Application of continuum laws in discontinuity analysis based on a regularised displacement jump

The application of continuum constitutive laws in embedded strong discontinuity analysis is examined. By adopting a regularised discontinuity (approximating the unbounded strain field resulting from a displacement jump with a bounded function), the strain field in a body is always bounded, hence continuum laws can be applied. However, this must be done with some caution since the ‘fictitious’ strain state at the discontinuity can lead to spurious behaviour that does not arise in the conventional application of classical constitutive laws. Particularly addressed is stress locking as a function of the displacement regularisation in some plasticity models. It is also shown that the regularisation function can have a serious impact on convergence behaviour for some types of constitutive models

A phase-field model for fractures in incompressible solids

Within this work, we develop a phase-field description for simulating fractures in incompressible materials. Standard formulations are subject to volume-locking when the solid is (nearly) incompressible. We propose an approach that builds on a mixed form of the displacement equation with two unknowns: a displacement field and a hydro-static pressure variable. Corresponding function spaces have to be chosen properly. On the discrete level, stable Taylor-Hood elements are employed for the displacement-pressure system. Two additional variables describe the phase-field solution and the crack irreversibility constraint. Therefore, the final system contains four variables: displacements, pressure, phase-field, and a Lagrange multiplier. The resulting discrete system is nonlinear and solved monolithically with a Newton-type method. Our proposed model is demonstrated by means of several numerical studies based on two numerical tests. First, different finite element choices are compared in order to investigate the influence of higher-order elements in the proposed settings. Further, numerical results including spatial mesh refinement studies and variations in Poisson's ratio approaching the incompressible limit, are presented

The TDNNS method for Reissner-Mindlin plates

A new family of locking-free finite elements for shear deformable Reissner-Mindlin plates is presented. The elements are based on the "tangential-displacement normal-normal-stress" formulation of elasticity. In this formulation, the bending moments are treated as separate unknowns. The degrees of freedom for the plate element are the nodal values of the deflection, tangential components of the rotations and normal-normal components of the bending strain. Contrary to other plate bending elements, no special treatment for the shear term such as reduced integration is necessary. The elements attain an optimal order of convergence

Parameter-robust discretization and preconditioning of Biot's consolidation model

Biot's consolidation model in poroelasticity has a number of applications in science, medicine, and engineering. The model depends on various parameters, and in practical applications these parameters ranges over several orders of magnitude. A current challenge is to design discretization techniques and solution algorithms that are well behaved with respect to these variations. The purpose of this paper is to study finite element discretizations of this model and construct block diagonal preconditioners for the discrete Biot systems. The approach taken here is to consider the stability of the problem in non-standard or weighted Hilbert spaces and employ the operator preconditioning approach. We derive preconditioners that are robust with respect to both the variations of the parameters and the mesh refinement. The parameters of interest are small time-step sizes, large bulk and shear moduli, and small hydraulic conductivity.Comment: 24 page

Reliability approach for safe designing on a locking system

The aim of this work is to predict the failure probability of a locking system. This failure probability is assessed using complementary methods: the First-Order Reliability Method (FORM) and Second-Order Reliability Method (SORM) as approximated methods, and Monte Carlo simulations as the reference method. Both types are implemented in a specific software [Phimeca software. Software for reliability analysis developed by Phimeca Engineering S.A.] used in this study. For the Monte Carlo simulations, a response surface, based on experimental design and finite element calculations [Abaqus/Standard User’s Manuel vol. I.], is elaborated so that the relation between the random input variables and structural responses could be established. Investigations of previous reliable methods on two configurations of the locking system show the large sturdiness of the first one and enable design improvements for the second one

Reliability approach for safe designing on a locking system

The aim of this work is to predict the failure probability of a locking system. This failure probability is assessed using complementary methods: the First-Order Reliability Method (FORM) and Second-Order Reliability Method (SORM) as approximated methods, and Monte Carlo simulations as the reference method. Both types are implemented in a specific software [Phimeca software. Software for reliability analysis developed by Phimeca Engineering S.A.] used in this study. For the Monte Carlo simulations, a response surface, based on experimental design and finite element calculations [Abaqus/Standard User’s Manuel vol. I.], is elaborated so that the relation between the random input variables and structural responses could be established. Investigations of previous reliable methods on two configurations of the locking system show the large sturdiness of the first one and enable design improvements for the second one