A multiscale mechanobiological model of bone remodelling predicts site-specific bone loss in the femur during osteoporosis and mechanical disuse

We propose a multiscale mechanobiological model of bone remodelling to investigate the site-specific evolution of bone volume fraction across the midshaft of a femur. The model includes hormonal regulation and biochemical coupling of bone cell populations, the influence of the microstructure on bone turnover rate, and mechanical adaptation of the tissue. Both microscopic and tissue-scale stress/strain states of the tissue are calculated from macroscopic loads by a combination of beam theory and micromechanical homogenisation. This model is applied to simulate the spatio-temporal evolution of a human midshaft femur scan subjected to two deregulating circumstances: (i) osteoporosis and (ii) mechanical disuse. Both simulated deregulations led to endocortical bone loss, cortical wall thinning and expansion of the medullary cavity, in accordance with experimental findings. Our model suggests that these observations are attributable to a large extent to the influence of the microstructure on bone turnover rate. Mechanical adaptation is found to help preserve intracortical bone matrix near the periosteum. Moreover, it leads to non-uniform cortical wall thickness due to the asymmetry of macroscopic loads introduced by the bending moment. The effect of mechanical adaptation near the endosteum can be greatly affected by whether the mechanical stimulus includes stress concentration effects or not.Comment: 25 pages, 10 figure

Biomechanics and Remodelling for Design and Optimisation in Oral Prosthesis and Therapeutical Procedure

The purpose of dental prostheses is to restore the oral function for edentulous patients. Introducing any dental prosthesis into mouth will alter biomechanical status of the oral environment, consequently inducing bone remodelling. Despite the advantageous benefits brought by dental prostheses, the attendant clinical complications and challenges, such as pain, discomfort, tooth root resorption, and residual ridge reduction, remain to be addressed. This thesis aims to explore several different dental prostheses by understanding the biomechanics associated with the potential tissue responses and adaptation, and thereby applying the new knowledge gained from these studies to dental prosthetic design and optimisation. Within its biomechanics focus, this thesis is presented in three major clinical areas, namely prosthodontics, orthodontics and dental implantology. In prosthodontics, the oral mucosa plays a critical role in distributing occlusal forces a denture to the underlying bony structure, and its response is found in a complex, dynamic and nonlinear manner. It is discovered that interstitial fluid pressure in mocosa is the most important indicator to the potential resorption induced by prosthetic denture insertion, and based on this finding, patient-specific analysis is performed to investigate the effects caused by various types of dentures and prediction of the bone remodelling activities. In orthodontic treatments, a dynamic algorithm is developed to analyse and predict potential bone remodelling around the target tooth during orthodontic treatment, thereby providing a numerical approach for treatment planning. In dental implantology, a graded surface morphology of an implant is designed to improve osseointegration over that of a smooth uniform surface in both the short and long term. The graded surface can be optimised to achieve the best possible balance between the bone-implant contact and the peak Tresca stress for the specific clinical application need

