Variational Continuum Multiphase Poroelasticity PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Variational Continuum Multiphase Poroelasticity PDF full book. Access full book title Variational Continuum Multiphase Poroelasticity by Roberto Serpieri. Download full books in PDF and EPUB format.
Author: Roberto Serpieri
Publisher: Springer
ISBN: 9811034524
Category : Science
Languages : en
Pages : 207
Get Book Here
Book Description
This book collects the theoretical derivation of a recently presented general variational macroscopic continuum theory of multiphase poroelasticity (VMTPM), together with its applications to consolidation and stress partitioning problems of interest in several applicative engineering contexts, such as in geomechanics and biomechanics. The theory is derived based on a purely-variational deduction, rooted in the least-Action principle, by considering a minimal set of kinematic descriptors. The treatment herein considered keeps a specific focus on the derivation of most general medium-independent governing equations. It is shown that VMTPM recovers paradigms of consolidated use in multiphase poroelasticity such as Terzaghi's stress partitioning principle and Biot's equations for wave propagation. In particular, the variational treatment permits the derivation of a general medium-independent stress partitioning law, and the proposed variational theory predicts that the external stress, the fluid pressure, and the stress tensor work-associated with the macroscopic strain of the solid phase are partitioned according to a relation which, from a formal point of view, turns out to be strictly compliant with Terzaghi's law, irrespective of the microstructural and constitutive features of a given medium. Moreover, it is shown that some experimental observations on saturated sandstones, generally considered as proof of deviations from Terzaghi's law, are ordinarily predicted by VMTPM. As a peculiar prediction of VMTPM, the book shows that the phenomenon of compression-induced liquefaction experimentally observed in cohesionless mixtures can be obtained as a natural implication of this theory by a purely rational deduction. A characterization of the phenomenon of crack closure in fractured media is also inferred in terms of macroscopic strain and stress paths. Altogether the results reported in this monograph exemplify the capability of VMTPM to describe and predict a large class of linear and nonlinear mechanical behaviors observed in two-phase saturated materials.
Author: Roberto Serpieri
Publisher: Springer
ISBN: 9811034524
Category : Science
Languages : en
Pages : 207
Get Book Here
Book Description
This book collects the theoretical derivation of a recently presented general variational macroscopic continuum theory of multiphase poroelasticity (VMTPM), together with its applications to consolidation and stress partitioning problems of interest in several applicative engineering contexts, such as in geomechanics and biomechanics. The theory is derived based on a purely-variational deduction, rooted in the least-Action principle, by considering a minimal set of kinematic descriptors. The treatment herein considered keeps a specific focus on the derivation of most general medium-independent governing equations. It is shown that VMTPM recovers paradigms of consolidated use in multiphase poroelasticity such as Terzaghi's stress partitioning principle and Biot's equations for wave propagation. In particular, the variational treatment permits the derivation of a general medium-independent stress partitioning law, and the proposed variational theory predicts that the external stress, the fluid pressure, and the stress tensor work-associated with the macroscopic strain of the solid phase are partitioned according to a relation which, from a formal point of view, turns out to be strictly compliant with Terzaghi's law, irrespective of the microstructural and constitutive features of a given medium. Moreover, it is shown that some experimental observations on saturated sandstones, generally considered as proof of deviations from Terzaghi's law, are ordinarily predicted by VMTPM. As a peculiar prediction of VMTPM, the book shows that the phenomenon of compression-induced liquefaction experimentally observed in cohesionless mixtures can be obtained as a natural implication of this theory by a purely rational deduction. A characterization of the phenomenon of crack closure in fractured media is also inferred in terms of macroscopic strain and stress paths. Altogether the results reported in this monograph exemplify the capability of VMTPM to describe and predict a large class of linear and nonlinear mechanical behaviors observed in two-phase saturated materials.
Author: Holm Altenbach
Publisher: Springer
ISBN: 3319705636
Category : Science
Languages : en
Pages : 463
Get Book Here
Book Description
This book presents a collection of contributions on the advanced mechanics of materials and mechanics of structures approaches, written in honor of Professor Kienzler. It covers various topics related to constitutive models for advanced materials, recent developments in mechanics of configuration forces, as well as new approaches to the efficient modeling and analysis of engineering structures.
