Gerhard A. Holzapfel – författare

Nonlinear Solid Mechanics a Continuum Approach for Engineering Gerhard A. Holzapfel Graz University of Technology, Austria With a modern, comprehensive approach directed towards computational mechanics, this book covers a unique combination of subjects at present unavailable in any other text. It includes vital information on 'variational principles' constituting the cornerstone of the finite element method. In fact this is the only method by which Nonlinear Solid Mechanics is utilized in engineering practice. The book opens with a fundamental chapter on vectors and tensors. The following chapters are based on nonlinear continuum mechanics - an inevitable prerequisite for computational mechanicians. In addition, continuum field theory (applied to a representative sample of hyperelastic materials currently used in nonlinear computations such as incompressible and compressible materials) is presented, as are transversely isotropic materials, composite materials, viscoelastic materials and hyperelastic materials with isotropic damage. Another central chapter is devoted to the thermodynamics of materials, covering both finite thermoelasticity and finite thermoviscoelasticity. Also included are:* an up-to-date list of almost 300 references and a comprehensive index* useful examples and exercises for the student* selected topics of statistical and continuum thermodynamics.Furthermore, the principle of virtual work (in both the material and spatial descriptions) is compared with two and three-field variational principles particularly designed to capture kinematic constraints such as incompressibility. All of the features combined result in an essential text for final year undergraduates, postgraduates and researchers in mechanical, civil and aerospace engineering and applied maths and physics.

Model Validation and Uncertainty Quantification in Biomechanics: From Soft Biological Tissue to Blood Flow provides a comprehensive overview of the latest technology in biomechanical modeling and analysis. Part I presents the foundational principles of modeling primary biomechanical systems, including the intricate workings of the cardiovascular system. This section also provides invaluable insights into essential topics such as sensitivity analysis, uncertainty quantification, machine learning, and surrogate modeling. In Part 2, the book transitions into an in-depth examination of the current state-of-the-art in model validation techniques across a diverse array of biomechanical disciplines, including the latest advancements and best practices. Part 3 introduces current and innovative approaches for quantifying uncertainties inherent in biomechanical modeling. Chapters range from established methodologies to emerging techniques, providing a comprehensive overview of the various strategies employed in addressing uncertainty in biomechanical studies. Finally, in Part 4, the book concludes with a focus on cutting-edge methods, specifically spotlighting the utilization of machine learning and surrogate modeling for both model validation and uncertainty quantification. Through real-world applications and case studies, this book provides an in-depth understanding of how these advanced techniques are reshaping the landscape of biomechanics research.Provides an overview of the basics of uncertainty quantification, sensitivity analysis, machine learning, and surrogate modelingFocuses on the underlying biomechanics and computational modeling of the cardiovascular systemIntroduces current and novel methods for quantifying uncertainties in various biomechanical applications

Model Validation and Uncertainty Quantification in Biomechanics: Sources and Methods of Uncertainty and Variability Analysis addresses the increasing need to incorporate uncertainty and variability into computational biomechanics. As biomechanical modeling becomes more central to clinical decision-making, deterministic approaches are no longer sufficient to describe biological complexity. This reference provides a systematic treatment of uncertainty quantification, enabling more reliable, patient-specific models in cardiovascular and soft tissue applications. The volume is structured into four main sections. It begins with probabilistic fundamentals and sensitivity analysis, establishing core principles for uncertainty-aware modeling. It then explores sources of uncertainty, including vascular modeling, imaging reconstruction, MRI, ultrasound elastography, and biological variability such as sex differences. The third section focuses on computational methods such as multi-fidelity modeling and Bayesian parameter identification. The final section presents practical applications in vascular systems, cardiac mechanics, and diagnostic techniques, emphasizing clinically relevant case studies.Model Validation and Uncertainty Quantification in Biomechanics: Sources and Methods of Uncertainty and Variability Analysis provides researchers and engineers with rigorous tools to assess model reliability and variability. By combining foundational theory with applied methodologies, it supports the development of robust, predictive biomechanical simulations, advancing translational research and precision medicine in healthcare engineering.Provides comprehensive foundations of uncertainty quantification and probabilistic modeling in biomechanicsExamines major sources of variability in imaging, vascular modeling, and biological systemsPresents advanced methods including Bayesian inference and multi-fidelity modeling techniques

The book is written by leading experts in the field presenting an up-to-date view of the subject matter in a didactically sound manner. It presents a review of the current knowledge of the behaviour of soft tissues in the cardiovascular system under mechanical loads, and the importance of constitutive laws in understanding the underlying mechanics is highlighted. Cells are also described together with arteries, tendons and ligaments, heart, and other biological tissues of current research interest in biomechanics. This includes experimental, continuum mechanical and computational perspectives, with the emphasis on nonlinear behaviour, and the simulation of mechanical procedures such as balloon angioplasty.

