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This work focuses on computational methods in continuum thermomechanics. The text is based on the author's lectures, which ensures a didactical and coherent buildup. The main emphasis is put on the presentation of ideas and qualitative considerations, illustrated by specific examples and applications. Conditions and explanations that are essential for the practical application of methods are discussed thoroughly.
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.
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Includes bibliographical references and index.
De Gruyter studies in mathematical physics