고분자 소재의 소성 변형 모사를 위한 데이터 기반 멀티스케일 해석

학위논문(박사)--서울대학교 대학원 :공과대학 기계항공공학부(멀티스케일 기계설계전공),2020. 2. 조맹효.본 논문에서는 고분자 기반 소재의 탄성 및 소성 변형에 대한 미시적 변형 메커니즘의 정성적 규명과, 정량적 모사를 위한 머신 러닝 기반의 멀티스케일 해석 방법론을 제시한다. 제안된 해석 방법론은 미시적 소성 변형 거동에 대한 분자 수준에서의 일반적인 메커니즘 규명과, 고분자 소재의 비선형 기계적 거동에 대해 실험의 도움 없이 정량적 예측을 가능케 하며, 도출된 다수의 데이터를 기반으로 학습된 구성 방정식 모델링을 통해 거시적 구조물의 비선형 거동을 예측한다. 특히, 제안된 멀티스케일 해석 방법론은 다양한 고분자 소재 자체의 고유한 구조–물성간의 관계를 고려한 구성방정식의 모델링을 가능케 하며, 이는 기존의 범용적 소성 거동에 대한 모델링에서 소재의 변형 특성에 일대일 맞춤화된 해석 모델로의 확장이라는 점에 그 의의가 있다. 원자 및 분자 스케일에서의 미시 구조의 동적 모사가 가능한 분자동역학 전산해석을 활용하여, 열경화성 소재의 한 종류인 에폭시 소재의 미시적 변형 메커니즘을 규명하였다. 특히, 가교제의 분자 구조 특성이 경화된 에폭시 소재의 거시적 소성 변형에 미치는 영향을 이해하기 위하여, 분자동역학 모델에 압축 변형을 가한 후 하중을 제거하는 동안 에너지, 응력, 구조적 변화를 관찰하였으며, 그 결과, 소성 변형 영역에서 방향족 가교제의 벤젠 고리 주변의 비가역적 접힘 현상의 거시적 소성 변형률에 대한 기여를 규명하였다. 이러한 벤젠고리 근처 비가역적 접힘 거동은 반복 하중 하에서 점진적으로 축적되며, 지방족 가교제 기반 에폭시 소재의 거시적 스케일에서의 소성 변형률 진전보다 더욱 빠른 진전을 야기함을 밝혀내었다. 분자동역학 전산해석은 원자의 거동을 모사하기 위하여 매우 짧은 펨토 초 (fs) 단위의 타임 스텝을 사용하기 때문에, 실험적 시간 스케일의 분자 거동을 모사하는데 제한이 있다. 이로 인하여, 분자동역학 전산해석과 실험간의 기계적 거동 예측 측면에서 정량적 괴리가 발생하게 되는데, 이를 고려하기 위하여 본 연구에서는 분자 동역학 전산해석을 이용하여 준정적 상태의 응력–변형률 선도를 예측하는 두가지 방법론을 제시하였다. 첫번째 방법론은 고분자 소재의 항복 응력의 평가에 대한 시간과 온도의 동일성을 이용하여 항복 응력에 대한 마스터 선도를 순차적으로 구축하여 준정적 상태에서의 항복 응력을 예측한다. 두번째 방법론은 고분자 소재의 고전적 항복 이론을 이용하여 기계적 물성을 통해 준정적 상태에서의 항복 응력을 예측한다. 변형 속도와 온도에 대한 항복 응력의 비선형 특성을 반영하기 위하여 첫번째 방법론에서는 기준 온도 보다 높은 온도 하에서의 고분자 사슬의 운동 특성을 준정적 상태의 항복 거동 예측에 이용하였으며, 두번째 방법론에서는 Cooperative 모델과 내부 응력을 도입하여 준정적 항복 응력을 예측하는 마스터 선도를 구축하였다. 이후 완성된 방법론을 통하여 다양한 온도, 압력 및 재료의 미시 구조 특성을 반영하여 준정적 상태의 응력–변형률 선도를 도출하였다. 본 연구에서는 분자동역학 전산해석을 통해 예측된 준정적 상태의 기계적 물성 및 응력–변형률 선도를 토대로, 다양한 온도, 압력 등 물리적 상황과 고분자 소재의 미시구조 특성을 반영하여 다양한 조합 하중 하의 거시적 구조물의 소성 변형을 모사하기 위한 구성방정식을 모델링을 하였다. 에폭시의 구조 특성을 반영하기 위해 다양한 가교율 하에서 도출된 준정적 상태의 물성 및 응력–변형률 선도를 도출하였고, 3차원 홀 구조물의 소성 변형을 모사하기 위한 유한요소해석을 수행하였다. 그 결과, 가교율에 따라 홀 주변부의 소성 변형률의 진전 속도가 상이함을 확인하였다. 특히, 본 연구에서는 조합 하중에 따른 거시적 소성 변형을 모사하기 위해 기존의 고전적 항복 함수의 도입 대신, 3차원 응력 공간에서의 고려된 고분자 소재의 항복 표면의 최초 형상 및 변형이 진행됨에 따라 나타나는 항복 표면의 진전을 정밀하게 모사하기 위한 항복 함수를 머신 러닝 학습을 통하여 도출하는 방법론을 개발하였다. 이를 위해, 다양한 하중 방향에서의 에폭시 소재의 항복 데이터를 분자동역학 해석을 통해 도출하였으며, 변형 속도의 영향을 고려하기 위해 준정적 상태의 항복 표면을 예측하기 위한 방법론을 개발하였다. 도출된 항복 데이터를 기반으로 항복 함수의 수학적 표현을 도출하기 위하여 머신 러닝 학습 방법의 일종인 유전 알고리즘 (Genetic algorithm) 을 도입하였으며, 항복 함수의 필수적 특성을 학습에 반영시키기 위한 제한 조건을 부과하였다. 학습을 통해 도출된 데이터 기반 항복 함수를 통해 소성 변형 모사를 위한 구성방정식을 정식화 하였으며, 이의 성능을 유한요소해석을 통해 기존의 고전적 항복 함수와 비교 검증하였다. 본 연구에서 제시된 고분자 소재의 소성 변형 전산 해석을 위한 머신 러닝 기반 멀티스케일 해석 방법론은 분자 스케일 수준의 소성 변형 메커니즘의 규명과 더불어, 소재 고유의 다축 변형 항복 특성에 기인한 구성방정식의 모델링을 통해 거시적 기계 거동을 실험 없이 정밀하게 예측할 수 있다. 이는 기존의 물리적, 수학적 고찰을 통해 고안될 수 밖에 없던 소성 모델링을 재료 자체의 고유한 변형 특성에 초점을 맞춘 모델링으로의 확장이 가능함을 의미하며, 제안된 방법론의 다양한 소재에 대한 적용을 통해 라이브러리화 할 수 있음을 의미한다. 따라서 제안된 해석 방법론은 단일 고분자 소재뿐만 아니라 고분자 소재 기반 다양한 복합재의 기계적 거동에 대한 예측 요구되는 모든 산업에서 전방위적으로 사용될 것으로 기대된다.In this dissertation, a data-driven multiscale framework has been established based on molecular dynamics (MD) simulations, finite element (FE) analysis, and a machine learning (ML) technique; this framework was aimed at elucidating the multi-axial elasto-plastic deformations of polymer materials. The proposed data-driven multiscale approach enables the construction of a macroscopic continuum model that has been customized for achieving unique deformation characteristics of the considered material, which are attributed to distinct microscopic