Mechanics of Deformable Solids: Linear, Nonlinear, Analytical and Computational Aspects

1. Basic mechanics.- 2. Variational formulations, work and energy theorems.- 3. Theory of beams (strength of materials).- 4. Torsion of beams.- 5. Theory of thin plates.- 6. Bending of thin plates in polar coordinates.- 7. Two-dimensional problems in Cartesian coordinates.- 8. Two-dimensional problems in polar coordinates.- 9. Thermo-elasticity.- 10. Elastic stability.- 11. Theory of thin shells.- 12. Elasto-plasticity.- 13. Elasto-viscoplasticity.- 14. Nonlinear continuum mechanics.- 15. Nonlinear elasticity.- 16. Finite-strain elasto-plasticity.- 17. Cyclic plasticity.- 18. Damage mechanics.- 19. Strain localization.- 20. Micro-mechanics of materials.- A. Cylindrical coordinates.- B. Cardan’s formulae.- C. Matrices for the representation of second- and fourth-order tensors.- C.1 Storage.- C.2 Change of coordinates.- D. Zero-stress constraints.- D.2 General small-strain models.- D.3 General finite-strain models.

Three subjects of major interest are contained in this textbook: Linear elasticity, mechanics of structures in linear isotropic elasticity, and nonlinear mechanics including computational algorithms. Engineering and mathematics are in a reasonable balance: After the simplest possible, intuitive approach follows the mathematical formulation and analysis. Computational methods occupy a good portion of the book. There are several worked out problems in each chapter and additional exercises at the end of the book. Very often, mathematical expressions are given in more than one notation. The book is intended primarily for students and practising engineers in mechanical and civil engineering. Most of them will be faced with problems of advanced materials and should have a correct understanding of the basic ideas even if they use software to solve them. Students or experts from applied mathematics, materials science and other related fields will also find it useful.

Book for advanced students and engineers Based on lectures at the Catholic University of Louvain Unique is the treatment of the three subjects: - theory of linear elasticity - theory of structures - nonlinear mechanics Includes supplementary material: sn.pub/extras