By Apel N.

ISBN-10: 3937859004

ISBN-13: 9783937859002

The current paintings bargains with merely macroscopic descriptions of anisotropic fabric behaviour. Key facets are new advancements within the conception and numerics of anisotropicplasticity. After a quick dialogue of the category of solids by way of symmetry ameliorations a survey approximately illustration concept 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 bought 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 category of constitutive versions is bought for the alternative of logarithmic lines and an additive decomposition of the full pressure degree into elastic and plastic elements. The reputation of this category 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 conception. at the numerical part, implicit and particular integration algorithms and tension replace algorithms for anisotropic plasticity are built. Their numerical e+ciency crucially bases on their cautious building. certain concentration is wear algorithms which are appropriate for variational formulations. as a result of their (incremental) capability estate, the corresponding algorithms will be formulated by way of symmetric amounts. a discounted garage eRort and no more required solver ability are key benefits in comparison to their normal opposite numbers.

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

**Example text**

The latter was done by Rivlin & Ericksen [108] for two symmetric second-order tensors and extended by Smith [130] to sets of first-order and symmetric as well as skew-symmetric second-order tensors. So the main task is to determine a set of isotropic invariants I := {I1 , I2 , . . , In } so that the coordinates of the tensor agencies are uniquely determined by the values of the invariants through the equations [v s ]i = f (I1 , I2 , . . , In ) s = 1, . . a [As ]ij = f (I1 , I2 , . . , In ) s = 1, .

22) results in a different coordinate representation. As a measure of the possible eight orientations between the tensors v and A, two additional relative invariants are introduced ¯v ¯ · A¯ v · Av = v ¯ 2v ¯. 25), assume the representation v = vm where v = v · v is the length of the vector and m = v/ v its direction. 26) due to the linear dependence cos2 θ1 + cos2 θ2 + cos2 θ3 = 1. 25) appear in the form v · Av = v 2 (λ1 − λ3 ) cos2 θ1 + v 2 (λ2 − λ3 ) cos2 θ2 v · A2 v = v 2 (λ21 − λ23 ) cos2 θ1 + v 2 (λ22 − λ23 ) cos2 θ2 .

22) where Q ∈ O(3). e. 3 3 A= i=1 λi n i ⊗ n i = i=1 ¯ . 23) 42 Representations of Anisotropic Tensor Functions ¯ i transforms according to The vector v = vi ni = v¯i n ¯i . 22) results in a different coordinate representation. As a measure of the possible eight orientations between the tensors v and A, two additional relative invariants are introduced ¯v ¯ · A¯ v · Av = v ¯ 2v ¯. 25), assume the representation v = vm where v = v · v is the length of the vector and m = v/ v its direction. 26) due to the linear dependence cos2 θ1 + cos2 θ2 + cos2 θ3 = 1.

### Approaches to the Description of Anisotropic Material Behaviour at Finite Elastic and Plastic Deformations. Theory and Numerics by Apel N.

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