Shock Loading of Heteromodular Elastic Materials under Plane-Strain Condition

2021 ◽  
Vol 887 ◽  
pp. 634-639
Author(s):  
Olga V. Dudko ◽  
Alexandr A. Mantsybora
Keyword(s):  
Plane Strain ◽  
Shock Loading ◽  
Plane Shock ◽  
Elastic Materials ◽  
Deformation Properties ◽  
Tension And Compression ◽  
Isotropic Elasticity ◽  
Self Similar ◽  
Stress Dependent ◽  
Quasi Longitudinal Wave

The paper discusses the results of mathematical modeling the two-dimensional nonlinear dynamics of heteromodular elastic materials. The resistance of these materials under tension and compression is various. The deformation properties of the heteromodular medium are described within the framework of the isotropic elasticity theory with stress-dependent elastic moduli. In the plane strain case, it is shown that only two types of the nonlinear deformation waves can appear in the heteromodular elastic materials: a plane-polarized quasi-longitudinal wave and a plane-polarized quasi-transverse wave. Basing on obtained properties of the plane shock waves, two plane self-similar boundary value problems are formulated and solved.

On expansion waves generated by the refraction of a plane shock at a gas interface

1967 ◽  
Vol 30 (2) ◽  
pp. 385-402 ◽  
Author(s):  
L. F. Henderson
Keyword(s):  
Expansion Wave ◽  
Plane Shock ◽  
Wave System ◽  
Expansion Waves ◽  
Reflected Wave ◽  
Expansion Fan ◽  
New Type ◽  
Self Similar ◽  
Fixed Boundaries ◽  
Mapping Theory

The paper deals with the regular refraction of a plane shock at a gas interface for the particular case where the reflected wave is an expansion fan. Numerical results are presented for the air–CH4 and air–CO2 gas combinations which are respectively examples of ‘slow–fast’ and ‘fast–slow’ refractions. It is found that a previously unreported condition exists in which the reflected wave solutions may be multi-valued. The hodograph mapping theory predicts a new type of regular–irregular transition for a refraction in this condition. The continuous expansion wave type of irregular refraction is also examined. The existence of this wave system is found to depend on the flow being self-similar. By contrast the expansion wave becomes centred when the flow becomes steady. Transitions within the ordered set of regular solutions are examined and it is shown that they may be either continuous or discontinuous. The continuous types appear to be associated with fixed boundaries and the discontinuous types with movable boundaries. Finally, a number of almost linear relations between the wave strengths are noted.

Damage and healing mechanics in plane stress, plane strain, and isotropic elasticity

2020 ◽  
Vol 29 (8) ◽  
pp. 1246-1270 ◽  
Author(s):  
George Z Voyiadjis ◽  
Chahmi Oucif ◽  
Peter I Kattan ◽  
Timon Rabczuk
Keyword(s):  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Elastic Energy ◽  
Elastic Stiffness ◽  
Self Healing ◽  
Theoretical Formulation ◽  
Stiffness Reduction ◽  
Energy Equivalence ◽  
Isotropic Elasticity

The present paper presents a theoretical formulation of different self-healing variables. Healing variables based on the recovery in elastic modulus, shear modulus, Poisson's ratio, and bulk modulus are defined. The formulation is presented in both scalar and tensorial cases. A new healing variable based on elastic stiffness recovery in proposed, which is consistent with the continuum damage-healing mechanics. The evolution of the healing variable calculated based on cross-section as function of the healing variable calculated based on elastic stiffness is presented in both hypotheses of elastic strain equivalence and elastic energy equivalence. The components of the fourth-rank healing tensor are also obtained in the case of isotropic elasticity, plane stress, and plane strain. It is found that the healing variable calculated based on elastic stiffness reduction is greater than the one calculated based on cross-section reduction in the case of the hypothesis of elastic energy equivalence. It is also shown that the healing tensor fits the boundary conditions of the healing variable in the case of scalar formulation.

Mechanics of Foamed Elastic Materials

1963 ◽  
Vol 36 (3) ◽  
pp. 597-610 ◽  
Author(s):  
A. N. Gent ◽  
A. G. Thomas
Keyword(s):  
Three Dimensional ◽  
Theoretical Treatment ◽  
Viscous Damping ◽  
Elastic Materials ◽  
Dimensional Network ◽  
Closed Cell ◽  
Tension And Compression ◽  
Flow Through ◽  
Open Cell Foams ◽  
Small Deformations

Abstract The deformation of a foamed elastic material, both in tension and compression, and its resistance to tearing and to tensile rupture, have recently been derived on the basis of a model consisting of a large number of thin threads joined at their ends to form a three-dimensional network. A general account of this theoretical treatment, and the evidence for it, is presented. The theory is extended to deal with small deformations of closed-cell foams; relations for Young's modulus and Poisson's ratio are derived. The viscous damping of open-cell foams due to air flow through the network of threads is also discussed.

