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Staggered explicit-implicit time-discretization for elastodynamics with dissipative internal variables. (English) Zbl 1481.65189

Summary: An extension of the two-step staggered time discretization of linear elastodynamics in stress-velocity form to systems involving internal variables subjected to a possibly non-linear dissipative evolution is proposed. The original scheme is thus enhanced by another step for the internal variables which, in general, is implicit, although even this step might be explicit if no spatial gradients of the internal variables are involved. Using an abstract Banach-space formulation, a priori estimates and convergence are proved under a CFL condition. The developed three-step scheme finds applications in various problems of continuum mechanics at small strain. Here, we consider in particular plasticity, viscoelasticity (creep), diffusion in poroelastic media, and damage.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
65Z05 Applications to the sciences
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74R20 Anelastic fracture and damage
74S05 Finite element methods applied to problems in solid mechanics
76S05 Flows in porous media; filtration; seepage
76A10 Viscoelastic fluids
26A33 Fractional derivatives and integrals
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