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    Abaqus Inc elastoplastic numerical analysis model
    Elastoplastic Numerical Analysis Model, supplied by Abaqus Inc, used in various techniques. Bioz Stars score: 86/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/elastoplastic+numerical+analysis+model/3d+model/pmc12901156-37-6-21
    Average 86 stars, based on 1 article reviews
    elastoplastic numerical analysis model - by Bioz Stars, 2026-11
    86/100 stars

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    other:

    Article Title: Physics-informed neural networks for constitutive modeling and multiphysics coupling in viscoelastic materials: Applications to asphalt pavement mechanics.
    Article Snippet: Viscoelastic materials are widely used in fields such as transportation engineering, biomedical systems, and polymer science.. Their strong nonlinearity, time-dependent behavior, and coupled multiphysics responses pose substantial challenges for modeling and analysis.. Conventional constitutive models typically rely on a large number of experimental parameters and physical assumptions, which limit their ability to accurately capture the complex, multi-scale, and multiphysics behaviors of viscoelastic materials.

    Article Title: Investigation of wear in CoCrMo hip implants under realistic loading conditions: a contact mechanics-based experimental approach
    Article Snippet: Metal-on-metal CoCrMo implants in total hip arthroplasty (THA) have raised concerns due to in-vivo degradation mechanisms that remain incompletely understood.. Computational studies have linked early CoCrMo implant failures to younger, more active patients, showing that high-load activities can generate substantially greater contact pressures than simple walking conditions.. This study experimentally investigates the tribological performance of CoCrMo alloy under four physiological loading conditions of ISO standard, walking, stair descent and ascent, using an integrated kinematic, wear, and surface characterization analysis.

    Article Title: Coupled effects of high-pressure water and mode mixity on the fracture properties and crack kinematics of concrete-rock interfaces.
    Article Snippet: Interfacial SIFs were extracted using a 2D ABAQUS model, employing the Interaction Integral method to decouple Mode I and II components.

    Shear:

    Article Title: Computational models for predicting bone fracture healing: a review of modeling approaches, predictions, and emerging strategies
    Article Snippet: FEM , Octahedral shear strain; Interstitial fluid velocity; MSC diffusion , 2D axisymmetric model of titanium dental implant; ANSYS Mechanical APDL; Biot’s poroelasticity theory; cyclic loading ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_r$$\end{document} z r , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_h$$\end{document} z h ); 30-day simulation , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_h$$\end{document} z h + \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\textrm{avg}}$$\end{document} S avg led to bone formation; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\textrm{max}}$$\end{document} S max resulted in fibrous tissue; fluid velocity peaked near 0.1–12 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document} μ m/s (P1); slower stabilization in P2 and P3 , No validation , Linear elastic materials; 2D geometry; No directional influence of fluid flow on MSC migration , Irandoust and Müftü ( ) . .. FEM , Shear strain; Interstitial fluid velocity; MSC proliferation and migration , 3D poroelastic model; Abaqus 54 simulations; Random dispersion cell model; Scaffold with porosity 30–70%, stiffness 750–1250 MPa, dissolution 0–1%/iteration; Loading 1–2 MPa , 71% bone regeneration under baseline; High porosity enhances bone but reduces stiffness; High dissolution rates cause collapse; Medium rates optimize outcome; Young’s modulus more critical under high load , No experimental validation , Assumes uniform nutrient supply; excludes apoptosis; linear degradation kinetics , Byrne et al. ( ) . .. FEM , Hand grip dynamic loading (axial compression, 100 N at 1–2 Hz and >3 Hz); poroelasticity; mechanobiochemical model (MSC differentiation, solute transport, cell migration) , CT-based geometry in COMSOL; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx $$\end{document} ≈ 65,000 tetrahedral elements (bone, callus, marrow, implant); axial dynamic loading at varied rates , Moderate frequencies (1–2 Hz) enhance healing and chondrocyte transport (up to 1700% volarly); 2 Hz with 3 mm gap optimizes indirect bone formation; high frequency (>3 Hz) detrimental , Experimental validation with 5 sawbone specimens under cyclic axial loading; close match between predicted and measured displacement/stiffness , Only axial loading considered; no local IFM measured; simplified early-stage biology; constant loading magnitude; no time-dependent callus properties , Liu et al. ( ) .

