Finite plastic constitutive laws for finite deformations

Bergander, H.

doi:10.1007/bf01176818

Cited by 7 publications

(3 citation statements)

References 21 publications

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“…(31)] are not major-symmetric. Bergander [5] mentions that Kichhoffs stress tensor J~ is routinely used in modern constitutive models, though sometimes without any justification other than convenience. The above discussion shows that using specific stress (or Kirchhoffs stress tensor, Jg) endows an appealing major symmetriy to the conjugate modulus tensor.…”

Section: Major-symmetry Of Tangent Tensorsmentioning

confidence: 99%

Caveats concerning conjugate stress and strain measures for frame indifferent anisotropic elasticity

Brannon

1998

Acta Mechanica

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Summary. Small-distortion constitutive laws are often extemporaneously generalized to large deformations by merely applying them in the unrotated material frame or, equivalently, by using polar rates. This approach does render the resulting constitutive model indifferent to large superimposed rigid rotations, but it may lead to incorrect predictions for both the magnitude and direction of stress whenever there is significant material distortion. To demonstrate this claim, an exact large-deformation solution is derived for the stress in an idealized fiber-reinforced composite. This example shows that the Cauchy tangent stiffness tensor (corresponding to the conjugate pair of Cauchy stress and the symmetric part of the velocity gradient) must evolve in both magnitude and direction whenever the material distorts. Volume changes necessarily lead to a loss of major-symmetry of this Cauchy tangent stiffness tensor, which can be rectified by instead using specific or Kirchhoff stress. A previous work that correctly pointed out the need for the Cauchy stiffness tensor to distort is shown to have overlooked an additional contribution from the rate of distortion. Some of the anomalous properties of the Cauchy stiffness tensor are eradicated by instead using the second Piola-Kirchhoff stress or, equivalently, convected coordinates. Such an approach, however, demands accurate measurements of large-distortion material response, not only to obtain physically realistic results, but also to avoid potential instabilities in numerical computations.

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Section: Major-symmetry Of Tangent Tensorsmentioning

confidence: 99%

Caveats concerning conjugate stress and strain measures for frame indifferent anisotropic elasticity

Brannon

1998

Acta Mechanica

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“…So, in the strength theory, the Tsa-Wu criterion has a tensor polynomial (see, e.g., [272]) failure surface depending on stresses. The onset of yielding in some cases of elastic-plastic materials has also a quadratic yield condition (see, e.g., [26]) generalizing some classical criteria, as, for example, the von Mises equivalent stress criterion. Stress potential in power-law creep is a nonlinear function of equivalent stresses (see, e.g., [42], [59], [233]).…”

Section: Estimation Of Field Fluctuations and Effective Energy-based ...mentioning

confidence: 99%

Peridynamic Micromechanics of Random Structure Composites

Buryachenko¹

2012

Local and Nonlocal Micromechanics of Heterogeneous Materials

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We consider a static peridynamic (proposed by Silling, see J. Mech. Phys. Solids 2000; 48:175-209) composite materials (CMs) of both the random and periodic structures. In the framework of the second background of micromechanics (also called computational analytical micromechanics, CAM), one proved that local micromechanics (LM) and peridynamic micromechanics (PM) are formally similar to each other for CM of both random and periodic structures. It allows straightforward generalization of LM methods to their PM counterparts. It turns out that a plurality of micromechanics phenomena [e.g. statistically homogeneous and inhomogeneous media, inhomogeneous loading (inhomogeneous body force is included), nonlinear and nonlocal constitutive laws of phases, and coupled physical phenomena] can be analyzed by one universal tool (called CAM), which is sufficiently flexible and based on physically clear hypotheses that can be modified and improved if necessary (up to abandonment of these hypotheses) in the framework of a unique scheme for analyses of a wide class of mentioned problems. The schemes of these approaches are considered in the current paper.

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“…[49]) failure surface depending on stresses. Onset of yielding in the some case of elastic-plastic composites has also a quadratic yield condition (see, e.g., [7]) generalizing some classical criteria, as, for example, the von Mises equivalent stress criterion. Stress potential in power-law creep is a nonlinear function of equivalent stresses (see, e.g.…”

Section: Introductionmentioning

confidence: 99%

Estimations of Effective Energy-Based Criteria in Nonlinear Phenomena in Peridynamic Micromechanics of Random Structure Composites

Buryachenko¹

2023

J Peridyn Nonlocal Model

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The basic feature of the peridynamic model considered is a continuum description of a material behavior as the integrated nonlocal force interactions between infinitesimal particles. In contrast to these classical local and nonlocal theories, the peridynamic equation of motion introduced by Silling (J. Mech. Phys. Solids 2000; 48:175-209) is free of any spatial derivatives of displacement. For random structure composite materials (CMs) being considered, a linearized theory of bond-based peridynamics was proposed before for multiphase constituents of arbitrary geometry. It is demonstrated that many nonlinear phenomena (such as, e.g. plasticity, damage, and fatigue) in both local micromechanics and peridynamic one are described by energy-based criteria which are, in its turn, depend on the second moments of the local fields. Analyses of these nonlinear phenomena in peridynamics imply the availability of the direct numerical simulation that is only possible for CMs of deterministic structure (e.g. either a finite sample or periodic structure CMs). Consideration of random structure CMs with nonlinear phenomena requires an acceptance of some additional assumptions. The corresponding approaches in local micromechanics are well developed. A goal of the current study is bridging the gap between the linearized peridynamic micromechanics gathering momentum and a wide class of nonlinear phenomena for random structure CMs. It is performed by a straightforward generalization of the concept of the field second moments (used in energy-based criteria) developed before in nonlinear local micromechanics to their peridynamic counterparts. The method proposed is most advantageously applicable due to identity (with an accuracy to notations) of the operator forms of the new general integral equations (GIEs) for both the local micromechanics of random structure CMs and peridynamic one.

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Finite plastic constitutive laws for finite deformations

Cited by 7 publications

References 21 publications

Caveats concerning conjugate stress and strain measures for frame indifferent anisotropic elasticity

Caveats concerning conjugate stress and strain measures for frame indifferent anisotropic elasticity

Peridynamic Micromechanics of Random Structure Composites

Estimations of Effective Energy-Based Criteria in Nonlinear Phenomena in Peridynamic Micromechanics of Random Structure Composites

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