Paul Steinmann is a full professor at FAU Erlangen-Nuernberg, where he is active since 2007, and co-director of the GCEC in Glasgow. He is a member of GACM, GAMM and EUROMECH and was member of the managing board of ECCOMAS, member of the IACM general council, and president of the DEKOMECH (German Committee for Mechanics), the adhering organisation to IUTAM. He supervises several doctoral and postdoctoral researchers in the fields of material modelling, multi-scale methods, multi-physics problems, non-standard continua, configurational-failure-fracture mechanics, biomechanics as well as general developments in finite element and discretisation methods.

• 1 Introduction.-  2 Kinematics in Bulk Volumes.-  3 Kinematics on Dimensionally Reduced Smooth Manifolds.-  4 Kinematics at Singular Sets.-  5 Generic Balances.-  6 Kinematical 'Balances'*.-  7 Mechanical Balances.-  8 Consequences of Mechanical Balances.-  9 Virtual Work.-  10 Variational Setting.-  11 Thermo-Dynamical Balances.- 12 Consequences of Thermo-Dynamical Balances.- 13 Computational Setting.

Paul Steinmann is a full professor at FAU Erlangen-Nuernberg, where he is active since 2007, and co-director of the GCEC in Glasgow. He is a member of GACM, GAMM and EUROMECH and was member of the managing board of ECCOMAS, member of the IACM general council, and president of the DEKOMECH (German Committee for Mechanics), the adhering organisation to IUTAM. He supervises several doctoral and postdoctoral researchers in the fields of material modelling, multi-scale methods, multi-physics problems, non-standard continua, configurational-failure-fracture mechanics, biomechanics as well as general developments in finite element and discretisation methods.

• 1 Introduction.-  2 Kinematics in Bulk Volumes.-  3 Kinematics on Dimensionally Reduced Smooth Manifolds.-  4 Kinematics at Singular Sets.-  5 Generic Balances.-  6 Kinematical 'Balances'*.-  7 Mechanical Balances.-  8 Consequences of Mechanical Balances.-  9 Virtual Work.-  10 Variational Setting.-  11 Thermo-Dynamical Balances.- 12 Consequences of Thermo-Dynamical Balances.- 13 Computational Setting.