A multidimensional anisotropic strength criterion based on Kelvin modes

Arramon, Yves P.; Mehrabadi, Morteza M.; Martin, David W.; Cowin, Stephen C.

doi:10.1016/s0020-7683(98)00338-2

Cited by 40 publications

(22 citation statements)

References 22 publications

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“…This general form of the cubic tensor failure criterion can be shown that encompasses all other failure criteria, which are currently available [9][10][11][12].…”

Section: Mathematical Frameworkmentioning

confidence: 97%

A Simple Heuristic Algorithm to Determine the Set of Closed Surfaces of the Cubic Tensor Polynomial~!2009-04-24~!2009-09-17~!2010-06-09~!

Asteris

2010

TOAMJ

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A simple heuristic algorithm, which determines the set of closed surfaces of the cubic tensor polynomial, is proposed. The algorithm is based on the requirement of positive Gaussian curvature (Stoker's Theorem) for closed surfaces, excluding domains of tensor values, which do not provide closed surface solutions, and focus the search in the remaining domains. The identification of the closed surfaces is an important factor in both theory and applications, such as the failure behavior of anisotropic bodies. An example of applying successfully the algorithm to a material, which has a distinct anisotropic behavior, is presented.

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“…This general form of the cubic tensor failure criterion can be shown that encompasses all other failure criteria, which are currently available [9][10][11][12].…”

Section: Mathematical Frameworkmentioning

confidence: 97%

A Simple Heuristic Algorithm to Determine the Set of Closed Surfaces of the Cubic Tensor Polynomial~!2009-04-24~!2009-09-17~!2010-06-09~!

Asteris

2010

TOAMJ

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“…The normalized stress vector σ and strain vector ε are defined as (Chen 1984;Arramon et al 2000;Kuang et al 2003) σ…”

Section: Normalized Stress and Strain Vectorsmentioning

confidence: 99%

Preliminary Knowledge and Continuum Thermodynamics

Kuang

2013

Theory of Electroelasticity

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In this chapter, some basic knowledge of elastic theory, electrodynamics, and thermodynamics which will be applied in this book are introduced. Some extensions in continuum thermodynamics are proposed. It is shown that together with the first law of thermodynamics, a physical variational principle (PVP) is also held. The physical variational principle gives a true process for all virtual possible process satisfying the geometrical constrained conditions. The physical variational principle is considered to be one of the fundamental physical principles for quasistatic system, which can be used to derive governing equations in continuum mechanics and other fields. When the temperature varies with time, the inertial entropy or inertial heat theory is proposed. This theory is consistent with current classical thermodynamic theory. From this theory, the temperature wave equation with finite phase velocity is derived in a very simple fashion. It is shown that the time arrived to equilibrium of the temperature is about 1 ns $ 1 ps when an internal heat source with a Heaviside step heat function is applied. Keywords Basic knowledge • Physical variational principle • Inertial entropy BackgroundJacques and Pierre Curie brothers discovered the piezoelectric effect in 1880 (Sun and Zhang 1984; Ikeda 1990). They found out that a mechanical stress applied on crystals such as tourmaline, quartz, and Rochelle salt could produce electrical charges, and the voltage was proportional to the stress. Piezoelectric can also work in reverse, generating a strain by the application of an electric field. Centrosymmetric classes of crystals are always not piezoelectric, but a few kinds of crystals are still not piezoelectric though lacking a center of symmetry. The pyroelectric effect was found in eighteenth century (Lang 2005), earlier than piezoelectric effect. Most ferroelectric crystals are strongly piezoelectric and pyroelectric. First applications were piezoelectric ultrasonic submarine detector and quartz clocks

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“…Kuang et al (2003) extended the Kelvin theory (Chen 1984;Ruhlevskii 1984;Arramon et al 2000) to piezoelectric materials. In material there is a direction M, along which Γ and Σ are parallel in the nine-dimensional space.…”

Section: Normalized Generalized Stress and Strain Vectors In Piezoelementioning

confidence: 99%

Failure Theories of Piezoelectric Materials

Kuang

2013

Theory of Electroelasticity

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In this chapter failure experiments and theories in piezoelectric materials are discussed. In present time the precision of experiments should still be improved. The failure theory in solids is very complicated and there is no unified critical criterion. It is clear that the critical energy for different failure version is different. Especially the version of brittle tension failure is significantly different with other versions. In piezoelectric ceramics the failure energy density of an electric field is much higher than that in mechanical loading. In this chapter the generalized stress intensity factor criterions; total, mechanical, and local energy release rate criterions; strain energy density factor criterion; modal strain energy density factor theory; small-scale domain switching theory; failure criterion of conductive cracks with charge-free zone model are studied. Some simple electric breakdown theories of solid dielectrics are also discussed.Keywords Failure theories • Generalized stress intensity factor • Energy release rate • Modal strain energy • Charge-free zone model • Electric breakdown Experimental StudiesThe change of the microstructure, including plastic yielding, phase transformation, and failure theory, in solids is very complicated, and in present time there is no unified critical criterion to show these changes exactly. In general the change of the internal microstructure in the materials is caused by deformation, electromagnetic field and temperature. Experiments show that except the failure under tension, before failure the continuous deformation is revealed and then follows the change of the microstructure, so the failure and plastic yielding, etc. often posses the similar criterion. However, the failure of a brittle material under tension is less connected to the continuous deformation, so it should often be discussed in different theory. The experiments are necessary to get the practical failure criterions in engineering. Many experiments for failure have been carried out. Because the piezoelectric specimens are thin and small, manufacturing an ideal crack is very difficult. Usually the crack

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A multidimensional anisotropic strength criterion based on Kelvin modes

Cited by 40 publications

References 22 publications

A Simple Heuristic Algorithm to Determine the Set of Closed Surfaces of the Cubic Tensor Polynomial~!2009-04-24~!2009-09-17~!2010-06-09~!

A Simple Heuristic Algorithm to Determine the Set of Closed Surfaces of the Cubic Tensor Polynomial~!2009-04-24~!2009-09-17~!2010-06-09~!

Preliminary Knowledge and Continuum Thermodynamics

Failure Theories of Piezoelectric Materials

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