Elastic-Plastic Stress Field in a Coated Continuous Fibrous Composite Subjected to Thermomechanical Loading

1999 ◽  
Vol 66 (3) ◽  
pp. 750-757 ◽  
Author(s):  
L. You ◽  
S. Long ◽  
L. Rohr
Keyword(s):  
Stress Field ◽  
Governing Equation ◽  
Yield Criterion ◽  
Fibrous Composite ◽  
Closed Form Solution ◽  
Metallic Matrix ◽  
Form Solution ◽  
Concentric Cylinders ◽  
The Matrix ◽  
Strain Relationship

A micromechanics investigation was performed in the present work to analyze the stress field in a coated continuous fibrous composite subjected to thermal and mechanical loading based on a four-concentric-cylinders model. A temperature-independent stress-plastic strain relationship for the metallic matrix and coating layer with linear strain-hardening behaviour were introduced. Tresca’s yield criterion and the associated flow law were employed to derive the governing equation of the coating and matrix. The closed-form solution of the governing equation was obtained. Some numerical examples were given. The numerical results indicate that the plasticity of the coating greatly decreases the circumferential and axial stresses in the coating itself, but has very limited influence on the stresses in other constituents of the composite. The plasticity of the matrix imposes no significant influence on all the stresses in the composite.

scholarly journals A Novel Closed-Form Solution for Circular Openings in Generalized Hoek-Brown Media

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Qing Xiang Meng ◽  
Wei Wang
Keyword(s):  
Rock Mass ◽  
Closed Form ◽  
Hydrostatic Stress ◽  
Yield Criterion ◽  
Closed Form Solution ◽  
Form Solution ◽  
Preliminary Design ◽  
Exact Integration ◽  
Sensitive Factor ◽  
Brittle Rock Mass

A novel closed-form solution is presented in this paper for the estimation of displacements around circular openings in a brittle rock mass subject to a hydrostatic stress field. The rock mass is assumed to be elastic-brittle-plastic media governed by the generalized Hoek-Brown yield criterion. The present closed-form solution was validated by employing the existing analytical solutions. Results of several example cases are analyzed to show that, with the simplified assumption, a novel closed-form solution is derived and found to be in an excellent agreement with those obtained by using the exact integration method with mathematical software. Parametric sensitivity analysis is carried out and the parameterartends to be the sensitive factor. As a closed-form solution that does not require transformation technique and the use of any numerical method, this work can provide a better choice in the preliminary design for circular opening.

Eigenstresses in Anisotropic Films

1991 ◽  
Vol 239 ◽  
Author(s):  
Ferdinando Auricchio ◽  
Mauro Ferrari
Keyword(s):  
Stress Field ◽  
Experimental Determination ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Ceramic Film ◽  
Stress States ◽  
Resultant Stress ◽  
Structural Theories

ABSTRACTA closed-form solution for a macroscopically homogeneous, fully anisotropie layer subject to non-uniform through-thickness eigenstrain is presented, and employed in determining the three-dimensional deformation and stress states of a thermally loaded ceramic film with microstructure-induced macroscopic anisotropy. The resultant stress field is compared with those that could be deduced by experimental determination of the curvature and the classical structural theories.

AN INNOVATIVE SOLUTION IN CLOSED FORM AND NUMERICAL ANALYSIS FOR DISSIMILAR ELLIPTICAL INCLUSION IN PLANE ELASTICITY

2014 ◽  
Vol 06 (06) ◽  
pp. 1450080 ◽  
Author(s):  
Y. Z. CHEN
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Plane Elasticity ◽  
Form Solution ◽  
Complex Potentials ◽  
Infinite Matrix ◽  
Elliptical Inclusion ◽  
The Matrix ◽  
Innovative Solution ◽  
Remote Loading

This paper provides a closed form solution for dissimilar elliptical inclusion in plane elasticity. A dissimilar elliptical inclusion is embedded in the infinite matrix with different elastic properties. The infinite matrix is applied by the constant remote loading. Complex variable method is used and two sets of the complex potentials are assumed in the analysis. One set is used for the matrix portion, and other for the inclusion portion. Catching the idea from the eigenstrain problem, we can assume the stresses in the inclusion to be constant. From the continuity conditions for stresses and displacements along the interface, we can get the two sets of the complex potentials in a closed form. In the analysis, an adequate form of the complex potential defined in the elliptical inclusion portion is analyzed in detail.

Effective Yield Criterion Accounting for Microvoid Coalescence

2013 ◽  
Vol 81 (3) ◽  
Author(s):  
A. Amine Benzerga ◽  
Jean-Baptiste Leblond
Keyword(s):  
Boundary Conditions ◽  
Limit Analysis ◽  
Yield Criterion ◽  
Closed Form Solution ◽  
Yield Function ◽  
Form Solution ◽  
Homogenization Theory ◽  
Porous Solids ◽  
Microvoid Coalescence ◽  
Effective Yield

