Limit analysis problem and its penalization

The contribution is focused on solution of the kinematic limit analysis problem within associative perfect plasticity. It is a constrained minimization problem describing a collapse state of an investigated body. Two different penalization methods are presented and interpreted as the truncation method and the indirect incremental method, respectively. It is shown that both methods are meaningful even within the continuous setting of the problem. Convergence with respect to penalty and discretization parameters is discussed. The indirect incremental method can be simply implemented within current elastoplastic codes

Estimation of EDZ zones in great depths by elastic-plastic models

summary:This contribution is devoted to modeling damage zones caused by the excavation of tunnels and boreholes (EDZ zones) in connection with the issue of deep storage of spent nuclear fuel in crystalline rocks. In particular, elastic-plastic models with Mohr-Coulomb or Hoek-Brown yield criteria are considered. Selected details of the numerical solution to the corresponding problems are mentioned. Possibilities of elastic and elastic-plastic approaches are illustrated by a numerical example

Limit analysis and inf-sup conditions on convex cones

This paper is focused on analysis and reliable computations of limit loads in perfect plasticity. We recapitulate our recent results arising from a continuous setting of the so-called limit analysis problem. This problem is interpreted as a convex optimization subject to conic constraints. A related inf-sup condition on a convex cone is introduced and its importance for theoretical and numerical purposes is explained. Further, we introduce a penalization method for solving the kinematic limit analysis problem. The penalized problem may be solved by standard finite elements due to available convergence analysis using a simple local mesh adaptivity. This solution concept improves the simplest incremental method of limit analysis based on a load parametrization of an elastic-perfectly plastic problem

Robust algorithms for limit load and shear strength reduction methods

This paper is focused on continuation techniques and Newton-like methods suggested for numerical determination of safety factors within stability assessment. Especially, we are interested in the stability of slopes and related limit load and shear strength reduction methods. We build on computational plasticity and the finite element method, but we mainly work on an algebraic level to be the topic understandable for broader class of scientists and our algorithms more transparent. The presented algorithms are based on the associated plasticity to be more robust. For non-associated models, we use Davis-type approximations enabling us to apply the associated approach. A particular attention is devoted to the Mohr-Coulomb elastic-perfectly plastic constitutive problem. On this example, we explain some important features of the presented methods which are beyond the algebraic settings of the problems. We also summarize the Mohr-Coulomb constitutive solution and some implementation details

Limit analysis and inf-sup conditions on convex cones

This paper is focused on analysis and reliable computations of limit loads in perfect plasticity. We recapitulate our recent results arising from a continuous setting of the so-called limit analysis problem. This problem is interpreted as a convex optimization subject to conic constraints. A related inf-sup condition on a convex cone is introduced and its importance for theoretical and numerical purposes is explained. Further, we introduce a penalization method for solving the kinematic limit analysis problem. The penalized problem may be solved by standard finite elements due to available convergence analysis using a simple local mesh adaptivity. This solution concept improves the simplest incremental method of limit analysis based on a load parametrization of an elastic-perfectly plastic problem

Numerical solution of perfect plastic problems with contact: part II - numerical realization

This contribution is a continuation of our contribution denoted as PART I, where the discretized contact problem for elasto-perfectly plastic bodies was studied and suitable numerical methods were introduced. In particular, frictionless contact boundary conditions and Hencky’s material model with the von Mises criterion are considered. Here we describe some implementation details and present several numerical examples

Numerical solution of perfect plastic problems with contact: part I - theory and numerical methods

The contribution deals with a static case of discretized elasto-perfectly plastic problems obeying Hencky’s law in combination with frictionless contact boundary conditions. The main interest is focused on the analysis of the formulation in terms of displacements, limit load analysis and related numerical methods. This covers the study of: i) the dependence of the solution set on the loading parameter ζ, ii) relation between ζ and the parameter α representing the work of external forces, iii) loading process controlled by ζ and by α, iv) numerical methods for solving problems with prescribed value of ζ and α

RTIN-based strategies for local mesh refinement

summary:Longest-edge bisection algorithms are often used for local mesh refinements within the finite element method in 2D. In this paper, we discuss and describe their conforming variant. A particular attention is devoted to the so-called Right-Triangulated Irregular Network (RTIN) based on isosceles right triangles and its tranformation to more general domains. We suggest to combine RTIN with a balanced quadrant tree (QuadTree) decomposition. This combination does not produce hanging nodes within the mesh refinements and could be extended to tetrahedral meshes in 3D

How to simplify return-mapping algorithms in computational plasticity: part 2 –implementation details and experiments

The paper is devoted to numerical solution of a small-strain quasi-static elastoplastic problem. It is considered an isotropic model containing the Drucker-Prager yield criterion, a non-associative flow rule and a nonlinear hardening law. The problem is discretized by the implicit Euler and finite element methods. It is used an improved return-mapping scheme introduced in ”PART 1” and the semismooth Newton method. Algorithmic solution is described and efficiency of the improved scheme is illustrated on numerical examples