    Migration:

    Article Title: Computational models for predicting bone fracture healing: a review of modeling approaches, predictions, and emerging strategies
    Article Snippet: FEM , Octahedral shear strain; Interstitial fluid velocity; MSC diffusion , 2D axisymmetric model of titanium dental implant; ANSYS Mechanical APDL; Biot’s poroelasticity theory; cyclic loading ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_r$$\end{document} z r , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_h$$\end{document} z h ); 30-day simulation , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_h$$\end{document} z h + \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\textrm{avg}}$$\end{document} S avg led to bone formation; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\textrm{max}}$$\end{document} S max resulted in fibrous tissue; fluid velocity peaked near 0.1–12 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document} μ m/s (P1); slower stabilization in P2 and P3 , No validation , Linear elastic materials; 2D geometry; No directional influence of fluid flow on MSC migration , Irandoust and Müftü ( ) . .. FEM , Shear strain; Interstitial fluid velocity; MSC proliferation and migration , 3D poroelastic model; Abaqus 54 simulations; Random dispersion cell model; Scaffold with porosity 30–70%, stiffness 750–1250 MPa, dissolution 0–1%/iteration; Loading 1–2 MPa , 71% bone regeneration under baseline; High porosity enhances bone but reduces stiffness; High dissolution rates cause collapse; Medium rates optimize outcome; Young’s modulus more critical under high load , No experimental validation , Assumes uniform nutrient supply; excludes apoptosis; linear degradation kinetics , Byrne et al. ( ) . .. FEM , Hand grip dynamic loading (axial compression, 100 N at 1–2 Hz and >3 Hz); poroelasticity; mechanobiochemical model (MSC differentiation, solute transport, cell migration) , CT-based geometry in COMSOL; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx $$\end{document} ≈ 65,000 tetrahedral elements (bone, callus, marrow, implant); axial dynamic loading at varied rates , Moderate frequencies (1–2 Hz) enhance healing and chondrocyte transport (up to 1700% volarly); 2 Hz with 3 mm gap optimizes indirect bone formation; high frequency (>3 Hz) detrimental , Experimental validation with 5 sawbone specimens under cyclic axial loading; close match between predicted and measured displacement/stiffness , Only axial loading considered; no local IFM measured; simplified early-stage biology; constant loading magnitude; no time-dependent callus properties , Liu et al. ( ) .

    Article Title: Computational models for predicting bone fracture healing: a review of modeling approaches, predictions, and emerging strategies
    Article Snippet: FEM , Deviatoric strain, pore pressure, fluid velocity, cell diffusion , Axisymmetric 2D poroelastic model of ovine tibia with 3 mm fracture gap; ABAQUS 2379 elements; adaptive mechanobiological algorithm in MATLAB; 120 iterations; axial loading (300 N or biofeedback to 600 N) , All classic algorithms reproduced fracture healing stages; only Lacroix model predicted callus resorption; deviatoric strain alone sufficient for correct prediction; pore pressure and fluid velocity alone are insufficient , Qualitative comparison with previous results , No explicit modeling of mitosis, apoptosis, neovascularization; simplified cell migration; model time not physical , Isaksson et al. ( ) . .. 3D poroelastic FEM , Deviatoric strain, interstitial fluid velocity , Seven coupled nonlinear PDEs governing MSCs, fibroblasts, chondrocytes, and osteoblasts; mechanoregulation drives migration, proliferation, differentiation, apoptosis, and matrix production; implemented in ABAQUS , Reproduced spatially and temporally healing: periosteal intramembranous ossification, sequential fibrous and cartilaginous formation in gap, endochondral ossification; higher loads (400–500 N) delayed or prevented healing; periosteal stripping and cartilage impairment led to delayed bridging , Comparison with previous phenomenological model; qualitative agreement with experimental observations , No vascularization or growth factor modeling; binary cell thresholds; neglect of volumetric growth , Isaksson et al. ( ) . .. FEM , Volumetric strain; diffusing biological potential , 2D lattice-based FEM with rotational symmetry; implemented in MATLAB; mechanical solver via DUNE; 112 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document} × 120 grid, 1-day steps until 60 days; tissue maturation as modulus increase , Model reproduced periosteal ossification, cartilage bridging, and realistic callus progression; best results with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c=10$$\end{document} c = 10 (periosteal), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c=0.1$$\end{document} c = 0.1 (marrow), and thresholds \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_\textrm{Sb}=1.5\%$$\end{document} M Sb = 1.5 % , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_\textrm{Sc}=4\%$$\end{document} M Sc = 4 % , Pixel-wise comparison with averaged histological images from 32 sheep tibial osteotomies across 6 healing stages; mismatch \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx $$\end{document} ≈ 6.2% , No modeling of bone resorption/remodeling; assumes linear elasticity, rotational symmetry; lacks vascularization and signaling , Vetter et al. ( ) .