structural features. In particular, the macroscopic continuum model is established based on the data-driven yield function, which is formulated by numerous multi-axial stress-strain behaviors that are systematically derived from MD simulations. Furthermore, to conduct multiscale analysis without any experimental support, certain methods have been developed to derive quasi-static stress-strains that overcome the timescale limitations of classical MD simulations. The main focus of this thesis is divided into three parts: qualitative analysis of microscopic deformation mechanisms of polymer materials, development of methods to overcome timescale limitations of MD simulations, and ML-based constitutive modeling through symbolic data mining. With regard to the characterizations of microscopic deformation mechanisms, the nature of the inelastic-deformation characteristics of highly crosslinked epoxy polymers is examined at the microscopic level with respect to the differences in the structural network topologies. It is examined by microscopic deformation simulations that the structural differences that arise from different types of curing agents (aliphatic and aromatic) cause the different irreversible folding behaviors of a local epoxy network. Following the qualitative analysis on the deformation mechanisms, a calibration of the timescale difference between MD simulations and experiments is necessitated for achieving the quantitative analysis on plastic deformations; this is because the stress evaluated by MD simulations is not comparable to that of the experiments due to its extremely high strain rate. Two kinds of methods are developed to derive the quasi-static stress-strain profiles. The first approach is to use a 0 K solution of Argon theory to estimate internal stress and adopt the cooperative model to represent the nonlinear nature of yield stress on strain rate and temperature. The second approach is to predict the quasi-static yields by temperature accelerations by using time and temperature equivalence. A method to derive a hardening law under different strain rates is also established and demonstrated based on the yield stress-strain rate relation. Based on deformation mechanisms and strain rate calibration methods, a multiscale framework is completed by developing a 3–dimensional constitutive model of the epoxy polymer from the data-driven yield function, which is formulated by a number of multi-axial yield data adopting a machine learning technique. The primary focus here is to confirm that the customized yield functions of various materials can be derived only from the yield data set without any prior knowledge on the primary stress invariants and functional structures; herein, the yield data set represents the unique multi-axial hardening behavior. To validate the proposed method for yield function mining, the development history of the classical yield functions, such as von-Mises, Drucker-Prager, Tresca, Mohr-Coulomb, and paraboloidal yield functions are reproduced from the proposed approach simultaneously; this successfully characterizes the influence of the dispersion of the yield data set. The proposed framework facilitates the understanding of intrinsic deformation features of polymer materials; further, it enables the construction of the data-driven plasticity model