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Strain Tensor (strain + tensor)

Distribution by Scientific Domains
Mathematics and Statistics37%

Selected Abstracts

Multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2010
Flavio V. Souza
Abstract Multiscale computational techniques play a major role in solving problems related to viscoelastic composites due to the complexities inherent to these materials. In this paper, a numerical procedure for multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks is proposed in which the (global scale) homogenized viscoelastic incremental constitutive equations have the same form as the local-scale viscoelastic incremental constitutive equations, but the homogenized tangent constitutive tensor and the homogenized incremental history-dependent stress tensor at the global scale depend on the amount of damage accumulated at the local scale. Furthermore, the developed technique allows the computation of the full anisotropic incremental constitutive tensor of viscoelastic solids containing evolving cracks (and other kinds of heterogeneities) by solving the micromechanical problem only once at each material point and each time step. The procedure is basically developed by relating the local-scale displacement field to the global-scale strain tensor and using first-order homogenization techniques. The finite element formulation is developed and some example problems are presented in order to verify the approach and demonstrate the model capabilities. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Optimal solid shell element for large deformable composite structures with piezoelectric layers and active vibration control

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2005
X. G. Tan
Abstract In this paper, we present an optimal low-order accurate piezoelectric solid-shell element formulation to model active composite shell structures that can undergo large deformation and large overall motion. This element has only displacement and electric degrees of freedom (dofs), with no rotational dofs, and an optimal number of enhancing assumed strain (EAS) parameters to pass the patch tests (both membrane and out-of-plane bending). The combination of the present optimal piezoelectric solid-shell element and the optimal solid-shell element previously developed allows for efficient and accurate analyses of large deformable composite multilayer shell structures with piezoelectric layers. To make the 3-D analysis of active composite shells containing discrete piezoelectric sensors and actuators even more efficient, the composite solid-shell element is further developed here. Based on the mixed Fraeijs de Veubeke,Hu,Washizu (FHW) variational principle, the in-plane and out-of-plane bending behaviours are improved via a new and efficient enhancement of the strain tensor. Shear-locking and curvature thickness locking are resolved effectively by using the assumed natural strain (ANS) method. We also present an optimal-control design for vibration suppression of a large deformable structure based on the general finite element approach. The linear-quadratic regulator control scheme with output feedback is used as a control law on the basis of the state space model of the system. Numerical examples involving static analyses and dynamic analyses of active shell structures having a large range of element aspect ratios are presented. Active vibration control of a composite multilayer shell with distributed piezoelectric sensors and actuators is performed to test the present element and the control design procedure. Copyright © 2005 John Wiley & Sons, Ltd. [source]

On the design of energy,momentum integration schemes for arbitrary continuum formulations.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004
Applications to classical, chaotic motion of shells
Abstract The construction of energy,momentum methods depends heavily on three kinds of non-linearities: (1) the geometric (non-linearity of the strain,displacement relation), (2) the material (non-linearity of the elastic constitutive law), and (3) the one exhibited in displacement-dependent loading. In previous works, the authors have developed a general method which is valid for any kind of geometric non-linearity. In this paper, we extend the method and combine it with a treatment of material non-linearity as well as that exhibited in force terms. In addition, the dynamical formulation is presented in a general finite element framework where enhanced strains are incorporated as well. The non-linearity of the constitutive law necessitates a new treatment of the enhanced strains in order to retain the energy conservation property. Use is made of the logarithmic strain tensor which allows for a highly non-linear material law, while preserving the advantage of considering non-linear vibrations of classical metallic structures. Various examples and applications to classical and non-classical vibrations and non-linear motion of shells are presented, including (1) chaotic motion of arches, cylinders and caps using a linear constitutive law and (2) large overall motion and non-linear vibration of shells using non-linear constitutive law. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Refined mixed finite element method for the elasticity problem in a polygonal domain

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2002
M. Farhloul
Abstract The purpose of this article is to study a mixed formulation of the elasticity problem in plane polygonal domains and its numerical approximation. In this mixed formulation the strain tensor is introduced as a new unknown and its symmetry is relaxed by a Lagrange multiplier, which is nothing else than the rotation. Because of the corner points, the displacement field is not regular in general in the vicinity of the vertices but belongs to some weighted Sobolev space. Using this information, appropriate refinement rules are imposed on the family of triangulations in order to recapture optimal error estimates. Moreover, uniform error estimates in the Lamé coefficient , are obtained for , large. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 323,339, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10009 [source]

Quantitative description of the tilt of distorted octahedra in ABX3 structures

ACTA CRYSTALLOGRAPHICA SECTION B, Issue 2 2007
Rafael Tamazyan
A description of the tilt of octahedra in ABX3 perovskite-related structures is proposed that can be used to extract the unique values for the tilt parameters ,, , and , of ABX3 structures with regular and distorted octahedra up to the point symmetry , from atomic coordinates and lattice parameters. The geometry of the BX6 octahedron is described by three B,X bond lengths (r1, r2, r3) and three X,B,X bond angles (,12, ,13 and ,23) or alternatively by a local strain tensor together with an average B,X bond length. Connections between the proposed method and Glazer's tilt system are discussed. The method is used to analyze structural transformations of I2/c, Pbnm and Immm structures. The proposed description allows the analysis of group,subgroup relations for the ABX3 structures with distorted octahedra, in terms of octahedral deformations and tilting. The method might also be of interest in the study of the phase transitions in the family of ABX3 structures. [source]

Constraints on deformation mechanisms during folding provided by rock physical properties: a case study at Sheep Mountain anticline (Wyoming, USA)

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2010
K. Amrouch
SUMMARY The Sheep Mountain anticline (Wyoming, USA) is a well-exposed asymmetric, basement-cored anticline that formed during the Laramide orogeny in the early Tertiary. In order to unravel the history of strain during folding, we carried out combined anisotropy of magnetic susceptibility (AMS), anisotropy of P -wave velocity (APWV) and Fry strain analyses. The results are compared to previously published stress,strain data from calcite twins at the microscopic scale and from fracture sets at the mesoscopic scale, and are used to discuss the kinematics and mechanics of forced folding. The results obtained in sandstone and carbonate lithologies demonstrate a good agreement between (1) the principal axes of the AMS and APWV tensors, (2) stress,strain tensors derived from calcite twins, (3) Fry strain axes and mesoscopic fracture sets. Furthermore, these tensors are coaxial with the main structural trends of the anticline. The differences between AMS and APWV fabrics on one hand, and the differential stress values of the forelimb and the backlimb on the other hand, emphasize how the macroscopic asymmetry of Sheep Mountain anticline affects the strain pattern at the microscopic scale. The data set presented in this paper offers a consistent mechanical scenario for the development of Sheep Mountain anticline. [source]

Differentiable structure of the set of coaxial stress,strain tensors,

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2009
Josep Clotet
Abstract In order to study stress,strain tensors, we consider their representations as pairs of symmetric 3 × 3-matrices and the space of such pairs of matrices partitioned into equivalence classes corresponding to change of bases. We see that these equivalence classes are differentiable submanifolds; in fact, orbits under the action of a Lie group. We compute their dimension and obtain miniversal deformations. Finally, we prove that the space of coaxial stress,strain tensors is a finite union of differentiable submanifolds. Copyright © 2008 John Wiley & Sons, Ltd. [source]