    Dispersion:

    Article Title: Computational models for predicting bone fracture healing: a review of modeling approaches, predictions, and emerging strategies
    Article Snippet: FEM , Octahedral shear strain; Interstitial fluid velocity; MSC diffusion , 2D axisymmetric model of titanium dental implant; ANSYS Mechanical APDL; Biot’s poroelasticity theory; cyclic loading ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_r$$\end{document} z r , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_h$$\end{document} z h ); 30-day simulation , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_h$$\end{document} z h + \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\textrm{avg}}$$\end{document} S avg led to bone formation; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\textrm{max}}$$\end{document} S max resulted in fibrous tissue; fluid velocity peaked near 0.1–12 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document} μ m/s (P1); slower stabilization in P2 and P3 , No validation , Linear elastic materials; 2D geometry; No directional influence of fluid flow on MSC migration , Irandoust and Müftü ( ) . .. FEM , Shear strain; Interstitial fluid velocity; MSC proliferation and migration , 3D poroelastic model; Abaqus 54 simulations; Random dispersion cell model; Scaffold with porosity 30–70%, stiffness 750–1250 MPa, dissolution 0–1%/iteration; Loading 1–2 MPa , 71% bone regeneration under baseline; High porosity enhances bone but reduces stiffness; High dissolution rates cause collapse; Medium rates optimize outcome; Young’s modulus more critical under high load , No experimental validation , Assumes uniform nutrient supply; excludes apoptosis; linear degradation kinetics , Byrne et al. ( ) . .. FEM , Hand grip dynamic loading (axial compression, 100 N at 1–2 Hz and >3 Hz); poroelasticity; mechanobiochemical model (MSC differentiation, solute transport, cell migration) , CT-based geometry in COMSOL; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx $$\end{document} ≈ 65,000 tetrahedral elements (bone, callus, marrow, implant); axial dynamic loading at varied rates , Moderate frequencies (1–2 Hz) enhance healing and chondrocyte transport (up to 1700% volarly); 2 Hz with 3 mm gap optimizes indirect bone formation; high frequency (>3 Hz) detrimental , Experimental validation with 5 sawbone specimens under cyclic axial loading; close match between predicted and measured displacement/stiffness , Only axial loading considered; no local IFM measured; simplified early-stage biology; constant loading magnitude; no time-dependent callus properties , Liu et al. ( ) .

    Dissolution:

    Article Title: Computational models for predicting bone fracture healing: a review of modeling approaches, predictions, and emerging strategies
    Article Snippet: FEM , Octahedral shear strain; Interstitial fluid velocity; MSC diffusion , 2D axisymmetric model of titanium dental implant; ANSYS Mechanical APDL; Biot’s poroelasticity theory; cyclic loading ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_r$$\end{document} z r , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_h$$\end{document} z h ); 30-day simulation , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_h$$\end{document} z h + \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\textrm{avg}}$$\end{document} S avg led to bone formation; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\textrm{max}}$$\end{document} S max resulted in fibrous tissue; fluid velocity peaked near 0.1–12 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document} μ m/s (P1); slower stabilization in P2 and P3 , No validation , Linear elastic materials; 2D geometry; No directional influence of fluid flow on MSC migration , Irandoust and Müftü ( ) . .. FEM , Shear strain; Interstitial fluid velocity; MSC proliferation and migration , 3D poroelastic model; Abaqus 54 simulations; Random dispersion cell model; Scaffold with porosity 30–70%, stiffness 750–1250 MPa, dissolution 0–1%/iteration; Loading 1–2 MPa , 71% bone regeneration under baseline; High porosity enhances bone but reduces stiffness; High dissolution rates cause collapse; Medium rates optimize outcome; Young’s modulus more critical under high load , No experimental validation , Assumes uniform nutrient supply; excludes apoptosis; linear degradation kinetics , Byrne et al. ( ) . .. FEM , Hand grip dynamic loading (axial compression, 100 N at 1–2 Hz and >3 Hz); poroelasticity; mechanobiochemical model (MSC differentiation, solute transport, cell migration) , CT-based geometry in COMSOL; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx $$\end{document} ≈ 65,000 tetrahedral elements (bone, callus, marrow, implant); axial dynamic loading at varied rates , Moderate frequencies (1–2 Hz) enhance healing and chondrocyte transport (up to 1700% volarly); 2 Hz with 3 mm gap optimizes indirect bone formation; high frequency (>3 Hz) detrimental , Experimental validation with 5 sawbone specimens under cyclic axial loading; close match between predicted and measured displacement/stiffness , Only axial loading considered; no local IFM measured; simplified early-stage biology; constant loading magnitude; no time-dependent callus properties , Liu et al. ( ) .

