Continua with microstructure modelled by the geometry of higher-order contact

In the paper, the Finslerian-geometry-oriented model of the continuum with microstructure is formulated within the frame of Newtonian-Eshelbian contin uum mechanics, based on the information characterizing a structure-dependen t evolution of state variables. In this approach, position- and direction-d ependent deformation and strain measures are used to describe the motion of the continuum with microstructure at the macro- and microlevel. The variat ional arguments for a Lagrangian functional defined on the Finslerian bundl e are used to derive dynamic balance laws, boundary and transversality cond itions for macro- and microstresses of deformational and configurational ty pe. The dissipation inequality for the thermo-inelastic deformation process es is formulated by the sufficiency condition of Weierstrass type for the a ction integral. The presented geometric technique is illustrated in the fol lowing examples. The damage tensor, identified with a measure of reduction of load carrying area elements caused by the development of microcracks or microvoids. is defined on the tangent bundle using the lifting technique. T he macro-micro constitutive equations and the associated phenomenological c onstitutive relations for the thermo-inelastic processes are derived in ter ms of the free energy functional and a dissipation potential. A strain-indu ced crack propagation criterion, defined by the difference between the stra in energy release rate and the rate of the surface energy of the crack, is formulated for the kinking of cracks. (C) 2001 Elsevier Science Ltd. All ri ghts reserved.