scholarly journals Strain Localization of Orthotropic Elasto–Plastic Cohesive–Frictional Materials: Analytical Results and Numerical Verification

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2040
Author(s):  
Sungchul Kim ◽  
Miguel Cervera ◽  
Jian-Ying Wu ◽  
Michele Chiumenti
Keyword(s):  
Plane Strain ◽  
Plastic Flow ◽  
Plane Stress ◽  
Strain Localization ◽  
Numerical Results ◽  
Flow Rule ◽  
Numerical Verification ◽  
Applied Loading ◽  
Analytical Results ◽  
Frictional Materials

Strain localization analysis for orthotropic-associated plasticity in cohesive–frictional materials is addressed in this work. Specifically, the localization condition is derived from Maxwell’s kinematics, the plastic flow rule and the boundedness of stress rates. The analysis is applicable to strong and regularized discontinuity settings. Expanding on previous works, the quadratic orthotropic Hoffman and Tsai–Wu models are investigated and compared to pressure insensitive and sensitive models such as von Mises, Hill and Drucker–Prager. Analytical localization angles are obtained in uniaxial tension and compression under plane stress and plane strain conditions. These are only dependent on the plastic potential adopted; ensuing, a geometrical interpretation in the stress space is offered. The analytical results are then validated by independent numerical simulations. The B-bar finite element is used to deal with the limiting incompressibility in the purely isochoric plastic flow. For a strip under vertical stretching in plane stress and plane strain as well as Prandtl’s problem of indentation by a flat rigid die in plane strain, numerical results are presented for both isotropic and orthotropic plasticity models with or without tilting angle between the material axes and the applied loading. The influence of frictional behavior is studied. In all the investigated cases, the numerical results provide compelling support to the analytical prognosis.

A Large Rotation Matrix for Nonlinear Framed Structures, Part 2: Numerical Verification

2014 ◽  
Vol 1065-1069 ◽  
pp. 2034-2039
Author(s):  
Jin Duan ◽  
Yun Gui Li
Keyword(s):  
Cantilever Beam ◽  
Numerical Results ◽  
Rotation Matrix ◽  
Numerical Verification ◽  
Structural Stiffness ◽  
Pure Bending ◽  
Large Rotation ◽  
Framed Structures ◽  
Analytical Results ◽  
Good Agreement

In this paper, some numerical verifications would be presented and discussed, mainly including the following three types: (1) the pure bending beam in which the structural stiffness would maintain the original value and not change along with the load; (2) the clamped arc-beam in which the structural stiffness would decrease gradually with the increment of load and the structure would be buckling at some certain load value; and (3) the cantilever beam in which the structural stiffness would increase significantly with the increment of load. For all of the above examples, the present results are in good agreement with the analytical results and numerical results in other literatures, testifying and illustrating the validity of the large rotation matrix for nonlinear framed structure, which is developed in the part 1 of this paper.

Studies on Plastic Flow of Anisotropic Metals

1956 ◽  
Vol 23 (3) ◽  
pp. 444-450
Author(s):  
L. W. Hu
Keyword(s):  
Stress Distribution ◽  
Internal Pressure ◽  
Strain Hardening ◽  
Plane Strain ◽  
Plastic Flow ◽  
Plane Stress ◽  
Biaxial Tension ◽  
Plastic Behavior ◽  
Theory Of Plastic Flow ◽  
Walled Cylinder

Abstract This investigation deals with a study of the plastic behavior of anisotropic metals. By extending Hill’s theory of plastic flow of anisotropic metals, plastic stress-strain relations for anisotropic materials with strain hardening are developed. Applications of these relations are also made to plane-stress and plane-strain problems with anisotropy. The effect of anisotropy on the stress distribution and on the pressure to produce yielding in a thick-walled cylinder under internal pressure is discussed. The influence of anisotropy on the interpretation of conventional biaxial tension-tension and tension-torsion tests is also considered in this study.

Constraints on Moving Strong Discontinuity Surfaces in Dynamic Plane-Stress or Plane-Strain Deformations of Stable Elastic-Ideally Plastic Materials

1990 ◽  
Vol 57 (3) ◽  
pp. 569-576 ◽  
Author(s):  
Yinong Shen ◽  
W. J. Drugan
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Yield Condition ◽  
Strong Discontinuity ◽  
Dynamic Crack Propagation ◽  
Small Displacement ◽  
Flow Rule ◽  
Dynamic Crack ◽  
Plastic Materials ◽  
Discontinuity Surfaces

For dynamic deformations of compressible elastic-ideally plastic materials in the practically important cases of plane stress and plane strain, we investigate the possible existence of propagating surfaces of strong discontinuity (across which components of stress, strain, or material velocity jump) within a small-displacement-gradient formulation. For each case, an explicit proof of the impossibility of such a propagating surface (except at an elastic wave speed) is achieved for isotropic materials satisfying a Huber-Mises yield condition and associated flow rule, and we show that our method of proof can be generalized to a large class of anisotropic materials. Nevertheless, we demonstrate that moving surfaces of strong discontinuity cannot be ruled out for all stable (i.e., satisfying the maximum plastic work inequality) materials, as in the case of a material whose yield surface contains a linear portion. A clear knowledge of the conditions under which dynamically propagating strong discontinuity surfaces can and cannot exist is crucial to the attainment of correct and complete solutions to such practical elastic-plastic problems as dynamic crack propagation, impact and rapidly moving load problems, high-speed forming, cutting, and other manufacturing processes.

scholarly journals BOUND STATES IN WEAKLY DEFORMED WAVEGUIDES: NUMERICAL VERSUS ANALYTICAL RESULTS

2017 ◽  
Vol 59 (2) ◽  
pp. 200-214 ◽  
Author(s):  
PAOLO AMORE ◽  
JOHN P. BOYD ◽  
FRANCISCO M. FERNÁNDEZ ◽  
MARTIN JACOBO ◽  
PETR ZHEVANDROV
Keyword(s):  
Excellent Agreement ◽  
Bound States ◽  
Analytical Approach ◽  
Numerical Results ◽  
Numerical Verification ◽  
Analytical Results ◽  
Perturbative Method

We study bound states in weakly deformed and heterogeneous waveguides, and compare analytical predictions using a recently developed perturbative method with precise numerical results for three different configurations: a homogeneous asymmetric waveguide, a heterogenous asymmetric waveguide and a homogeneous broken strip. We have found excellent agreement between the analytical and numerical results in all the examples; this provides a numerical verification of the analytical approach.

Effective Elastic Constants for Thick Perforated Plates With Square and Triangular Penetration Patterns

1971 ◽  
Vol 93 (4) ◽  
pp. 935-942 ◽  
Author(s):  
T. Slot ◽  
W. J. O’Donnell
Keyword(s):  
Plane Strain ◽  
Elastic Constants ◽  
Plane Stress ◽  
Numerical Results ◽  
Exact Formulation ◽  
Perforated Plates ◽  
Effective Elastic Constants ◽  
Wide Range ◽  
The Relationship ◽  
Generalized Plane Strain

An exact formulation is presented of the relationship between the effective elastic constants for thick perforated plates (generalized plane strain) and thin perforated plates (plane stress). Extensive numerical results covering a wide range of ligament efficiencies and Poisson’s ratios are given for plates with square and triangular penetration patterns.

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