deformation gradient tensorLie derivativeGauss theoremConservation of massmomentum and energyconstitutive equations1. Mathematics 2. Kinematics 3. The stress tensor 4. Introduction to material modeling 5. Ideal gas 6. Fluids 7. Elastic material models 8. Continuum mixture theory 9. Growth models 10. ...
In standard continuum mechanics theory (Malvern, 1969), the deformation gradient F is based on an underlying displacement field u: F=∂x∂X=∂(X+u)∂X=1+∂u∂X. As such, the nine components of F are not independent, but are actually interrelated because they are derived from ...
In continuum mechanics, R is called rotation tensor while U and v are referred to as the right and left stretch tensor, respectively.doi:10.1007/978-3-540-36047-6_8Mikhail ItskovSpringer International Publishing
摘要: In the paper, the coupling between the well-posedness of models for the continuum mechanics and thermodynamics is studied.关键词: continuum mechanics and thermodynamic elements deformation gradient polar decomposition - stretches and rotation strain measures velocity gradient and rate of deformation ...
The main goal of this work is to examine various aspects of `inelastic continuum mechanics': first, fundamental aspects of a general finite deformation theory based on a multiplicative decomposition of the deformation gradient with special emphasis on the incompatibility of the so-called intermediate ...
Introduction To Tensor Calculus and Continuum Mechanics 热度: An Introduction to Continuum Mechanics Morton E Gurtin 热度: Magnus An Introduction to Formal Logic (2006).pdf 热度: http:.gerebysiegel_01 LectureNotes: IntroductionintoContinuumMechanics ...
These transformations are merely geometric transformations obtained from the deformation gradient and, hence, are valid regardless of any constitutive equation employed for the solid. Then, advantage of this fact may be taken in order to simplify the form of constitutive equations and their numerical ...
We call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of...
Mechanics Problems#Governing Equations#Strain–displacement equations#Equations of motion#Constitutive equations#Boundary conditions#Solution of Two-Dimensional Problems#Plane strain problems#Plane stress problems#Airy stress function#Fluid Mechanics Problems#Governing Equations#Summary of Equations for Fluids#...
deformation gradientelastoplasitc decompositionkinematicspolar decompositionstrain measurementsSummary This chapter contains sections titled: Kinematics Mechanical Equilibrium Thermodynamicsdoi:10.1002/9783527631483.ch3Dr. Franz RotersMPI für Eisenforschung GmbH, Abt. Mikrostrukturphysik, Max-Planck-Str. 1, 40237 ...