J. Lubliner

A plastic-damage model for concrete

In this paper a constitutive model based on an internal variable-formulation of plasticity theory for the non-linear analysis of concrete is presented. The model uses a new yield criterion which matches experimental data quite well and it accounts for both elastic and plastic stiffness degradations effects. Onset and amount of cracking can be studied by a simple postprocessing of the finite-element plasticity solution. The accuracy of the model is checked with some examples of application.

A constitutive model for anisotropic damage in fiber-composites

Abstract A constitutive model for anisotropic damage is developed to describe the elastic-brittle behavior of fiber-reinforced composites. The main objective of the paper focuses on the relationship between damage of the material and the effective elastic properties for the purpose of stress analysis of structures. A homogenized continuum is adopted for the constitutive theory of anisotropic damage and elasticity. Internal variables are introduced to describe the evolution of the damage state under loading and as a subsequence the degradation of the material stiffness. The corresponding rate-equations are subjected to the laws of thermomechanics. Emphasis is placed on a suitable coupling among the equations for the rates of the damage variables with respect to different damage modes. Evolution equations for the progression of the passive damage variables complete the kinetic equations. Most material parameters are obtained from uniaxial and simple shear tests as demonstrated by the example.

Shape-memory alloys: macromodelling and numerical simulations of the superelastic behavior

Shape-memory alloys show features not present in materials traditionally used in engineering; as a consequence, they are the basis for innovative applications. A review of the available literature shows a dearth of computational tools to support the design process of shape-memory-alloy devices. A major reason is that conventional inelastic models do not provide an adequate framework for representing the unusual macrobehavior of shape-memory materials. The present work focuses on a new family of inelastic models, based on an internal-variable formalism and known as generalized plasticity. Generalized plasticity is adopted herein as framework for the development of one- and three-dimensional constitutive models for shape-memory materials. The proposed constitutive models reproduce some of the basic features of shape-memory alloys, such as superelasticity, different material behavior in tension and compression, and the single-variant-martensite reorientation process. For isothermal conditions the implementation of the model in a finite-element scheme and the form of the algorithmically consistent tangent are discussed in detail. Numerical simulations of typical tests performed on shape-memory materials (e.g. uniaxial loading, four-point bending and three-point bending tests) are presented and compared with available experimental data. Based on the overall developments, it appears that the proposed approach is a viable basis for the development of an effective computational tool to be used in the simulation of shape-memory-alloy devices.

On the thermodynamic foundations of non-linear solid mechanics

Abstract Non-equilibrium thermodynamics with internal variables governed by rate equations is explored as a foundation for non-linear solid mechanics. Rate equations are studied as to type, yielding descriptions of viscoelastic, viscoplastic, and plastic behavior. The special case of uncoupled instantaneous elasticity is considered, as well as materials exhibiting combined behavior.

Generalized plasticity and shape-memory alloys

The theory of the generalized plasticity model is reviewed. A special form for multiaxial behavior, based on the Drucker-Prager flow potential, is proposed. The model is applied to a simplified representation of the behavior of shape-memory alloys, with numerical examples.

A maximum-dissipation principle in generalized plasticity

SummaryIt is shown that in large-deformation generalized plasticity a local maximum-dissipation postulate is equivalent to the condition that the plastic strain rate (in the sense of Rice) cannot oppose the total strain rate, when strain space is regarded as a Riemannian manifold with the instantaneous Lagrangian tangent elastic stiffness as the metric tensor. From this condition, normality conditions in strain space (in this sense) and in the space of the second Piola-Kirchhoff stress (in the usual sense) are derived. With the additive decomposition of strain, the loading surface has essentially the same properties as in infinitesimal-strain plasticity. For the multiplicative decomposition, approximate normality rules are derived.

On the one-dimensional theory of blood flow in the larger vessels

Abstract A theory of one-dimensional flow is derived to include outflow due to branching and/or vessel permeability. A result of the derivation is that an outflow term appears in the momentum balance as well as the equation of mass conservation. Even in a simplified version of the momentum balance the outflow term remains, a fact evidently unnoticed thus far, and it is proposed that this equation replace that previously used. The derivation proceeds without resource to assumptions of axisymmetry, broadening the field of potential applications of the theory to the venous circulation, and it is shown that only a minor change is engendered by this generalization.

On the structure of the rate equations of materials with internal variables

SummaryRate equations for internal variables are not invariant under transformations to other sets of internal variables if such transformations involve the external variables (deformation, temperature), unless the rate equations include the rates of the external variables as well. The simplest invariant rate equations are linear in the external-variable rates; for materials with such rate equations, thermodynamic relations are studied, and conditions are obtained for the reducibility of such rate equations to a form without external-variable rates. Materials with plastic behavior have rate equations that are piecewise linear in the external-variable rates, and thermodynamic relations for such materials are studied as well.ZusammenfassungGeschwindigkeitsgleichungen der inneren Zustandsvariablen sind nicht invariant gegen Transformation auf andere innere Zustandsvariable, wenn diese Transformation äußere Zustandsvariable (Deformation, Temperatur) einschließt, außer die Geschwindigkeitsgleichungen enthalten auch Ableitungen äußerer Zustandsvariablen nach der Zeit. Die einfachsten invarianten Geschwindigkeitsgleichungen sind linear in den Ableitungen der äußeren Zustandsvariablen. Für durch solche Gleichungen beschreibbare Werkstoffe werden thermodynamische Beziehungen untersucht und Bedingungen für die Reduzierbarkeit dieser Geschwindigkeitsgleichungen auf Formen, die keine Ableitungen äußerer Zustandsvariablen enthalten, abgeleitet. Werkstoffe mit plastischem Verhalten besitzen Geschwindigkeitsgleichungen, die abschnittsweise linear in den Ableitungen der äußeren Zustandsvariablen sind. Thermodynamische Beziehungen solcher Stoffe werden ebenfalls untersucht.

Normality rules in large-deformation plasticity

Abstract It is shown that in large-deformation plasticity the maximum-dissipation postulate is equivalent to a six-dimensional and not a nine-dimensional normality rule, just as in small-deformation plasticity.

Stressed mirror polishing. 1: A technique for producing nonaxisymmetric mirrors

The theoretical basis is developed for a technique to fabricate nonaxisymmetric mirrors. Stresses are applied to a mirror blank that would have the effect of elastically deforming a desired surface into a sphere. A sphere is then polished into the blank, and upon release of the applied stress, the spherical surface deforms into the desired one. The method can be applied iteratively, so arbitrary accuracy should be possible. Calculations of the stresses and deformations are carried out in detail for an off-axis section of a paraboloid. For a very general class of surfaces, it is sufficient to only impose appropriate stresses at the edge of the blank plus a uniform pressure on the back.