On the Construction of Constitutive Equations for Orthotropic Materials with Different Properties under Tension and Compression in Creep

2020 ◽  
Keyword(s):  
Constitutive Equations ◽  
Orthotropic Materials ◽  
Tension And Compression

A Fracture Theory for Brittle Anisotropic Materials

1974 ◽  
Vol 96 (2) ◽  
pp. 91-96 ◽  
Author(s):  
T. G. Priddy
Keyword(s):  
Orthotropic Materials ◽  
Necessary Condition ◽  
Material Strength ◽  
Interaction Coefficients ◽  
Cubic Equation ◽  
Simple Cubic ◽  
Failure Theory ◽  
Tension And Compression ◽  
Fracture Theory ◽  
Macroscopic Failure

This paper outlines the development of a general macroscopic failure theory. The result is a relatively simple cubic equation where interaction coefficients for tension-tension and compression-compression strengths may be defined separately. Approximations for biaxial and triaxial normal stress interactions are included to reduce the number of experimental data to nine for brittle three-dimensionally orthotropic materials and to two for brittle isotropic materials. A necessary condition that the theory closely describe brittle isotropic material strength is satisfied for a comprehensive set of cast iron biaxial strength data. The surface is graphically illustrated for various materials.

Thermal Elastic Constitutive Equation of Orthotropic Materials

2017 ◽  
Vol 863 ◽  
pp. 93-101
Author(s):  
Chen Li ◽  
Hai Ren Wang ◽  
Yan An Miao ◽  
Li Zhao
Keyword(s):  
Constitutive Equation ◽  
Elastic Constant ◽  
Elastic Constants ◽  
Representation Theorem ◽  
Constitutive Equations ◽  
Orthotropic Materials ◽  
Tensor Function ◽  
Tensor Method ◽  
Scalar Invariant ◽  
Depth Study

In the finite deformation range, the numbers of orthotropic 2n order elastic constants are studied on the basis of tensor function and of its representation theorem. On the basis of elastic constant research, the elastic orthotropic constitutive equation is derived by using the tensor method. Based on orthotropic elastic constitutive equations an in-depth study on the constitutive theory of orthotropic nonlinear thermal elasticity is carried out, and by considering the deformation produced by the coupling of temperature and load, nonlinear orthotropic thermoelastic constitutive equation is further derived with representation of the tensor invariant and scalar invariant. The constitutive equations could be used very convenient to the application in reality.

A Viscoplastic Constitutive Theory for Monolithic Ceramics—I

1998 ◽  
Vol 120 (1) ◽  
pp. 155-161 ◽  
Author(s):  
L. A. Janosik ◽  
S. F. Duffy
Keyword(s):  
Potential Function ◽  
Constitutive Equations ◽  
Hydrostatic Stress ◽  
Functional Dependence ◽  
Threshold Function ◽  
Cauchy Stress ◽  
Creep Stress ◽  
Flow Potential ◽  
Tension And Compression ◽  
Monolithic Ceramics

This paper, which is the first of two in a series, provides an overview of a viscoplastic constitutive model that accounts for time-dependent material deformation (e.g., creep, stress relaxation, etc.) in monolithic ceramics. Using continuum principles of engineering mechanics, the complete theory is derived from a scalar dissipative potential function first proposed by Robinson (1978), and later utilized by Duffy (1988). Derivations based on a flow potential function provide an assurance that the inelastic boundary value problem is well posed, and solutions obtained are unique. The specific formulation used here for the threshold function (a component of the flow potential function) was originally proposed by Willam and Warnke (1975) in order to formulate constitutive equations for time-independent classical plasticity behavior observed in cement and unreinforced concrete. Here constitutive equations formulated for the flow law (strain rate) and evolutionary law employ stress invariants to define the functional dependence on the Cauchy stress and a tensorial state variable. This particular formulation of the viscoplastic model exhibits a sensitivity to hydrostatic stress, and allows different behavior in tension and compression.

Constitutive equations of creep under changing multiaxial stresses for materials with different behavior in tension and compression

2004 ◽  
Vol 68 (4) ◽  
Author(s):  
A. Zolochevsky ◽  
S. Sklepus ◽  
Yu. Kozmin ◽  
A. Kozmin ◽  
D. Zolochevsky ◽  
...  
Keyword(s):  
Constitutive Equations ◽  
Tension And Compression
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