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An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids. (English) Zbl 0783.73024
Summary: Key qualitative features of solutions exhibiting strong discontinuities in rate-independent inelastic solids are identified and exploited in the design of a new class of finite element approximations. The analysis shows that the softening law must be re-interpreted in a distributional sense for the continuum solutions to make mathematical sense and provides a precise physical interpretation to the softening modulus. These results are verified by numerical simulations employing a regularized discontinuous finite element method which circumvent the strong mesh- dependence exhibited by conventional methods, without resorting to viscosity or introducing additional ad-hoc parameters. The analysis is extended to a new class of anisotropic rate-independent damage models for brittle materials.

MSC:
74C99 Plastic materials, materials of stress-rate and internal-variable type
74S05 Finite element methods applied to problems in solid mechanics
74R99 Fracture and damage
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