Irreversibility and alternate minimization in phase field fracture: a viscosity approach
| Autor: | Stefano Almi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
Work (thermodynamics) Field (physics) Applied Mathematics General Mathematics Mathematical analysis Phase (waves) General Physics and Astronomy Phase field models Monotonic function 35Q74 49J45 74R05 74R10 Nonlinear system Mathematics - Analysis of PDEs Phase field Convergence (routing) Fracture (geology) FOS: Mathematics Fracture mechanics Alternate minimization Vanishing viscosity Analysis of PDEs (math.AP) |
| DOI: | 10.1007/s00033-020-01357-x |
| Popis: | This work is devoted to the analysis of convergence of an alternate (staggered) minimization algorithm in the framework of phase field models of fracture. The energy of the system is characterized by a nonlinear splitting of tensile and compressive strains, featuring non-interpenetration of the fracture lips. The alternating scheme is coupled with an $$L^{2}$$ L 2 -penalization in the phase field variable, driven by a viscous parameter $$\delta >0$$ δ > 0 , and with an irreversibility constraint, forcing the monotonicity of the phase field only w.r.t. time, but not along the whole iterative minimization. We show first the convergence of such a scheme to a viscous evolution for $$\delta >0$$ δ > 0 and then consider the vanishing viscosity limit $$\delta \rightarrow 0$$ δ → 0 . |
| Databáze: | OpenAIRE |
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