Finite Elasticity Theory

David J. Steigmann is Professor of Mechanical Engineering at University of California at Berkeley. He has published extensively within his research interests, including finite elasticity, thin shells, the plasticity theory, and tensile structures. He sits on the editorial boards of ZAMP, Journal of Elasticity, Journal of the Mechanics of Materials and Structures, among others.

There are many textbooks and treatises on finite elasticity, but Finite Elasticity Theory by David J. Steigmann is special. First, it is at the same time concise and deep, without any dogmatism. Second, it achieves the difficult balance between scientific rigor and clear presentation. Moreover, and probably the most important aspect of this book, there is a subtle interplay between mathematical and physical rigor, two aspects that are rarely seen together in such works.

• 1: Concept of an elastic material 2: Observers and invariance 3: Mechanical power and hyperelasticity 4: Material symmetry 5: Fiber symmetry 6: Stress response in the presence of local constraints on the deformation 7: Some boundary-value problems for uniform isotropic incompressible materials 8: Some examples involving uniform, compressible isotropic materials 9: Material stability, strong ellipticity and smoothness of equilibria 10: Membrane theory 11: Stability and the energy criterion 12: Linearized theory, the second variation and bifurcation of equilibria 13: Elements of plasticity theory