A p-adaptive scheme for overcoming volumetric locking during isochoric plastic deformation

A p-adaptive scheme is developed in order to overcome volumetric locking in low order finite elements. A special adaptive scheme is used which is based on the partition of unity concept. This allows higher order polynomial terms to be added locally to the underlying finite element interpolations basis through the addition of extra degrees of freedom at existing nodes. During the adaptive process, no new nodes are added to the mesh. Volumetric locking is overcome by introducing higher order polynomial terms in regions where plastic flow occurs. The model is able to overcome volumetric locking for plane strain, axisymmetric and three-dimensional problems

Discrete analysis of localisation in three-dimensional solids

A procedure is illustrated for the determination of the normal direction of a discontinuity plane within a solid finite element. Using so-called embedded discontinuities, discrete constitutive models can be applied within a continuum framework. A significant difficulty within this method for three-dimensional problems is the determination of the normal direction for a discontinuity. Bifurcation analysis indicates the development of a discontinuity and multiple solution for the normal. The procedure developed here chooses the appropriate normal by exploiting features of the embedded discontinuity method

Embedded discontinuities for softening solids

Additional, discontinuous functions are added to the displacement field of standard finite elements in order to capture highly localised zones of intense straining. By embedding discontinuities within an element it is possible to effectively model localisation phenomena (such as fracture in concrete) with a relatively small number of finite elements. The displacement jump is regularised, producing bounded strains and allowing the application of classical strain softening constitutive laws. It is then possible to achieve mesh-objective results with respect to energy dissipation without resorting to higher-order continuum theories

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

Discontinuities in regularised media

Discontinuous interpolation of the problem fields in non-local and rate-dependent media is considered. The necessity of discontinuities in the analysis of failure processes and some of the requirements for the introduction of discontinuities in regularised media are discussed. The regularisation properties of a novel rate-dependent elastoplastic damage continuum model are presented

Discontinuous modelling of crack propagation in a gradient-enhanced continuum

A numerical model for the description of the combined continuous/discontinuous failure in a regularised strain-softening continuum is proposed. The continuum is regularised through the introduction of gradient terms into the constitutive equations. At the transition to discrete failure, the problem fields are enhanced through a discontinuous interpolation based on the partition of unity concept. The discretisation procedure is described in detail and numerical examples illustrate the performance of the combined continuous/discontinuous approach

Multi-level analysis of localisation problems

Localisation processes, such as shear banding and necking, have been investigated following a macroscopic and a microscopic approach. Both approaches have been formulated within a finite deformation plasticity framework. Additional terms have been used to regularise the problem and solve mesh dependency. In the macroscopic model viscosity is introduced as a means to control the thickness of the shear band, while in the microscopic model the nonlocal interaction of dislocations acts as a stabiliser. The micro-mechanical model is formulated in a crystal plasticity framework. A diffusion term that represents cross-slip of dislocations is included in the evolution equations for dislocation densities. The effect of the viscous term (macro-model) and the diffusion-like term (micro-model) in the constitutive relation on the resulting formation of localised shear modes is studied. An analysis of a strip in tension oriented for multiple slip is presented for both models

Simulating discontinuities in a gradient-enhanced continuum

A continuum-discrete model for failure in quasi-brittle materials is presented. The continuum is regularised through the introduction of gradient terms into the constitutive model. At the transition to discrete failure, the problem fields are enhanced through the use of a discontinuous interpolation. The continuum model is able to simulate micro-cracking, while a traction-free discontinuity represents the macro crack. The discretisation procedure is described in detail

A novel technique for modelling interfaces in reinforced brittle materials

A novel numerical technique for the modelling of interfaces is introduced for the analysis of reinforced brittle materials. The method exploits the partition of unity property of finite element shape functions. By considering finite element shape functions as partitions of unity, extra degrees of freedom are added to the nodes at the interface between the matrix and reinforcement. A gradient-enhanced damage model is used to simulate the continuum response. Numerical results for a three-point bending test and a pull-out test are presented. The numerical procedure proposed here is suitable for a great variety of applications ranging from discrete cracking and steel-concrete interaction in concrete to delamination processes in composite materials

Strong embedded discontinuities for simulating fracture in quasi-brittle materials

In this paper embedded strong discontinuities are used to model discrete cracking in materials like concrete. In the approach followed a discontinuous displacement field is considered and the deformation is localized at a surface of zero width. Both a damage law and a plasticity law are adopted to describe the constitutive relation between tractions and displacement jumps at the discontinuity surface. An algorithm is introduced to enforce the continuity of the crack path, permitting a clear identification of the discontinuities in the mesh. Both mode-I and mixed-mode cracking have been considered and the importance of the shear tractions on the global behaviour of a structure is assessed. With the formulation adopted it is concluded that: i) realistic crack patterns are obtained, similar to those found in experiments and ii) the dissipation of energy can be objectively found irrespective of the mesh that is used