Nonlinear Continuum Mechanics of Solids

This book applies approaches of nonlinear continuum mechanics used to model fracture and failures in soft materials. Two physical observations underlie mathematical theories described in this book. First, the energy of molecular bonds is bounded and, consequently, the macroscopic strain energy must be bounded. Second, the broken bonds are diffused and, consequently, highly localized material sink takes place. The first observation allows describing material failure as the damage initiation. The second observation allows modeling cracks as damage localization and propagation.

This book illustrates the deep roots of the geometrically nonlinear kinematics of generalized continuum mechanics in differential geometry. Besides applications to first- order elasticity and elasto-plasticity an appreciation thereof is particularly illuminating for generalized models of continuum mechanics such as second-order (gradient-type) elasticity and elasto-plasticity.

This book applies approaches of nonlinear continuum mechanics used to model fracture and failures in soft materials. Two physical observations underlie mathematical theories described in this book. First, the energy of molecular bonds is bounded and, consequently, the macroscopic strain energy must be bounded. Second, the broken bonds are diffused and, consequently, highly localized material sink takes place. The first observation allows describing material failure as the damage initiation. The second observation allows modeling cracks as damage localization and propagation.

This book illustrates the deep roots of the geometrically nonlinear kinematics of generalized continuum mechanics in differential geometry. Besides applications to first- order elasticity and elasto-plasticity an appreciation thereof is particularly illuminating for generalized models of continuum mechanics such as second-order (gradient-type) elasticity and elasto-plasticity.

This book illustrates the deep roots of the geometrically nonlinear kinematics of generalized continuum mechanics in differential geometry. Besides applications to first- order elasticity and elasto-plasticity an appreciation thereof is particularly illuminating for generalized models of continuum mechanics such as second-order (gradient-type) elasticity and elasto-plasticity.

by Paul Steinmann (Author)

The book opens with a derivation of kinematically nonlinear 3-D continuum mechanics for solids.