Measurement of rock elastic moduli in tension and in compression and its practical significance

1993 ◽  
Vol 30 (2) ◽  
pp. 338-347 ◽  
Author(s):  
B. Stimpson ◽  
Rui Chen
Keyword(s):  
Compressive Loading ◽  
Practical Significance ◽  
Published Data ◽  
Test Results ◽  
Compression Tests ◽  
Testing Technique ◽  
Tension Tests ◽  
Underground Openings ◽  
Deformation Properties ◽  
Tension And Compression

The moduli of deformation of rock in tension and in compression are generally assumed equal. However, many rocks show different deformation properties when loaded in tension and in compression. This property is usually referred to as bimodularity. In this paper, a new testing technique in which moduli in both tension and compression can be measured on the same specimen in the same compressive loading frame is described. Testing results from halite, potash, granite, and limestone indicate that moduli in compression and in tension are different for at least three of these materials. The new testing technique is validated against the standard uniaxial tension and uniaxial compression tests on potash and halite. Also, results from granite by the new testing technique are comparable with previously published data. The practical significance of rock bimodularity is discussed as well. It is demonstrated that this property significantly influences the deflection and stress distribution in a simple beam problem. Bimodularity also influences the interpretation of indirect rock tension test results and the prediction of roof deflection in underground openings. Ignoring bimodularity overestimates rock tensile strength in most of the indirect rock tension tests and underestimates roof deflection. Key words : rock, elastic modulus, bimodularity, testing technique.

scholarly journals Numerical study of an influence of material constants of a heteromodular elastic medium on solutions of plane self-similar problems of shock deformation

2020 ◽  
pp. 180-189
Author(s):  
Ольга Владимировна Дудко ◽  
Александр Анатольевич Манцыбора
Keyword(s):  
Boundary Conditions ◽  
Elastic Medium ◽  
Plane Strain ◽  
Dynamic Behavior ◽  
Dynamic Deformation ◽  
Numerical Study ◽  
Shock Load ◽  
Material Constants ◽  
Self Similar ◽  
Model Equations

В работе представлены результаты численного решения двумерных автомодельных задач динамики деформирования горных пород в условиях плоской деформации. Для описания динамического поведения материалов под действием ударной нагрузки выбрана модель разномодульной изотропно-упругой среды с сингулярной зависимостью между напряжениями и деформациями. Проведена серия вычислительных экспериментов для различных материалов и параметров краевых условий. В результате сделан вывод о существенном влиянии знака материальных констант, отвечающих в модели за проявление разномодульности, на характер решения в целом и поведение возникающих волн деформаций в частности. The paper presents the results of numerical solving 2D self-similar problems of the dynamic deformation of rocks under plane strain conditions. To describe the dynamic behavior of materials in question under the action of a shock load, a model of an isotropic-elastic heteromodular medium with a singular dependence between stresses and deformations is chosen. A series of computational experiments was carried out for various materials and parameters of the boundary conditions. As a result, it has been concluded that the sign of the material constants responsing for the manifestation of different modularity in the model equations has a significant effect on the solution as a whole and the behavior of the arising deformation waves in particular.

Effective Constitutive Equations for Porous Elastic Materials at Finite Strains and Superimposed Finite Strains

2003 ◽  
Vol 70 (6) ◽  
pp. 809-816 ◽  
Author(s):  
V. A. Levin ◽  
K. M. Zingermann
Keyword(s):  
Plane Strain ◽  
Constitutive Equations ◽  
Rigid Motion ◽  
Finite Deformations ◽  
Finite Strains ◽  
Effective Characteristics ◽  
Elastic Materials ◽  
Preliminary Loading ◽  
Nonlinear Elastic

A method is developed for derivation of effective constitutive equations for porous nonlinear-elastic materials undergoing finite strains. It is shown that the effective constitutive equations that are derived using the proposed approach do not change if a rigid motion is superimposed on the deformation. An approach is proposed for the computation of effective characteristics for nonlinear-elastic materials in which pores are originated after a preliminary loading. This approach is based on the theory of superimposed finite deformations. The results of computations are presented for plane strain, when pores are distributed uniformly.

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