Introduction to Nonlinear Thermomechanics: Theory and Finite-Element Solutions

ISBN-13: 9781447119081 / Angielski / Miękka / 2011 / 187 str.

Andrzej Sluzalec

Opis

Professor Sluzalec is a well-known and respected authority in the field of Computational Mechanics, and his personal experience forms the basis of the book. Introduction to Nonlinear Thermomechanics provides both an elementary and advanced exposition of nonlinear thermomechanics. The scope includes theoretical aspects and their rational application in thermal problems, thermo-elastoplasticity, finite strain thermoplasticity and coupled thermoplasticity. The use of numerical techniques for the solution of problems and implementation of basic theory is included. Engineers, technicians, researchers, and advanced students will find the book an extremely useful compendium of solutions to problems. The scope is such that it would also be an effective teaching aid.

Spis treści

I. Basic Considerations and Notions.- 1 A State of Stress and Strain.- 1.1 Stress.- 1.2 Strain.- 2 Finite Strains.- 2.1 Finite Strain Tensor in Material and Spatial Descriptions.- 2.2 Deformation Rate Tensor.- 2.3 Stress Measures.- 2.4 Final Remarks.- 3 Temperature.- 3.1 Heat Conduction.- 3.2 Heat Convection.- 3.3 Heat Radiation.- 3.4 Temperature Field in a Heat-Conducting Body.- 3.5 Navier-Stokes Equation.- 4 Thermodynamical Considerations.- 4.1 Thermomechanical Process.- 4.2 Formulation of the Constitutive Law.- II. Fundamentals of Elasticity and Plasticity Theory.- 5 Stress-Strain Curve.- 6 Elasticity.- 7 Plasticity.- 7.1 Idealization of Tension Test.- 7.2 Ideal Plasticity Theories.- 7.2.1 Yield Criteria.- 7.2.2 Hencky-Iljuszyn Deformation Theory.- 7.2.3 Plastic Flow Theory.- 7.2.4 Comparison of Flow Theory and Deformation Theory.- 7.2.5 Ideal Plasticity Theory for Finite Deformations.- 8 Work-Hardening Equation.- 8.1 Drucker Postulate.- 8.1.1 Stability of Plastic Material in the Drucker Sense..- 8.1.2 Associated Plastic Flow.- 8.2 Yield Surfaces for Work-Hardening Materials.- 8.2.1 Experimental Results.- 8.2.2 Isotropic Hardening.- 8.2.3 Kinematic Hardening.- III. Small Strain Thermo-Elasto-Plasticity.- 9 Equations for Thermo-Elasto-Plasticity.- 9.1 Isotropic Hardening.- 9.2 Kinematic Hardening.- 9.3 Elasto-Visco-Plasticity.- 10 Finite-Element Solution.- 10.1 Finite-Element Solution of Heat Flow Equations.- 10.1.1 Weighted Residual Method.- 10.1.2 Variational Formulation.- 10.1.3 Time Integration Schemes for Nonlinear Heat Conduction.- 10.1.4 Stability Analysis.- 10.2 Finite-Element Solution of Navier-Stokes Equations.- 10.3 Modelling of the Phase Change Process.- 10.4 Examples of Thermal Problems.- 10.4.1 Heat Flow with Phase Change..- 10.4.2 Navier-Stokes Equations.- 10.5 Finite-Element Solution of Thermo-Elasto-Plastic Problems.- 10.5.1 Variational Formulation.- 10.5.2 Integration.- 10.5.3 Methods of Iterative Accumulation.- 10.5.4 Tangent Stiffness Matrices.- 10.6 Examples of Thermo-Elasto-Plastic Analyses.- IV. Creep.- 11 Theoretical Background to Creep.- 11.1 Creep and Relaxation Tests.- 11.2 Creep at Constant Uniaxial Stress.- 11.2.1 Time Functions.- 11.2.2 Stress Functions.- 11.2.3 Temperature Functions.- 11.2.4 Stress and Time Functions.- 11.3 Creep Theories with Time-Dependent Uniaxial Stress.- 11.3.1 Total Strain Theory.- 11.3.2 Time Hardening Theory.- 11.3.3 Strain Hardening Theory.- 11.3.4 Heredity Theory.- 11.4 Creep Theories in Complex Stress State.- 11.4.1 Creep Theory of Deformational Type.- 11.4.2 Flow Theories and Creep Potential.- 11.4.3 Generalization of Strain Hardening Theory.- 12 Creep Rupture.- 12.1 Experimental Studies.- 12.2 Ductile Rupture Theories.- 12.3 Brittle Rupture Theories.- 12.4 Rupture of Mixed Type.- 13 Constitutive Equations for Thermo-Elasto-Plastic and Creep Analysis.- 14 Finite-Element Formulation.- 14.1 Matrix Equation for Thermo-Elasto-Plastic and Creep Problems.- 14.2 Remarks on Solution Procedures.- 14.3 Examples.- V. Finite Strains.- 15 Finite Strain Models.- 16 Constitutive Equations.- 16.1 Non-Isothermal Plastic Flow.- 16.2 Multiplicative Decomposition of the Deformation Gradient.- 17 Finite-Element Formulation for Non-Isothermal Plastic Flow.- 17.1 Total Lagrange Formulation.- 17.2 Updated Lagrange and Updated Lagrange-Jaumann Formulations.- 17.3 Updated Lagrange-Hughes Formulation.- VI. Coupled Thermo-Plasticity.- 18 Equations of Coupled Thermo-Plasticity.- 18.1 Heat Transfer Equations.- 18.2 Finite-Element Formulation for the Heat Flow Equation.- 18.3 Internal Dissipation function.- 18.4 Stress-Strain Relations in Coupled Thermo-Plasticity.- 18.4.1 Thermo-Elasto-Plastic Model Based on Additive Decomposition of Strain.- 18.4.2 Thermo-Rigid Plastic and Thermo-Rigid Visco-Plastic Models.- 18.4.3 Remarks on Other Models.- 18.5 Coupled Thermomechanical Algorithm.- 18.6 Examples.- References and Further Reading.

O autorze

The author is a well-known and respected authority in the field of Computational Mechanics and his personal experience forms the basis of the book.