The book presents a state-of-the-art overview of biomechanical and mechanobiological modeling and simulation of soft biological tissues. Seven well-known scientists working in that particular field discuss topics such as biomolecules, networks and cells as well as failure, multi-scale, agent-based, bio-chemo-mechanical and finite element models appropriate for computational analysis. Applications include arteries, the heart, vascular stents and valve implants as well as adipose, brain, collagenous and engineered tissues.The mechanics of the whole cell and sub-cellular components as well as the extracellular matrix structure and mechanotransduction are described. In particular, the formation and remodeling of stress fibers, cytoskeletal contractility, cell adhesion and the mechanical regulation of fibroblast migration in healing myocardial infarcts are discussed. The essential ingredients of continuum mechanics are provided. Constitutive models of fiber-reinforced materials with anemphasis on arterial walls and the myocardium are discussed and the important influence of residual stresses on material response emphasized. The mechanics and function of the heart, the brain and adipose tissues are discussed as well. Particular attention is focused on microstructural and multi-scale modeling, finite element implementation and simulation of cells and tissues.

The book presents a state-of-the-art overview of biomechanical and mechanobiological modeling and simulation of soft biological tissues. Seven well-known scientists working in that particular field discuss topics such as biomolecules, networks and cells as well as failure, multi-scale, agent-based, bio-chemo-mechanical and finite element models appropriate for computational analysis. Applications include arteries, the heart, vascular stents and valve implants as well as adipose, brain, collagenous and engineered tissues.The mechanics of the whole cell and sub-cellular components as well as the extracellular matrix structure and mechanotransduction are described. In particular, the formation and remodeling of stress fibers, cytoskeletal contractility, cell adhesion and the mechanical regulation of fibroblast migration in healing myocardial infarcts are discussed. The essential ingredients of continuum mechanics are provided. Constitutive models of fiber-reinforced materials with anemphasis on arterial walls and the myocardium are discussed and the important influence of residual stresses on material response emphasized. The mechanics and function of the heart, the brain and adipose tissues are discussed as well. Particular attention is focused on microstructural and multi-scale modeling, finite element implementation and simulation of cells and tissues.

The book presents a state-of-the-art overview of biomechanical and mechanobiological modeling and simulation of soft biological tissues. Seven well-known scientists working in that particular field discuss topics such as biomolecules, networks and cells as well as failure, multi-scale, agent-based, bio-chemo-mechanical and finite element models appropriate for computational analysis. Applications include arteries, the heart, vascular stents and valve implants as well as adipose, brain, collagenous and engineered tissues.The mechanics of the whole cell and sub-cellular components as well as the extracellular matrix structure and mechanotransduction are described. In particular, the formation and remodeling of stress fibers, cytoskeletal contractility, cell adhesion and the mechanical regulation of fibroblast migration in healing myocardial infarcts are discussed. The essential ingredients of continuum mechanics are provided. Constitutive models of fiber-reinforced materials with anemphasis on arterial walls and the myocardium are discussed and the important influence of residual stresses on material response emphasized. The mechanics and function of the heart, the brain and adipose tissues are discussed as well. Particular attention is focused on microstructural and multi-scale modeling, finite element implementation and simulation of cells and tissues.

This book contains a collection of papers that were presented at the IUTAM Symposium on Mechanics of Biological Tissue, which was held in Graz, A- tria,fromJune27toJuly2,2004.ThesettingofGrazwasveryappropriatefor the symposium since it is the city where such illustriousscientistsasJohannes Kepler, Ernst Mach, Ludwig Boltzmann, Erwin Schr. odinger and Otto Kratky spent parts of their lives, while the cultural life of Graz provided ample - portunity for complementing the scienti?c proceedings. Graz has an historic centre, which is one of the best preserved old town centres in Europe, and which was added to the UNESCO world cultural heritage list in 1999. Thesymposiumbroughttogether96participantsfromuniversities,research centres and clinics in 19 countries. There were 42 oral presentations, incl- ing 7 keynote lectures, and 15 poster presentations. The keynote lectures were given by P.B. Canham (University of Western Ontario, Canada), S.C. Cowin (City University of New York, USA), K. Hayashi (Osaka University, Japan), J.D. Humphrey (Texas A&M University, USA), P.J. Hunter (University of Auckland, New Zealand), R.S. Lakes (University of Wisconsin, USA), and P.D.Richardson (Brown University, USA).