that is distinct from the conventional yield models. The proposed methodologies can be extended to a broad class of polymer materials by considering a variety of factors associated with nanoscale physics; in particular, the methods can address the problems that cannot be solved with the existing models or governing equations.1. Introduction 1 1.1. Necessity of a data-driven multiscale framework for the plasticity of polymers 1 1.2. Microscopic deformation mechanisms of amorphous polymers 3 1.3. Full-atomic molecular dynamics and timescale limitations 6 1.4. Classical yielding theories for polymer plasticity 9 1.5. Development of yield criterion for multi-axial deformations 11 1.6. Outline of the thesis 15 2. Atomistic model constructions and deformation simulations 18 2.1. All-atom MD modeling and derivation of physical properties 18 2.2. Deformation simulations 24 2.2.1. Uniaxial deformation simulations 24 2.2.2. Uniaxial loading-unloading simulations 26 2.2.3. Cyclic deformation simulations 28 2.2.4. Multi-axial deformation simulations 30 3. Qualitative analysis on the elasto-plastic deformations of epoxy polymers 41 3.1. Influence of the molecular structure of curing agent on plastic deformations 41 3.1.1. Microscopic deformation mechanisms 41 3.1.2. Dihedral energy analysis 55 3.1.3. Strain-rate dependency of plastic dihedral-angle behaviors 59 3.2. Influence of the molecular structure of curing agent on ratcheting behaviors 61 3.2.1. Ratcheting behaviors and stiffness evolutions 61 3.2.2. Microscopic structural analysis 66 3.2.3. Relationship between epoxy structure and ratcheting behavior 70 3.3. Summary 74 4. Methods to overcome timescale limitations of classical molecular dynamics 98 4.1. Prediction of quasi-static constitutive laws by temperature-accelerated method 98 4.1.1. Theoretical background 98 4.1.2. Investigation on deformation characteristics and physical properties 100 4.1.3. Scheme for prediction of quasi-static solutions 104 4.2. Prediction of quasi-static constitutive laws by classical yielding theory 116 4.2.1. Prediction of quasi-static yields and construction of master curve 116 4.2.2. Effects of temperature, pressure, and crosslinking density 122 4.2.3. Construction of quasi-static constitutive laws 125 4.3. Summary 127 5. Classical yield function based constitutive modeling for multi-axial plastic deformations 143 5.1. Constitutive modeling based on paraboloidal yield function 143 5.2. Finite element analysis: one-element mesh validations 147 5.3. Finite element analysis: open-hole deformation tests 150 5.4. Summary 151 6. Machine learning based data-driven constitutive modeling for multi-axial plastic deformations 155 6.1. Reproduction of classical yield functions by symbolic regression 155 6.1.1. Symbolic regression 155 6.1.2. Symbolic data mining of classical yield functions 157 6.2. Development of data-driven yield function 163 6.2.1. MD characterizations on evolution of yield surface 163 6.2.2. Construction of data-driven yield function 166 6.2.3. Validation of the mined yield function 169 6.3. Constitutive modeling based on data-driven yield function 170 6.4. Finite element analysis: one-element mesh validations 173 6.5. Characteristics of data-driven yield function 174 6.6. Summary 179 7. Conclusions and recommendations 192 References 195 Abstract 207Docto