Author: Mario Di Paola
Publisher: Materials Research Forum LLC
ISBN: 1644902435
Category : Technology & Engineering
Languages : en
Pages : 746
Get Book Here
Book Description
The book presents the proceedings of the XXV National Congress of the Italian Association of Theoretical and Applied Mechanics (Palermo, September 2022). The topics cover theoretical, computational, experimental and technical-applicative aspects. Chapters: Fluid Mechanics, Solid Mechanics, Structural Mechanics, Mechanics of Machine, Computational Mechanics, Biomechanics, Masonry Modelling and Analysis, Dynamical Systems in Civil and Mechanical Structures, Control and Experimental Dynamics, Mechanical Modelling of Metamaterials and Periodic Structures, Novel Stochastic Dynamics, Signal Processing Techniques for Civil Engineering Applications, Vibration-based Monitoring and Dynamic Identification of Historic Constructions, Modeling and Analysis of Nanocomposites and Small-Scale Structures, Gradient Flows in Mechanics and Continuum Physics, Multibody Systems Vibration Analysis, Mechanics of Renewable Energy Systems, Mathematical Modeling and Experimental Techniques for Quantification and Prediction of Fluid Dynamic Noise, and Advanced Process Mechanics. Keywords: Fluid Mechanics, Solid Mechanics, Structural Mechanics, Mechanics of Machine, Computational Mechanics, Biomechanics, Masonry Modelling and Analysis, Dynamical Systems in Civil and Mechanical Structures, Control and Experimental Dynamics, Mechanical Modelling of Metamaterials and Periodic Structures, Novel Stochastic Dynamics, Signal Processing Techniques for Civil Engineering Applications, Vibration-based Monitoring and Dynamic Identification of Historic Constructions, Modeling and Analysis of Nanocomposites and Small-Scale Structures, Gradient Flows in Mechanics and Continuum Physics, Multibody Systems Vibration Analysis, Mechanics of Renewable Energy Systems, Mathematical Modeling and Experimental Techniques for Quantification and Prediction of Fluid Dynamic Noise, and Advanced Process Mechanics.
Author: V. Komkov
Publisher: Springer Science & Business Media
ISBN: 9789027726391
Category : Mathematics
Languages : en
Pages : 292
Get Book Here
Book Description
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Author: Holm Altenbach
Publisher: Springer
ISBN: 3319317210
Category : Science
Languages : en
Pages : 456
Get Book Here
Book Description
This volume is devoted to an actual topic which is the focus world-wide of various research groups. It contains contributions describing the material behavior on different scales, new existence and uniqueness theorems, the formulation of constitutive equations for advanced materials. The main emphasis of the contributions is directed on the following items - Modelling and simulation of natural and artificial materials with significant microstructure, - Generalized continua as a result of multi-scale models, - Multi-field actions on materials resulting in generalized material models, - Theories including higher gradients, and - Comparison with discrete modelling approaches
Author: Victor Berdichevsky
Publisher: Springer Science & Business Media
ISBN: 3540884696
Category : Science
Languages : en
Pages : 433
Get Book Here
Book Description
The book reviews the two features of the variational approach: its use as a universal tool to describe physical phenomena and as a source for qualitative and quantitative methods of studying particular problems. Berdichevsky’s work differs from other books on the subject in focusing mostly on the physical origin of variational principles as well as establishing their interrelations. For example, the Gibbs principles appear as a consequence of the Einstein formula for thermodynamic fluctuations rather than as the first principles of the theory of thermodynamic equilibrium. Mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for the direct study of variational problems. In addition, a thorough account of variational principles discovered in various branches of continuum mechanics is given. This book, the second volume, describes how the variational approach can be applied to constructing models of continuum media, such as the theory of elastic plates; shells and beams; shallow water theory; heterogeneous mixtures; granular materials; and turbulence. It goes on to apply the variational approach to asymptotical analysis of problems with small parameters, such as the derivation of the theory of elastic plates, shells and beams from three-dimensional elasticity theory; and the basics of homogenization theory. A theory of stochastic variational problems is considered in detail too, along with applications to the homogenization of continua with random microstructures.
Author: Francesco dell'Isola
Publisher: Springer Science & Business Media
ISBN: 3709109833
Category : Technology & Engineering
Languages : en
Pages : 363
Get Book Here
Book Description
F. dell'Isola, L. Placidi: Variational principles are a powerful tool also for formulating field theories. - F. dell'Isola, P. Seppecher, A. Madeo: Beyond Euler-Cauchy Continua. The structure of contact actions in N-th gradient generalized continua: a generalization of the Cauchy tetrahedron argument. - B. Bourdin, G.A. Francfort: Fracture. - S. Gavrilyuk: Multiphase flow modeling via Hamilton's principle. - V. L. Berdichevsky: Introduction to stochastic variational problems. - A. Carcaterra: New concepts in damping generation and control: theoretical formulation and industrial applications. - F. dell'Isola, P. Seppecher, A. Madeo: Fluid shock wave generation at solid-material discontinuity surfaces in porous media. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest to scientists and engineers. In this book three fundamental aspects of the variational formulation of mechanics will be presented: physical, mathematical and applicative ones. The first aspect concerns the investigation of the nature of real physical problems with the aim of finding the best variational formulation suitable to those problems. The second aspect is the study of the well-posedeness of those mathematical problems which need to be solved in order to draw previsions from the formulated models. And the third aspect is related to the direct application of variational analysis to solve real engineering problems.
