arXiv subjects

Martin Cermak

Publications and source records attributed to Martin Cermak.

3 recordsLinked to original sources

arXiv2015

Subdifferential-based implicit return-mapping operators in Mohr-Coulomb plasticity

The paper is devoted to a constitutive solution, limit load analysis and Newton-like methods in elastoplastic problems containing the Mohr-Coulomb yield criterion. Within the constitutive problem, we introduce a self-contained derivation of the implicit return-mapping solution scheme using a recent subdifferential-based treatment. Unlike conventional techniques based on Koiter's rules, the presented scheme a priori detects a position of the unknown stress tensor on the yield surface even if the constitutive solution cannot be found in closed form. This fact eliminates blind guesswork from the scheme, enables to analyze properties of the constitutive operator, and simplifies construction of the consistent tangent operator which is important for the semismooth Newton method applied on the incremental boundary value elastoplastic problem. The incremental problem in Mohr-Coulomb plasticity is combined with the limit load analysis. Beside a conventional direct method of the incremental limit analysis, a recent indirect one is introduced and its advantages are described. The paper contains 2D and 3D numerical experiments on slope stability with publicly available Matlab implementations.

cs.CE↗

arXiv2015

An improved return-mapping scheme for nonsmooth yield surfaces: PART I - the Haigh-Westergaard coordinates

The paper is devoted to the numerical solution of elastoplastic constitutive initial value problems. An improved form of the implicit return-mapping scheme for nonsmooth yield surfaces is proposed that systematically builds on a subdifferential formulation of the flow rule. The main advantage of this approach is that the treatment of singular points, such as apices or edges at which the flow direction is multivalued involves only a uniquely defined set of non-linear equations, similarly to smooth yield surfaces. This paper (PART I) is focused on isotropic models containing: $a)$ yield surfaces with one or two apices (singular points) laying on the hydrostatic axis; $b)$ plastic pseudo-potentials that are independent of the Lode angle; $c)$ nonlinear isotropic hardening (optionally). It is shown that for some models the improved integration scheme also enables to a priori decide about a type of the return and investigate existence, uniqueness and semismoothness of discretized constitutive operators in implicit form. Further, the semismooth Newton method is introduced to solve incremental boundary-value problems. The paper also contains numerical examples related to slope stability with available Matlab implementation.

cs.CE↗

arXiv2012

Thin static charged dust Majumdar-Papapetrou shells with high symmetry in D >= 4

We present a systematical study of static D >= 4 space-times of high symmetry with the matter source being a thin charged dust hypersurface shell. The shell manifold is assumed to have the following structure S_(beta) X R^(D-2-beta), beta (in the interval <0,...,D-2>) is dimension of a sphere S_(beta). In case of (beta) = 0, we assume that there are two parallel hyper-plane shells instead of only one. The space-time has Majumdar-Papapetrou form and it inherits the symmetries of the shell manifold - it is invariant under both rotations of the S_(beta) and translations along R^(D-2-beta). We find a general solution to the Einstein-Maxwell equations with a given shell. Then, we examine some flat interior solutions with special attention paid to D = 4. A connection to D = 4 non-relativistic theory is pointed out. We also comment on a straightforward generalisation to the case of Kastor-Traschen space-time, i.e. adding a non-negative cosmological constant to the charged dust matter source.

gr-qc↗