    Biomarker Discovery:

    Article Title: Computational models for predicting bone fracture healing: a review of modeling approaches, predictions, and emerging strategies
    Article Snippet: FEM , Octahedral shear strain; Interstitial fluid velocity; MSC diffusion , 2D axisymmetric model of titanium dental implant; ANSYS Mechanical APDL; Biot’s poroelasticity theory; cyclic loading ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_r$$\end{document} z r , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_h$$\end{document} z h ); 30-day simulation , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_h$$\end{document} z h + \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\textrm{avg}}$$\end{document} S avg led to bone formation; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\textrm{max}}$$\end{document} S max resulted in fibrous tissue; fluid velocity peaked near 0.1–12 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document} μ m/s (P1); slower stabilization in P2 and P3 , No validation , Linear elastic materials; 2D geometry; No directional influence of fluid flow on MSC migration , Irandoust and Müftü ( ) . .. FEM , Shear strain; Interstitial fluid velocity; MSC proliferation and migration , 3D poroelastic model; Abaqus 54 simulations; Random dispersion cell model; Scaffold with porosity 30–70%, stiffness 750–1250 MPa, dissolution 0–1%/iteration; Loading 1–2 MPa , 71% bone regeneration under baseline; High porosity enhances bone but reduces stiffness; High dissolution rates cause collapse; Medium rates optimize outcome; Young’s modulus more critical under high load , No experimental validation , Assumes uniform nutrient supply; excludes apoptosis; linear degradation kinetics , Byrne et al. ( ) . .. FEM , Hand grip dynamic loading (axial compression, 100 N at 1–2 Hz and >3 Hz); poroelasticity; mechanobiochemical model (MSC differentiation, solute transport, cell migration) , CT-based geometry in COMSOL; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx $$\end{document} ≈ 65,000 tetrahedral elements (bone, callus, marrow, implant); axial dynamic loading at varied rates , Moderate frequencies (1–2 Hz) enhance healing and chondrocyte transport (up to 1700% volarly); 2 Hz with 3 mm gap optimizes indirect bone formation; high frequency (>3 Hz) detrimental , Experimental validation with 5 sawbone specimens under cyclic axial loading; close match between predicted and measured displacement/stiffness , Only axial loading considered; no local IFM measured; simplified early-stage biology; constant loading magnitude; no time-dependent callus properties , Liu et al. ( ) .

    Stripping Membranes:

    Article Title: Computational models for predicting bone fracture healing: a review of modeling approaches, predictions, and emerging strategies
    Article Snippet: FEM , Deviatoric strain, pore pressure, fluid velocity, cell diffusion , Axisymmetric 2D poroelastic model of ovine tibia with 3 mm fracture gap; ABAQUS 2379 elements; adaptive mechanobiological algorithm in MATLAB; 120 iterations; axial loading (300 N or biofeedback to 600 N) , All classic algorithms reproduced fracture healing stages; only Lacroix model predicted callus resorption; deviatoric strain alone sufficient for correct prediction; pore pressure and fluid velocity alone are insufficient , Qualitative comparison with previous results , No explicit modeling of mitosis, apoptosis, neovascularization; simplified cell migration; model time not physical , Isaksson et al. ( ) . .. 3D poroelastic FEM , Deviatoric strain, interstitial fluid velocity , Seven coupled nonlinear PDEs governing MSCs, fibroblasts, chondrocytes, and osteoblasts; mechanoregulation drives migration, proliferation, differentiation, apoptosis, and matrix production; implemented in ABAQUS , Reproduced spatially and temporally healing: periosteal intramembranous ossification, sequential fibrous and cartilaginous formation in gap, endochondral ossification; higher loads (400–500 N) delayed or prevented healing; periosteal stripping and cartilage impairment led to delayed bridging , Comparison with previous phenomenological model; qualitative agreement with experimental observations , No vascularization or growth factor modeling; binary cell thresholds; neglect of volumetric growth , Isaksson et al. ( ) . .. FEM , Volumetric strain; diffusing biological potential , 2D lattice-based FEM with rotational symmetry; implemented in MATLAB; mechanical solver via DUNE; 112 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document} × 120 grid, 1-day steps until 60 days; tissue maturation as modulus increase , Model reproduced periosteal ossification, cartilage bridging, and realistic callus progression; best results with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c=10$$\end{document} c = 10 (periosteal), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c=0.1$$\end{document} c = 0.1 (marrow), and thresholds \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_\textrm{Sb}=1.5\%$$\end{document} M Sb = 1.5 % , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_\textrm{Sc}=4\%$$\end{document} M Sc = 4 % , Pixel-wise comparison with averaged histological images from 32 sheep tibial osteotomies across 6 healing stages; mismatch \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx $$\end{document} ≈ 6.2% , No modeling of bone resorption/remodeling; assumes linear elasticity, rotational symmetry; lacks vascularization and signaling , Vetter et al. ( ) .

