Components of Stress and Strain Tensors

2004 ◽  
pp. 22-30
Author(s):  
Andrzej Służalec
Keyword(s):  
Stress And Strain ◽  
Strain Tensors

Linear elastic eigenstates of the compliance tensor for trigonal crystals

2000 ◽  
Vol 215 (1) ◽  
pp. 1-9 ◽  
Author(s):  
P.S. Theocaris ◽  
D.P. Sokolis
Keyword(s):  
Strain Energy ◽  
Elastic Strain Energy ◽  
Symmetric Tensor ◽  
Stress And Strain ◽  
Linear Elastic ◽  
Trigonal System ◽  
Compliance Tensor ◽  
Characteristic Values ◽  
Strain Tensors ◽  
Elastic Strain Energy Density

The spectral decomposition of the compliance fourth-rank tensor, representative of a trigonal crystalline or other anisotropic medium, is offered in this paper, and its characteristic values and idempotent fourth-rank tensors are established, with respect to the Cartesian tensor components. Consequently, it is proven that the idempotent tensors serve to analyse the second-rank symmetric tensor space into orthogonal subspaces, resolving the stress and strain tensors for the trigonal medium into their eigentensors, and, finally, decomposing the total elastic strain energy density into distinct, autonomous components. Finally, bounds on the values of the compliance tensor components for the trigonal system, dictated by the classical thermodynamical argument for the elastic potential to be positive definite, are estimated by imposing the characteristic values of the compliance tensor to be strictly positive.

MATHEMATICAL MODEL OF MATERIALS OF STRUCTURES AND ELEMENTS OF RESTORED SOIL DAMS FOR NUMERICAL CALCULATIONS

2021 ◽  
pp. 46-51
Author(s):  
V. YA. ZHARNITSKIY ◽  
◽  
A. P. SMIRNOV
Keyword(s):  
Negative Impact ◽  
Emergency Situation ◽  
Numerical Calculations ◽  
Stress And Strain ◽  
Operational Parameters ◽  
Reliable Operation ◽  
Operational Factors ◽  
Materials Used ◽  
Technical Operation ◽  
Strain Tensors

Identified in the process of analyzing the operation of the structure, in the conditions of its operation, allow to assess the actual reserves of the bearing capacity of the structure and take effective measures to restore the operational parameters. The main criteria influencing the choice of mathematical models of materials for structures and elements of soil dams are more consistent with the model of the equation of state connecting the components of stress and strain tensors, as well as the rate of their change, which are obtained and tested for numerical calculations and have a full set of constants for materials used in the calculations of earth dams, the choice of their structures (concrete,reinforced concrete, soils, etc.). Reliable operation of soil dams is possible only if all proper conditions are met. The causes of dam accidents and their damage must be known not only to eliminate errors at the design and construction stages, but also during their operation. In order to exclude the negative impact of operational factors on the safety of soil HTS, it is necessary not only to strictly observe the rules of technical operation and take measures to exclude the possibility of an emergency situation during technological operations at facilities, but also to have methods for predictive justification of the restoration of strength and operational indicators of structures and elements of soil dams.

Microplane Model for Fracturing Damage of Triaxially Braided Fiber-Polymer Composites

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Ferhun C. Caner ◽  
Zdeněk P. Bažant ◽  
Christian G. Hoover ◽  
Anthony M. Waas ◽  
Khaled W. Shahwan
Keyword(s):  
Present Model ◽  
Material Model ◽  
Multiscale Model ◽  
Stress And Strain ◽  
Band Model ◽  
Braided Composites ◽  
Microplane Model ◽  
Explicit Finite Element ◽  
Crack Band ◽  
Strain Tensors

A material model for the fracturing behavior for braided composites is developed and implemented in a material subroutine for use in the commercial explicit finite element code ABAQUS. The subroutine is based on the microplane model in which the constitutive behavior is defined not in terms of stress and strain tensors and their invariants but in terms of stress and strain vectors in the material mesostructure called the “microplanes.” This is a semi-multiscale model, which captures the interactions between inelastic phenomena such as cracking, splitting, and frictional slipping occurring on planes of various orientations though not the interactions at a distance. To avoid spurious mesh sensitivity due to softening, the crack band model is adopted. Its band width, related to the material characteristic length, serves as the localization limiter. It is shown that the model can realistically predict the orthotropic elastic constants and the strength limits. More importantly, the present model can also fit the tests of size effect on the strength of notched specimens and the post-peak behavior, which have been conducted for this purpose. When used in the ABAQUS software, the model gives a realistic picture of the axial crushing of a braided tube by a divergent plug.

scholarly journals On Transient Thermal Stresses in an Infinite Thin Plate

1960 ◽  
Vol 12 (2) ◽  
pp. 69-73
Author(s):  
W. Derski
Keyword(s):  
Thin Plate ◽  
Thermal Stresses ◽  
Thermoelastic Stress ◽  
Additional Term ◽  
Elastic Solid ◽  
Rate Of Change ◽  
Stress And Strain ◽  
Infinite Extent ◽  
Transient Thermal ◽  
Strain Tensors

The presence of a non-steady state of temperature in an elastic solid gives rise to an additional term in the generalised Hooke's Law connecting the stress and strain tensors and terms involving the time rate of change of the dilatation. This time-dependent dilatation may produce so-called thermoelastic stress waves. The present note is concerned with the effects produced by these additional terms in a simple situation, in which the elastic solid is regarded as a thin plate of infinite extent. The distribution of temperature in the plate is produced by a point heat source of Dirac type.

Influence of Hydromechanical Couplings on the Resaturation of Engineered Barriers

1997 ◽  
Vol 506 ◽  
Author(s):  
T. Lassabatere
Keyword(s):  
Coupled Model ◽  
Stress And Strain ◽  
Mechanical State ◽  
State Equations ◽  
Swelling Clays ◽  
Engineered Barriers ◽  
Deformable Materials ◽  
Strain Tensors ◽  
Kinetics Of ◽  
Fully Coupled

ABSTRACTThis paper presents a fully coupled model for unsaturated deformable materials like swelling clays of engineered barriers. A thermodynamic framework is adopted which allows to take into account the influence of the mechanical variables (stress and strain tensors) upon the hydraulic part of the state equations (suction - water content relation). So, a fully coupled behaviour formulation is stated which, when combined with « classical » phenomenological relations, makes it possible to study the influence of the mechanical state of the barrier on the kinetics of its resaturation.

Sign in / Sign up

Export Citation Format

Share Document