Author: Younane N. Abousleiman
Publisher: CRC Press
ISBN: 9780415889506
Category : Technology & Engineering
Languages : en
Pages : 858
Get Book Here
Book Description
These proceedings represent the latest advances in the mechanics of porous materials, known as poromechanics. The porous materials considered are solids containing voids that are impregnated with fluid. The focus is on the mechanical interactions of the inhomogeneous solid with the single- or multi-phase fluid under the loading of mechanical force, fluid pressure, thermal, chemical, and magnetic fields. The response time can be in static, diffusional, and dynamic ranges. The length scale can start from nano, to micro, macro, and up to field scales. Its application covers many branches of science and engineering, including geophysics, geomechanics, composite materials, biomechanics, acoustics, seismicity, civil, mechanical, environmental, and petroleum engineering. The approaches taken include analytical, computational, and experimental. To honor the pioneering contributions of Maurice A. Biot (1905-1985) to poromechanics, the Biot Conference on Poromechanics was convened for the first time in Louvain-la-Neuve, Belgium in 1998. The success of the first conference led to the 2nd Biot Conference held in Grenoble, France in 2002. To celebrate the centennial birthday of Biot (May 25, 2005), the 3rd Biot Conference on Poromechanics was held at the University of Oklahoma, Norman, Oklahoma, U.S.A., on May 24-27, 2005.
Author: V. Komkov
Publisher: Springer
ISBN: 9789027721570
Category : Mathematics
Languages : en
Pages : 400
Get Book Here
Book Description
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Author:
Publisher:
ISBN:
Category : Continuum mechanics
Languages : en
Pages : 0
Get Book Here
Book Description
The world of smart materials has experienced a dramatic revolution in the last decades. Electro Active and Magneto Active Materials are some of the most iconic of these, among which, dielectric and magnetostrictive elastomers are becoming extremely popular due to their outstanding actuation capabilities, and in lesser degree, to their energy harvesting capabilities. A clear example illustrating these extraordinary capabilities has been reported in the experimental literature, which has shown unprecedented extreme electrically induced deformations for the most representative dielectric elastomer, namely the acrylic elastomer VHB 4910. This thesis is focused on the development of well-posed constitutive models for nonlinear electro-elasticity in scenarios characterised by extreme deformations and extreme electric fields. This fundamental objective represents the underlying ingredient for the novel variational and computational frameworks developed hereby in the context of electro-elasticity. Very remarkably, the similarity between the equations in both electro-elasticity and magneto-elasticity, enables the variational and computational frameworks developed to be extended to the latter scenario, characterised by magnetomechanical interactions. Despite the enormous interest of the experimental and computational scientific community, the definition of suitable constitutive models is still at its early stages for both electro and magneto active materials. In the more specic context of elasticity, considerable effort has been devoted to the denition of polyconvex energy functionals, which entail the most widely accepted constitutive restriction, namely the ellipticity or Legendre-Hadamard condition. This condition, strongly related to the material stability of the constitutive equations, ensures the well-posedness of the governing equations. An extension of the ellipticity condition to the context of nonlinear electro-elasticity and hence, magneto-elasticity, is proposed in this work, ensuring the well-posedness of the equations for the entire range of deformations and electric or magnetic fields. It is important to emphasise that in this work, the extension of the ellipticity condition to the field of electro-elasticity is exclusively based on material stability considerations. The energy functional encoding the constitutive response of the electro active material is defined according to a novel convex multi-variable representation in terms of an extended set of arguments which ensures material stability. The extended set of arguments, including those characterising the concept of polyconvexity in the more specic scenario of nonlinear elasticity, is further enriched with additional electromechanical entities. Unfortunately, proof of sequential weak lower semicontinuity of the proposed definition of multi-variable convexity is not provided in this work. This condition, and the additional requirement of appropriate coercivity conditions on the energy functional, would ensure the existence of minimisers. Nevertheless, although of extreme relevance and scientific interest, this topic is not in the scope of the thesis and could be the objective of further research ...