An effective yield function is derived for a porous ductile solid near a state of failure by microvoid coalescence. Homogenization theory combined with limit analysis are used to that end. A cylindrical cell is taken to contain a coaxial cylindrical void of finite height. Plastic flow in the intervoid matrix is described by J2 theory while regions above and below the void remain rigid. Velocity boundary conditions are employed which are compatible with an overall uniaxial straining for the cell, a postlocalization kinematics that is ubiquitous during the coalescence of neighboring microvoids in rate-independent solids. Such boundary conditions are not of the uniform strain rate kind, as is the case for Gursonlike models. A similar limit analysis problem for a square-prismatic cell containing a square-prismatic void was posed long ago (Thomason, P. F., 1985, “Three-Dimensional Models for the Plastic Limit–Loads at Incipient Failure of the Intervoid Matrix in Ductile Porous Solids,” Acta Metallurgica, 33, pp. 1079–1085). However, to date a closed-form solution to this problem has been lacking. Instead, an empirical expression of the yield function proposed therein has been widely used in the literature. The fully analytical expression derived here is intended to be used concurrently with a Gursonlike yield function in numerical simulations of ductile fracture.

Closed-form solution of Cattaneo equation including volumetric source in relation to laser short-pulse heating

2011 ◽  
Vol 89 (7) ◽  
pp. 761-767 ◽  
Author(s):  
H. Al-Qahtani ◽  
B.S. Yilbas
Keyword(s):  
Stress Field ◽  
Closed Form ◽  
Short Pulse ◽  
Closed Form Solution ◽  
Transformation Method ◽  
Substrate Material ◽  
Form Solution ◽  
Cooling Period ◽  
Wave Nature ◽  
Heating Model

The wave nature of the heating model is considered, incorporating the Cattaneo equation with the presence of a volumetric heat source. The volumetric heat generation resembles the step input laser short-pulse intensity. The governing of the heat equation is solved analytically using the Laplace transformation method. The stress field generated due to thermal contraction and expansion of the substrate material is formulated and the closed-form solution is presented. It is found that the wave nature of the heating is dominant during the period of the irradiated short-pulse; however, in the late cooling period, the wave nature of heating is replaced by diffusional heat conduction, governed by Fourier’s law. The stress field during the heating cycle is compressive and becomes tensile in the cooling cycle.

Ultimate Carrying Capacity of Elastic-Plastic Plates on a Pasternak Foundation

2014 ◽  
Vol 81 (5) ◽  
Author(s):  
L. Lanzoni ◽  
E. Radi ◽  
A. Nobili
Keyword(s):  
Yield Criterion ◽  
Plastic Region ◽  
Closed Form Solution ◽  
Form Solution ◽  
Flow Rule ◽  
Plastic Behavior ◽  
Elastic Plastic ◽  
Plastic Mechanism ◽  
Pasternak Elastic Foundation ◽  
Loaded Area

In the present work, the problem of an infinite elastic perfectly plastic plate under axisymmetrical loading conditions resting on a bilateral Pasternak elastic foundation is considered. The plate is assumed thin, thus making it possible to neglect the shear deformation according to the classical Kirchhoff theory. Yielding is governed by the Johansen's yield criterion with associative flow rule. A uniformly distributed load is applied on a circular area on the top of the plate. As the load is increased, a circular elastic-plastic region spreads out starting from the center of the loaded area, whereas the outer unbounded region behaves elastically. Depending on the size of the loaded area, a further increase of the load may originate two or three different elastic-plastic regions, corresponding to different yield loci. A closed form solution of the governing equations for each region is found for a special value of the ratio between Pasternak soil moduli. The performed analysis allows us to estimate the elastic-plastic behavior of the plate up to the onset of collapse, here defined by the formation of a plastic mechanism within the plate. The corresponding collapse load and the sizes of the elastic-plastic regions are thus found by imposing the boundary and continuity conditions between the different regions. The influence of the soil moduli, plate bending stiffness, and size of the loaded area on the ultimate bearing capacity of the plate is then investigated in detail.

Failure in Mohr–Coulomb soil cavities

2001 ◽  
Vol 38 (6) ◽  
pp. 1314-1320 ◽  
Author(s):  
A Gesualdo ◽  
V Minutolo ◽  
L Nunziante
Keyword(s):  
Yield Criterion ◽  
Closed Form Solution ◽  
Soft Rock ◽  
Optimization Procedure ◽  
Form Solution ◽  
Flow Rule ◽  
Upper Bound Theorem ◽  
Theoretical Formulation ◽  
Bound Theorem ◽  
Associated Flow Rule

In many cavities, resulting from both natural excavation and anthropic action, the phenomenon of the collapse of blocks from the cavity roof presents a serious safety hazard. In a previous publication the authors proposed a method to calculate the shape and dimensions of the collapsing block by means of the upper bound theorem of the plasticity theory. The soft rock material was modelled by means of the Mohr–Coulomb yield criterion, and the associated flow rule was considered for strain plastic velocity. The linear yield criterion was suitably regularized by means of a circle in the tensile zone. The boundary of the collapsing block is described by a paraboloid surface. An optimization procedure formulated in standard Kuhn–Tucker form and an analytical solution were obtained. The above-mentioned algorithm has been successfully applied to common soils of southern Italy. To validate the theoretical formulation, several numerical tests are performed. These tests show an optimal agreement with the closed-form solution. Therefore the proposed modelling may be used as an efficient guideline for the cavity-strengthening design.Key words: roof stability, regularized Mohr–Coulomb material, limit analysis, failure mechanics.

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