    Comparison:

    Article Title: Computational models for predicting bone fracture healing: a review of modeling approaches, predictions, and emerging strategies
    Article Snippet: FEM , Deviatoric strain, pore pressure, fluid velocity, cell diffusion , Axisymmetric 2D poroelastic model of ovine tibia with 3 mm fracture gap; ABAQUS 2379 elements; adaptive mechanobiological algorithm in MATLAB; 120 iterations; axial loading (300 N or biofeedback to 600 N) , All classic algorithms reproduced fracture healing stages; only Lacroix model predicted callus resorption; deviatoric strain alone sufficient for correct prediction; pore pressure and fluid velocity alone are insufficient , Qualitative comparison with previous results , No explicit modeling of mitosis, apoptosis, neovascularization; simplified cell migration; model time not physical , Isaksson et al. ( ) . .. 3D poroelastic FEM , Deviatoric strain, interstitial fluid velocity , Seven coupled nonlinear PDEs governing MSCs, fibroblasts, chondrocytes, and osteoblasts; mechanoregulation drives migration, proliferation, differentiation, apoptosis, and matrix production; implemented in ABAQUS , Reproduced spatially and temporally healing: periosteal intramembranous ossification, sequential fibrous and cartilaginous formation in gap, endochondral ossification; higher loads (400–500 N) delayed or prevented healing; periosteal stripping and cartilage impairment led to delayed bridging , Comparison with previous phenomenological model; qualitative agreement with experimental observations , No vascularization or growth factor modeling; binary cell thresholds; neglect of volumetric growth , Isaksson et al. ( ) . .. FEM , Volumetric strain; diffusing biological potential , 2D lattice-based FEM with rotational symmetry; implemented in MATLAB; mechanical solver via DUNE; 112 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document} × 120 grid, 1-day steps until 60 days; tissue maturation as modulus increase , Model reproduced periosteal ossification, cartilage bridging, and realistic callus progression; best results with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c=10$$\end{document} c = 10 (periosteal), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c=0.1$$\end{document} c = 0.1 (marrow), and thresholds \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_\textrm{Sb}=1.5\%$$\end{document} M Sb = 1.5 % , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_\textrm{Sc}=4\%$$\end{document} M Sc = 4 % , Pixel-wise comparison with averaged histological images from 32 sheep tibial osteotomies across 6 healing stages; mismatch \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx $$\end{document} ≈ 6.2% , No modeling of bone resorption/remodeling; assumes linear elasticity, rotational symmetry; lacks vascularization and signaling , Vetter et al. ( ) .

    Concentration Assay:

    Article Title: Instability Characteristics and Control of Steel Arch–Concrete Supported Deep Drifts under High In Situ Stress
    Article Snippet: .. A three-dimensional numerical model in ABAQUS is used to evaluate the original steel arch–concrete support system, showing that it mainly responds after deformation occurs, resulting in stress concentration at the arch feet, significant roof displacement, and local structural failure. ..



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    Abaqus Inc elastoplastic numerical analysis model
    Elastoplastic Numerical Analysis Model, supplied by Abaqus Inc, used in various techniques. Bioz Stars score: 86/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/elastoplastic+numerical+analysis+model/3d+model/pmc12901156-37-6-21
    Average 86 stars, based on 1 article reviews
    elastoplastic numerical analysis model - by Bioz Stars, 2026-11
    86/100 stars
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