Constitutive modeling for isotropic materials (HOST)

The results of the first year of work on a program to validate unified constitutive models for isotropic materials utilized in high temperature regions of gas turbine engines and to demonstrate their usefulness in computing stress-strain-time-temperature histories in complex three-dimensional structural components. The unified theories combine all inelastic strain-rate components in a single term avoiding, for example, treating plasticity and creep as separate response phenomena. An extensive review of existing unified theories is given and numerical methods for integrating these stiff time-temperature-dependent constitutive equations are discussed. Two particular models, those developed by Bodner and Partom and by Walker, were selected for more detailed development and evaluation against experimental tensile, creep and cyclic strain tests on specimens of a cast nickel base alloy, B19000+Hf. Initial results comparing computed and test results for tensile and cyclic straining for temperature from ambient to 982 C and strain rates from 10(exp-7) 10(exp-3) s(exp-1) are given. Some preliminary date correlations are presented also for highly non-proportional biaxial loading which demonstrate an increase in biaxial cyclic hardening rate over uniaxial or proportional loading conditions. Initial work has begun on the implementation of both constitutive models in the MARC finite element computer code

Design of dimensionally-stable laminated somposites subjected to hygro-thermo-mechanical loading by stochastic optimization methods

Thesis (Doctoral)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2011Includes bibliographical references (leaves: 147-150)Text in English; Abstract: Turkish and Englishxvii, 153 leavesThe materials used in aerospace structures such as antenna, satellites and missiles should have such features as low density, high stiffness, low coefficients of thermal and moisture expansions simultaneously. Fiber reinforced polymer composite materials can satisfy these requirements with an appropriate stacking sequence using optimization methods and hence dimensionally stable composites are obtained. In this thesis, two different materials carbon/epoxy and E-glass/epoxy composites are considered. Both materials have been used for optimization, stress and failure analysis. However, only for E-glass/epoxy, experimental studies have been performed including determination of stiffness, strength characteristics, Poisson's ratio, fiber volume fraction, glass transition temperature (Tg) and coefficient of thermal expansion (CTE). The objective of optimization part is to design the stacking sequence of the carbon/epoxy and E-glass/epoxy laminated composites having low CTE and high elastic moduli. In design process, multi-objective genetic algorithm optimization of the carbon/epoxy composite plates are verified by single-objective optimization approach by using the Genetic Algorithm (GA), Generalized Pattern Search (GPS) and Simulated Annealing (SA) algorithms. MATLAB Optimization Toolbox is used to obtain Pareto-optimal designs and global optimum points for different model problems. Stress and strain distributions are presented through the thickness of the laminates subjected to mechanical, thermal, and hygral loadings. Stress analysis results showed that effect of mechanical loads dominate to hygral and thermal loads. All the stochastic search methods carried out in the present thesis have produced almost the same results with different stacking sequences

Analytical Solutions and Multiscale Creep Analysis of Functionally Graded Cylindrical Pressure Vessels

This study deals with the time-dependent creep analysis of functionally graded thick-cylinders under various thermal and mechanical boundary conditions. Firstly, exact thermoelastic stress, and iterative creep solutions for a heat generating and rotating cylindrical vessel made of functionally graded thermal and mechanical properties are proposed. Equations of equilibrium, compatibility, stress-strain, and strain-displacement relations are solved to obtain closed-form initial stress and strain solutions. It is found that material gradient indices have significant influences on thermoelastic stress profiles. For creep analysis, Norton’s model is incorporated into rate forms of the above-mentioned equations to obtain time-dependent stress and strain results using an iterative method. Validity of our solutions are at first verified using finite element analysis, and numerical results found in the recent literature have been enhanced. Investigation of effects of material gradients reveals that radial variation of density and creep coefficient have significant effects on strains histories, while Young’s modulus and thermal property distributions only influence stress redistribution at an early stage of creep deformation. Next, a more realistic model of introducing microscale creep effects into a macroscopic modeling is employed to investigate the creep behavior of functionally graded hollow cylinders. Finite element (FE) simulations are employed to evaluate the position-dependent parameters associated with creep constitutive law at the microscale. A macroscopic FE model solves the non-linear boundary value problem to determine the time-varying creep stresses and strains. The framework proposed is capable of predicting the creep response of functionally graded pressure vessels based on the constitutive behavior of the creeping matrix, and volume fraction profile. Effective creep properties have been computed using three different micromechanical models and the homogenized creep response and its effect on the macroscopic behavior are compared. Considering the computational expenses associated with the large 3D finite element models, the simple 2D axisymmetric model is able to closely capture the creep behavior in such multiscale methods. Finally, a multi-objective particle swarm optimization algorithm is implemented to minimize the initial stress and final creep strain of functionally graded cylinder subjected to mechanical and thermal loads

