Numerical Continuum Mechanics.
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| Author / Creator: | Kukudzhanov, V. N. |
|---|---|
| Imprint: | Berlin : De Gruyter, 2012. |
| Description: | 1 online resource (447 pages) |
| Language: | English |
| Series: | De Gruyter Studies in Mathematical Physics ; v. 15 De Gruyter studies in mathematical physics. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11175782 |
Table of Contents:
- Preface; I Basic equations of continuum mechanics; 1 Basic equations of continuous media; 1.1 Methods of describing motion of continuous media; 1.1.1 Coordinate systems and methods of describing motion of continuous media; 1.1.2 Eulerian description; 1.1.3 Lagrangian description; 1.1.4 Differentiation of bases; 1.1.5 Description of deformations and rates of deformation of a continuous medium; 1.2 Conservation laws. Integral and differential forms; 1.2.1 Integral form of conservation laws; 1.2.2 Differential form of conservation laws; 1.2.3 Conservation laws at solution discontinuities.
- 1.2.4 Conclusions1.3 Thermodynamics; 1.3.1 First law of thermodynamics; 1.3.2 Second law of thermodynamics; 1.3.3 Conclusions; 1.4 Constitutive equations; 1.4.1 General form of constitutive equations. Internal variables; 1.4.2 Equations of viscous compressible heat-conducting gases; 1.4.3 Thermoelastic isotropic media; 1.4.4 Combined media; 1.4.5 Rigid-plastic media with translationally isotropic hardening; 1.4.6 Elastoplastic model; 1.5 Theory of plastic flow. Theory of internal variables; 1.5.1 Statement of the problem. Equations of an elastoplastic medium.
- 1.5.2 Equations of an elastoviscoplastic medium1.6 Experimental determination of constitutive relations under dynamic loading; 1.6.1 Experimental results and experimentally obtained constitutive equations; 1.6.2 Substantiation of elastoviscoplastic equations on the basis of dislocation theory; 1.7 Principle of virtual displacements. Weak solutions to equations of motion; 1.7.1 Principles of virtual displacements and velocities; 1.7.2 Weak formulation of the problem of continuum mechanics; 1.8 Variational principles of continuum mechanics; 1.8.1 Lagrange's variational principle.
- 1.8.2 Hamilton's variational principle1.8.3 Castigliano's variational principle; 1.8.4 General variational principle for solving continuum mechanics problems; 1.8.5 Estimation of solution error; 1.9 Kinematics of continuous media. Finite deformations; 1.9.1 Description of the motion of solids at large deformations; 1.9.2 Motion: deformation and rotation; 1.9.3 Strain measure. Green-Lagrange and Euler-Almansi strain tensors; 1.9.4 Deformation of area and volume elements; 1.9.5 Transformations: initial, reference, and intermediate configurations.
- 1.9.6 Differentiation of tensors. Rate of deformation measures1.10 Stress measures; 1.10.1 Current configuration. Cauchy stress tensor; 1.10.2 Current and initial configurations. The first and second Piola-Kirchhoff stress tensors; 1.10.3 Measures of the rate of change of stress tensors; 1.11 Variational principles for finite deformations; 1.11.1 Principle of virtual work; 1.11.2 Statement of the principle in increments; 1.12 Constitutive equations of plasticity under finite deformations; 1.12.1 Multiplicative decomposition. Deformation gradients; 1.12.2 Material description.