This book contains a collection of papers that were presented at the IUTAM Symposium on Mechanics of Biological Tissue, which was held in Graz, A- tria,fromJune27toJuly2,2004.ThesettingofGrazwasveryappropriatefor the symposium since it is the city where such illustriousscientistsasJohannes Kepler, Ernst Mach, Ludwig Boltzmann, Erwin Schr. odinger and Otto Kratky spent parts of their lives, while the cultural life of Graz provided ample - portunity for complementing the scienti?c proceedings. Graz has an historic centre, which is one of the best preserved old town centres in Europe, and which was added to the UNESCO world cultural heritage list in 1999. Thesymposiumbroughttogether96participantsfromuniversities,research centres and clinics in 19 countries. There were 42 oral presentations, incl- ing 7 keynote lectures, and 15 poster presentations. The keynote lectures were given by P.B. Canham (University of Western Ontario, Canada), S.C. Cowin (City University of New York, USA), K. Hayashi (Osaka University, Japan), J.D. Humphrey (Texas A&M University, USA), P.J. Hunter (University of Auckland, New Zealand), R.S. Lakes (University of Wisconsin, USA), and P.D.Richardson (Brown University, USA).

The book is written by leading experts in the field presenting an up-to-date view of the subject matter in a didactically sound manner. It presents a review of the current knowledge of the behaviour of soft tissues in the cardiovascular system under mechanical loads, and the importance of constitutive laws in understanding the underlying mechanics is highlighted. Cells are also described together with arteries, tendons and ligaments, heart, and other biological tissues of current research interest in biomechanics. This includes experimental, continuum mechanical and computational perspectives, with the emphasis on nonlinear behaviour, and the simulation of mechanical procedures such as balloon angioplasty.

This book contains a collection of papers that were presented at the IUTAM Symposiumon “Computer Models in Biomechanics: From Nano to Macro” held at Stanford University, California, USA, from August 29 to September 2, 2011.It contains state-of-the-art papers on:- Protein and Cell Mechanics: coarse-grained model for unfolded proteins, collagen-proteoglycan structural interactions in the cornea, simulations of cell behavior on substrates- Muscle Mechanics: modeling approaches for Ca2+–regulated smooth muscle contraction, smooth muscle modeling using continuum thermodynamical frameworks, cross-bridge model describing the mechanoenergetics of actomyosin interaction, multiscale skeletal muscle modeling- Cardiovascular Mechanics: multiscale modeling of arterial adaptations by incorporating molecular mechanisms, cardiovascular tissue damage, dissection properties of aortic aneurysms, intracranial aneurysms, electromechanics of the heart, hemodynamic alterations associated with arterial remodeling following aortic coarctation, patient-specific surgery planning for the Fontan procedure- Multiphasic Models: solutes in hydrated biological tissues, reformulation of mixture theory-based poroelasticity for interstitial tissue growth, tumor therapies of brain tissue, remodeling of microcirculation in liver lobes, reactions, mass transport and mechanics of tumor growth, water transport modeling in the brain, crack modeling of swelling porous media- Morphogenesis, Biological Tissues and Organs: mechanisms of brain morphogenesis, micromechanical modeling of anterior cruciate ligaments, mechanical characterization of the human liver, in vivo validation of predictive models for bone remodeling and mechanobiology, bridging scales in respiratory mechanics

This book contains a collection of papers that were presented at the IUTAM Symposiumon “Computer Models in Biomechanics: From Nano to Macro” held at Stanford University, California, USA, from August 29 to September 2, 2011.It contains state-of-the-art papers on:- Protein and Cell Mechanics: coarse-grained model for unfolded proteins, collagen-proteoglycan structural interactions in the cornea, simulations of cell behavior on substrates- Muscle Mechanics: modeling approaches for Ca2+–regulated smooth muscle contraction, smooth muscle modeling using continuum thermodynamical frameworks, cross-bridge model describing the mechanoenergetics of actomyosin interaction, multiscale skeletal muscle modeling- Cardiovascular Mechanics: multiscale modeling of arterial adaptations by incorporating molecular mechanisms, cardiovascular tissue damage, dissection properties of aortic aneurysms, intracranial aneurysms, electromechanics of the heart, hemodynamic alterations associated with arterial remodeling following aortic coarctation, patient-specific surgery planning for the Fontan procedure- Multiphasic Models: solutes in hydrated biological tissues, reformulation of mixture theory-based poroelasticity for interstitial tissue growth, tumor therapies of brain tissue, remodeling of microcirculation in liver lobes, reactions, mass transport and mechanics of tumor growth, water transport modeling in the brain, crack modeling of swelling porous media- Morphogenesis, Biological Tissues and Organs: mechanisms of brain morphogenesis, micromechanical modeling of anterior cruciate ligaments, mechanical characterization of the human liver, in vivo validation of predictive models for bone remodeling and mechanobiology, bridging scales in respiratory mechanics

This volume covers aspects of multiscale modeling of the mechanics and mechanobiology of soft biological tissues. The individual contributions focus on the constitutive modeling from the micro to the macro level in addition to computational modeling and simulation.It consists of peer-reviewed papers written by leading international authorities and will serve as a major state-of-the-art source of reference for the next few years. It includes both review articles and original articles. Previously published in the Journal of Elasticity, Volume 129, Issue 1-2, December 2017.