Determination of suitable values for parameters governing B-spline based evolutionary structural optimisation using the boundary element method

The basic evolutionary structural optimisation concept (ESO) has been developed for several years. Recently, the first ESO algorithm based on the boundary element method (BEM) has been presented. In this thesis, this algorithm is used for the 2D shape optimisation. The aim is to develop a greater understanding of the role of certain governing parameters that drive the optimisation using this algorithm, and to make recommendations as to appropriate values of these parameters that give rise to good optimal solutions most efficiently. Two problems, a short cantilever beam and a fillet, are selected as test cases in this work. By using a wide range of numerical tests, the performance of the optimisation has been evaluated using a variety of methods including mean performance analysis and multi-objective optimisation approaches using Pareto curves and weighted sums. Recommendations are made as to appropriate values of these parameters that give rise to good optimal solutions most efficiently. Sensitivity analysis is another important method in engineering design. In this work a new algorithm to undertake a sensitivity analysis has been developed and used in a small number of investigations for boundary element structural optimisation process. ESO is selected when computational efficiency is thought the most important consideration, since it can reach the optimum in fewer iterations and lower run-time compared with sensitivity analysis in structural optimisation

Microstructure modeling and crystal plasticity parameter identification for predicting the cyclic mechanical behavior of polycrystalline metals

Computational homogenization permits to capture the influence of the microstructure on the cyclic mechanical behavior of polycrystalline metals. In this work we investigate methods to compute Laguerre tessellations as computational cells of polycrystalline microstructures, propose a new method to assign crystallographic orientations to the Laguerre cells and use Bayesian optimization to find suitable parameters for the underlying micromechanical model from macroscopic experiments

A backward pre-stressing algorithm for efficient finite element implementation of in vivo material and geometrical parameters into fibril-reinforced mixture models of articular cartilage.

Classical continuum mechanics has been widely used for implementation of the material models of articular cartilage (AC) mainly with the aid of the finite element (FE) method, which, in many cases, considers the stress-free configuration as the initial configuration. On the contrary, the AC experimental tests typically begin with the pre-stressed state of both material and geometrical properties. Indeed, imposing the initial pre-stress onto AC models with the in vivo values as the initial state would result in nonphysiologically expansion of the FE mesh due to the soft nature of AC. This change in the model configuration can also affect the material behavior kinematically in the mixture models of cartilage due to the intrinsic compressibility of the tissue. Although several different fixed-point backward algorithms, as the most straightforward pre-stressing methods, have already been developed to incorporate these initial conditions into FE models iteratively, such methods focused merely on the geometrical parameters, and they omitted the material variations of the anisotropic mixture models of AC. To address this issue, we propose an efficient algorithm generalizing the backward schemes to restore stress-free conditions by optimizing both the involving variables, and we hypothesize that it can affect the results considerably. To this end, a comparative simulation was implemented on an advanced and validated multiphasic model by the new and conventional algorithms. The results are in support of the hypothesis, as in our illustrative general AC model, the material parameters experienced a maximum error of 16% comparing to the initial in vivo data when the older algorithm was employed, and it led to a maximum variation of 44% in the recorded stresses comparing to the results of the new method. We conclude that our methodology enhanced the model fidelity, and it is applicable in most of the existing FE solvers for future mixture studies with accurate stress distributions