Showing papers by "Peter Wriggers published in 1996"
TL;DR: In this article, the appearance of these modes is investigated analytically by means of a simple representative example, and it is shown that in compressive deformation states these elements depict stability modes which are associated with hour-glass forms and thus denote a rank deficiency for such deformations.
160 citations
TL;DR: In this article, a general formulation of thin incompressible membranes and the behavior of soft biotissues using the finite element method is presented, in particular the underlying hyperelastic model is chosen to examine the highly non-linear constitutive relation of blood vessels.
136 citations
TL;DR: In this paper, the authors considered the problem of stability of the enhanced strain elements in the presence of large deformations and proposed a new element based on a consistent formulation of the augmented gradient with respect to new orthogonality conditions which it retains with four enhanced modes volumetric and shear locking free behaviour of the original formulation.
Abstract: Considers the problem of stability of the enhanced strain elements in the presence of large deformations. The standard orthogonality condition between the enhanced strains and constant stresses ensures satisfaction of the patch test and convergence of the method in case of linear elasticity. However, this does not hold in the case of large deformations. By analytic derivation of the element eigenvalues in large strain states additional orthogonality conditions can be derived, leading to a stable formulation, regardless of the magnitude of deformations. Proposes a new element based on a consistent formulation of the enhanced gradient with respect to new orthogonality conditions which it retains with four enhanced modes volumetric and shear locking free behaviour of the original formulation and does not exhibit hour‐glassing for large deformations.
82 citations
TL;DR: In this article, a comparison of continuum and shell elements for thin shell problems is made, and Simo et al. [ Comput. Numer. Meth. Appl. Engng 110, 359-386 (1993)] are compared for finite elasto-plastic deformations.
71 citations
TL;DR: This paper discusses the family of enhanced strain elements in order to depict the positive and negative aspects related to these elements and uses numerical examples to underline the theoretical results.
Abstract: Numerical simulations of engineering problems require robust elements. For a broad range of applications these elements should perform well in bending dominated situations and also in cases of incompressibility. The element should be insensitive against mesh distortions which frequently occur due to modern mesh generation tools or during finite deformations. Possibly the elements should not lock in the thin limits and thus be applicable to shell problems. Furthermore due to efficiency reasons a good coarse mesh accuracy is required in nonlinear analysis. In this paper we discuss the family of enhanced strain elements in order to depict the positive and negative aspects related to these elements. Throughout this discussion we use numerical examples to underline the theoretical results.
69 citations
TL;DR: In this article, a constitutive modeling and numerical analysis of vascular segments covering finite strains is presented, with special attention paid to a two term potential that constitutes an essential foundation for accurate simulation within the entire strain domain.
Abstract: To explore the mechanical non-linear behaviour of anisotropic arterial walls on a computational basis, the formulation of a continuum based elastic potential is a major task and challenge to the analyst. The present communication is concerned with the constitutive modelling and numerical analysis of vascular segments covering finite strains. Special attention is paid to a two term potential that constitutes an essential foundation for accurate simulation within the entire strain domain. Axisymmetrical membrane elements are assembled to match the geometry of blood vessels. Numerical results confirm the theoretical approach by referring to experimental data of different rat arteries.
60 citations
TL;DR: In this paper, a modified enhanced strain methodology is presented for the development of three dimensional tri-linear elements based on Taylor expansions of the derivatives of the isoparametric and enhanced shape functions in local coordinates.
Abstract: Further development of three dimensional tri-linear elements based on a modified enhanced strain methodology is presented. The new formulation employs Taylor expansions of the derivatives of the isoparametric and enhanced shape functions in local coordinates. With this approach, only nine enhanced modes are needed for developing a dilatational-locking free element. Furthermore, the formulation permits a symbolic integration of the element tangent matrix, and more efficient static condensation procedure due to uncoupling of the enhanced modes. Good results in the analysis of thin shell structures, using only one 3D element in the thickness direction of the shell, are also presented.
39 citations
TL;DR: This paper applies a geometrical model and its discretization for contact which is valid for large deformations and the algorithms to integrate the interface laws will be discussed for the tangential stress components.
34 citations
27 citations
Journal Article•
TL;DR: In this article, the stability behavior of hyperelastic solids is characterized by two different kinds of instabilities: structural instabilities which occur under compressive stresses for moderate strains but large displacements; material instabilities can be observed only for certain constitutive relations (qualitative dependence).
12 citations
TL;DR: In this paper, a hybrid finite element formulation for the geometrically exact dynamics of rods with applications to chaotic motion is proposed, where the rod theory is developed for in-plane motions using the direct approach where the rods are treated as a one-dimensional Cosserat line.
Abstract: The paper is concerned with a hybrid finite element formulation for the geometrically exact dynamics of rods with applications to chaotic motion The rod theory is developed for in-plane motions using the direct approach where the rod is treated as a one-dimensional Cosserat line Shear deformation is included in the formulation Within the elements, a linear distribution of the kinematical fields is combined with a constant distribution of the normal and shear forces For time integration, the mid-point rule is employed Various numerical examples of chaotic motion of straight and initially curved rods are presented proving the powerfulness and applicability of the finite element formulation
TL;DR: In this article, a finite element model for the simulation of fast crack propagation under dynamic Mode I load conditions is developed, which accounts for viscoplastic material behavior, dynamic effects and contact in the crack zone.