materials: $$\Gamma $$-convergence and mechanical insight on the effect of grading. Thin-Walled Struct 159:107234

Costa M, Campello LB, Ryan M, Rochester J, Viceconti M, Dall’Ara E (2020) Effect of size and location of simulated lytic lesions on the structural properties of human vertebral bodies, a micro-finite element study. Bone Rep 12:100257

Gaziano P, Monaldo E, Falcinelli C, Vairo G (2022) Elasto-damage mechanics of osteons: a bottom-up multiscale approach. J Mech Phys Solids 167:104962

Hermann A, Shojaei A, Steglich D, Höche D, Zeller-Plumhoff B, Cyron CJ (2022) Combining peridynamic and finite element simulations to capture the corrosion of degradable bone implants and to predict their residual strength. Int J Mech Sci 220:107143

Steglich D, Besson J, Reinke I, Helmholz H, Luczak M, Garamus VM, Wiese B, öche DH, Cyron CJ, Willumeit-Römer R (2023) Strength and ductility loss of magnesium-gadolinium due to corrosion in physiological environment: experiments and modeling. J Mech Behav Biomed Mater 144:105939

Gizzi A, Cyron CJ, Falcinelli C, Vasta M (2024) Evolution of fiber distributions in homogenized constrained mixture models of soft tissue growth and remodeling: Uniaxial loading. J Mech Phys Solids 183:105491

Sardhara T, Shkurmanov A, Li Y, Shi S, Cyron CJ, Aydin RC, Ritter M (2024) Role of slice thickness quantification in the 3d reconstruction of fib tomography data of nanoporous materials. Ultramicroscopy 256:113878

Ober C, Loisel DA, Gilad Y (2008) Sex-specific genetic architecture of human disease. Nat Rev Genet 9(12):911–922

Barkaoui A, Ben Kahla R, Merzouki T, Hambli R (2017) Age and gender effects on bone mass density variation: finite elements simulation. Biomech Model Mechanobiol 16:521–535