Download Approaches to the Description of Anisotropic Material by Apel N. PDF

By Apel N.

The current paintings bargains with only macroscopic descriptions of anisotropic fabric behaviour. Key features are new advancements within the concept and numerics of anisotropicplasticity. After a brief dialogue of the class of solids via symmetry changes a survey approximately illustration idea of isotropic tensor services and tensor polynomials is given. subsequent substitute macroscopic methods to finite plasticity are mentioned. while contemplating a multiplicative decomposition of the deformation gradient into an elastic half and a plastic half, a 9 dimensional °ow rule is got that permits the modeling of plastic rotation. another process bases at the advent of a metric-like inner variable, the so-called plastic metric, that bills for the plastic deformation of the cloth. during this context, a brand new type of constitutive types is got for the alternative of logarithmic traces and an additive decomposition of the entire pressure degree into elastic and plastic elements. The popularity of this classification of versions is because of their modular constitution in addition to the a+nity of the constitutive version and the algorithms contained in the logarithmic pressure area to versions from geometric linear idea. at the numerical aspect, implicit and specific integration algorithms and pressure replace algorithms for anisotropic plasticity are constructed. Their numerical e+ciency crucially bases on their cautious development. precise concentration is wear algorithms which are compatible for variational formulations. as a result of their (incremental) power estate, the corresponding algorithms might be formulated when it comes to symmetric amounts. a discounted garage eRort and no more required solver skill are key benefits in comparison to their regular opposite numbers.

Show description

Read or Download Approaches to the Description of Anisotropic Material Behaviour at Finite Elastic and Plastic Deformations. Theory and Numerics PDF

Similar computational mathematicsematics books

Hybrid Systems: Computation and Control: Third International Workshop, HSCC 2000 Pittsburgh, PA, USA, March 23–25, 2000 Proceedings

This booklet constitutes the refereed complaints of the 3rd overseas Workshop on Hybrid platforms: Computation and keep an eye on, HSCC 2000, held in Pittsburgh, PA, united states in March 2000. The 32 revised complete papers awarded including abstracts of 4 invited talks have been rigorously reviewed and chosen from a complete of seventy one papers submitted.

Finite Element Method: A Practical Course

The Finite aspect strategy (FEM) has develop into an vital know-how for the modelling and simulation of engineering structures. Written for engineers and scholars alike, the purpose of the ebook is to supply the required theories and strategies of the FEM for readers with the intention to use a advertisement FEM package deal to unravel basically linear difficulties in mechanical and civil engineering with the main target on structural mechanics and warmth move.

Biological Magnetic Resonance - Volume 17: Structural Computation and Dynamics in Protein (Biological Magnetic Resonance)

Quantity 17 of organic Magnetic Resonance (Structure Computation and Dynamics) represents major advances in the biomolecular NMR box, with emphasis on advancements in the course of the contemporary years. This publication brings jointly the various world's most well known specialists who've supplied wide management in advancing the sphere.

Computational Logic in Multi-Agent Systems: 11th International Workshop, CLIMA XI, Lisbon, Portugal, August 16-17, 2010, Proceedings

This booklet constitutes the complaints of the eleventh foreign Workshop on Computational good judgment in Multi-Agent structures, CLIMA XI, held in Lisbon, Portugal, in August 2010. The 14 papers awarded have been conscientiously reviewed and chosen from 31 submissions. additionally four invited talks are offered. the aim of the CLIMA workshops is to supply a discussion board for discussing recommendations, in accordance with computational common sense, for representing, programming and reasoning approximately brokers and multi-agent platforms in a proper method.

Additional resources for Approaches to the Description of Anisotropic Material Behaviour at Finite Elastic and Plastic Deformations. Theory and Numerics

Sample text

28) This determines the possible orientations of the tensor v. 29) constitutes a functional basis for scalar-valued isotropic functions of a single vector and an symmetric second-order tensor, because these invariants characterize the coset of x = {v, A}. 2: The assumption of the existence of three distinct eigen-values of A also covers the cases of two and three equal eigen-values. In the first case, the characteristic space of A is a single line. 25)1 . 25)2 is superfluous. In the second case, the relative orientation of v and A is unspecified.

Figure 20: The symmetry of the motif located at the grid points may reduce the overall symmetry. Two-dimensional quadratic unit-cell with (a) quadratic motif has 4 mirror planes and one four-fold axis. (b) Rectangular motif reduces symmetries to two mirror planes and one two-fold axis. (c) Triangle motif allows only one mirror symmetry operation. of the so called inner symmetry of the motif with the symmetry of the 14 Bravais cells leads to 32 possible combinations, referred to as crystal classes.

The primitive unit-cell together with these symmetries is shown in figure 18. In the same way, the I- and F-centered Bravais cells PSfrag replacements a b c β Figure 18: The unit-cell for cubic symmetry is obtained by introducing a threefold diagonal axis to the primitive orthorhombic unit cell. In the same way the I- and F-centered Bravais lattices are obtained by their orthotropic counterparts. follow from their orthotropic counterparts by adding a threefold axis along the diagonal. As all the faces have to be equal, a C-centered cell does not exist in cubic systems.

Download PDF sample

Rated 4.58 of 5 – based on 32 votes