STABILITY CONSIDERATIONS FOR ELASTIC-PLASTIC PROCESSES WITH DAMAGE

Classical theory of plasticity is fairly complete with flow rules, convexity of yield surfaces, extremum principles, and the uniqueness theorem. For the strain-hardening plasticity, Drucker’s postulates are established and proven based on the plastic-work and energy principles. Plasticity models have been further applied to heterogeneous and cementitious materials with certain degrees of success. In this paper, the stability statements of strain-hardening and strain-softening processes in concrete are examined by utilizing thermodynamic potential functions in the stress space and by applying Euler’s theorem of homogenous functions. It is shown that by specifying a strain-hardening parameter to account for the plastic strains and a damage parameter to represent the effect of microcracking, the dissipation inequality can be used to establish the Drucker’s stability postulate for the plastic flow within the framework of the internal variable theory of thermodynamics. Using the same approach and assuming uncoupling between plastic flow and microcracking, the formation leads to a softening stability statement for damage processes in concrete.

Internal Variable Theory Formulated by One Extended Potential Function

In the kinetic rate laws of internal variables, it is usually assumed that the rates of internal variables depend on the conjugate forces of the internal variables and the state variables. The dependence on the conjugate force has been fully addressed around flow potential functions. The kinetic rate laws can be formulated with two potential functions, the free energy function and the flow potential function. The dependence on the state variables has not been well addressed. Motivated by the previous study on the asymptotic stability of the internal variable theory by J. R. Rice, the thermodynamic significance of the dependence on the state variables is addressed in this paper. It is shown in this paper that the kinetic rate laws can be formulated by one extended potential function defined in an extended state space if the rates of internal variables do not depend explicitly on the internal variables. The extended state space is spanned by the state variables and the rate of internal variables. Furthermore, if the rates of internal variables do not depend explicitly on state variables, an extended Gibbs equation can be established based on the extended potential function, from which all constitutive equations can be recovered. This work may be considered as a certain Lagrangian formulation of the internal variable theory.

A UNIFIED INELASTICITY AND DAMAGE MECHANICS FOR RUBBER-LIKE MATERIALS

The nonlinearities observed in the behavior of rubber and polymeric materials are influenced not only by the far-field stress conditions but also by the morphology, microstructures, and changes at the meso-level such as kinks, crosslinking, and micro tearing. Considering constants temperature applications, the occurrence of microtearing has a significant contribution on the performance of polymers, soft tissues and other rubber-like materials. In this paper, a unified damage mechanics and nonlinear elasticity approach is presented to model nonlinear behavior of rubber-like materials under constant temperatures. The theory is cast within the general framework of the internal variable theory of thermodynamics with large deformations where the Clausius-Duhem inequality is provoked to develop general damage potential. The strain energy density function is formulated in terms of an effective Lagrangian strain tensor that evolves with cumulative damage as cracking and micro-tearing take places. Piola-Kirchhoff (PK) stress tensor is presented and a new form of the damage response tensor is proposed. The model prediction is illustrated against experimental results with good agreement.

A Creep Damage Model for Rock Mass Based on Internal Variable Theory

The creep damage is discussed within Rice thermodynamic theory with internal state variable (ISV). A viscoelastic-viscoplastic model with damage is derived by giving the complementary energy density function and kinetic equations of ISVs. The viscoelastic equation covers classical component model, and three creep phases with hardening and damage effect can be described by this model. The model parameter cabibration is conducted through uniaxial creep test of analogue material by loading and unloading method. Then intrinsic thermodynamic properties in three creep stages are indicated. The thermodynamic state of material system tends to equilibrate without damage and depart from equilibrate with damage.

High Temperature Deformation Behavior of 8090 Al-Li Alloy

High temperature deformation behavior, especially the superplasticity of an 8090 Al-Li alloy, was studied within the recent framework of the internal variable theory of structural superplasticity. In this study, a series of load relaxation tests were conducted at various temperatures ranging from 200°C to 530°C to obtain the flow curves of log ε˙versus log ε. The effect of grain size was also examined by varying the grain sizes through a proper thermomechanical treatment. The flow curves were found to be composite curves consisting of contributions from grain boundary sliding (GBS) and grain matrix deformation (GMD) at superplastic temperatures. The activation energy obtained for GMD was 124.9 kJ/mole in the temperature range from 470°C to 530°C, very similar to that for self-diffusion in pure Al.