2015/05/05 by Tomáš Roubı́ček, Roubíček, Tomáš, Jan Valdman +1
Engineering · Materials Science · #35K87 #49N10 #65K15 #74A30 74C05 74R20 #86A17 #90C53 #Composite Material Mechanics #Elasticity and Material Modeling #FOS: Mathematics #Nonlocal and gradient elasticity in micro/nano structures #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1505.01018
openalex publication_date 2015/05/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The quasistatic, Prandtl-Reuss perfect plasticity at small strains is combined with a gradient, reversible (i.e. admitting healing) damage which influences both the elastic moduli and the yield stress. Existence of weak solutions of the resulted system of variational inequalities is proved by a suitable fractional-step discretisation in time with guaranteed numericalstability and convergence. After finite-element approximation, this scheme is computationally implemented and illustrative 2-dimensional simulations are performed. The model allows e.g. for application in geophysical modelling of re-occurring rupture of lithospheric faults. Resulted incremental problems are solved in MATLAB by quasi-Newton method to resolve elastoplasticity component of the solution while damage component is obtained by solution of a quadratic programming problem.