Mesh Alignment Research Articles

An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids

This paper presents an analysis of strong discontinuities in inelastic solids at finite strains. Solutions exhibiting this type of discontinuities, characterized by a discontinuous displacement field, are shown to make physical and mathematical sense in a classical multiplicative plasticity continuum model if the softening modulus is reinterpreted as a singular distribution.Physically, the strainsoftening is localized along the discontinuity. Conditions for the appearance of strong discontinuities in the geometrically nonlinear range are characterized, as it is the response of the material during localization. In addition, these analytical results are exploited in the design of a new class of finite element methods. The proposed methods fall within the class of enhanced strain methods, and lead to solutions independent of the mesh size and insensitive to mesh alignment, without requiring any regularization of the solutions by numerical parameters like a characteristic length.

Element-Embedded Localization Band Based on Regularized Displacement Discontinuity

The paper describes a new finite element, derived from the classical constant strain element, in the context of localization analysis of elastic-plastic materials. The formulation is based on the “enhanced strain” concept, which is extended to include regularized displacement discontinuities. As a result, the localization band is embedded within the element and the conventional displacement topology is preserved. The major advantage, as compared to the interelement representation, is that advanced mesh (re)alignment strategies are totally avoided and unstructured meshes are sufficient. An interesting feature of the element is that the condition for existence of an internal element discontinuity is identical to the classical condition for band-shaped localization. The element is combined with a cohesive crack model that is based on the Rankine criterion and a well-established calibration technique to achieve an objective response in the post peak softening range in terms of the dissipated (fracture) energy...

A patch test for mesh alignment effects in localized failure

AbstractComputation of failure mechanisms is of paramount importance for engineers assessing safety of structures. However, computation of failure loads and mechanisms presents numerical difficulties leading to wrong answers, especially in the case where failure consists in localization of plastic deformation or damage in localized zones. Here, the results depend on factors like mesh alignment and element distortion. The paper addresses the problem of designing a suitable patch test to assess element performance under localized failure. It will be shown how predictions of this test provide a reliable answer to the question of whether a particular element will or will not be suitable for such failure computations.

Continuum modelling of strong discontinuities in solid mechanics using damage models

Numerical simulation of strong discontinuities by using standard stress-strain constitutive equations including strain-softening is addressed. The concept of strong discontinuity analysis is introduced and driven, as a matter of example, into a standard continuum damage model. Then, the relevant features that make the constitutive equation compatible with the appearance of strong discontinuities are extracted. Those features are used in the design of a specific finite element approach to the strong discontinuity problem which is placed in the framework of the assumed enhanced strain methods. Numerical simulations show that mesh size and mesh alignment dependencies, typical of some continuum approaches, can be removed.

Finite‐Element Analysis of Elastoplastic Discontinuities

In the present paper we address the question of whether localized failure due to elastoplastic bifurcation can be captured within the fixed‐mesh approach. To this end, the theoretical framework of localization analysis of elastoplastic solids is revisited, and examples of weak discontinuities are presented for an elastic perfectly plastic Huber‐Mises material with focus on plane stress. The prominent role of finite‐element design (standard displacement versus enriched formulation) and orientation (aligned versus misaligned geometry) is demonstrated first at the element level, when a single element is uniformly stretched to the yield limit and subjected to localization at all Gauss points. The weak localization test probes the directional properties of the finite element when spatial discontinuities in the strain field are to be captured. This element test is subsequently extended to the structural level and is illustrated with the eigenanalysis of a flat steel bar that is uniformly stretched to the yield limit in uniaxial tension. The effect of mesh alignment is examined with a layer of finite elements that is gradually rotated towards the spatial discontinuity of elastoplastic bifurcation analysis.

Discontinuous displacement approximation for capturing plastic localization

AbstractIt is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries (interfaces) of the finite element subdivision. The regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept. As a by‐product of the regularization, an intrinsic band width is introduced as a ‘constitutive’ property rather than a geometric feature of the finite element mesh. In this way the spurious mesh sensitivity, which is obtained when the displacement approximation is continuous, can be avoided. Another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material. An interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface (up to within a scalar factor). An analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a ‘shear’ band for a general plasticity model. The significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress. It is shown that a unique structural post‐peak response (in accordance with non‐linear fracture mechanics) can be achieved when the plastic softening modulus is properly related to the bandwidth. The paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope.