A nonlocal elastoplastic damage theory recently proposed by Valanis (1992) is implemented into a finite element wave code. The model retains hyperbolicity even under strain softening, thus eliminating mesh-sensitivity. Convergence and mesh insensitivity are demonstrated numerically by solving the problem considered by Sandler and Wright (1984).

An efficient second-order numerical scheme is developed for integrating the endochronic plasticity equations of plastically incompressible solids, such as metals, for example. The numerical scheme is appropriate for use with finite element wave propagation codes based upon explicit time integration. Second-order accuracy is achieved by using Richardson extrapolation in connection with explicit integration of the governing equations. It is shown that Richardson extrapolation leads to more than an order of magnitude increase in computing speed over the usual approach, for comparable accuracy.

: The restrictions imposed by thermodynamics and uniqueness on non- associated elasto-plastic solids are explored. The postulates of Drucker and Illiushin are examined and it is shown that they can be violated while the second law of thermodynamics is satisfied. Some of the basic features of non- associated elasto-plastic solids are investigated, including continuity, path dependence and a rather peculiar feature in which the plastic tangent stiffness can exceed the elastic tangent stiffness. The question of uniqueness of initial value problems for non-associated elasto-plastic solids is examined; it is shown that the usual approach for proving uniqueness of associated elasto-plastic solids remains valid when the flow rule is non-associated. Finally, two types of non-associated plastic models that are widely used by the defense community in ground motion simulation studies are considered in detail, and the implication of the restrictions imposed on these models by thermodynamics are discussed. Keywords: Thermodynamics; Elastoplastic solids; Continuity; Path dependence.

An endochronic plasticity theory is developed which is intended to describe the nonlinear inelastic behavior of plain concrete over the stress range where significant cracking does not occur. The theory is isotropic and rate-independent. It exhibits the major features of concrete behavior, including shear-volumetric coupling, effect of hydrostatic compression on shear response, hardening, hysteresis and stress-path dependence. The theory is applied to, and successfully proof-tested against, an extensive set of complex multiaxial stress path data on plain concrete obtained by others using a true triaxial testing device.

Certain fundamental issues concerning the experimental basis for current phenomenological constitutive models of rock and concrete are discussed. Problems related to both quasi-static and dynamic response are treated. Within the first category are included the topics of strain softening, strain hardening, failure states, and failure modes below the brittle-ductile transition. The second category focuses upon the task of determining the strain rate-dependent of material properties.

This report describes the formulation and application of a new three-dimensional, nonlinear constitutive model for soils. The model is developed within the general framework of the Endochronic theory of plasticity with singular kernels, and incorporates basic concepts of critical state soil mechanics. Because of its ability to realistically represent the hysteretic behavior of soils during repeated unload-reload processes, the model is particularly useful for describing the response of soils to earthquake-type loading. Applications of the model to monotonic and cyclic multi-axial data for several drained soils are presented, and comparisons between predicted and measured responses are given.

This paper explores the physical bases of strain softening in rock, soil and concrete, in order to determine if such softening is a true property of these materials, and examines the effect that strain softening has on stress wave propagation in softening materials. It is concluded that the strain softening inferred in the usual manner from conventional laboratory tests is not a true material property of rock, soil and concrete and that strain softening can cause stress wave propagation problems for some softening materials to become ill-posed.

: A new endochronic plasticity model that has the capability to describe both densification and dilatency is described and applied to laboratory data from reconstructed ISST soils generated by the US Army Engineer Waterways Experiment Station. An efficient, explicit numerical scheme is developed for integrating the system of equations which govern the new model, and a corresponding computer program for the numerical scheme is given. In numerical studies conducted with the computer program, it was found that situations arise where the calculated intrinsic time increment takes on inadmissable values; this difficulty does not appear to be of numerical origin but instead due to the particular mathematical representations adopted in the model for some of the material functions. Further study is recommended to explore this problem. Keywords: Endochronic plasticity; Hydrostatic compression tests; Triaxial soil tests; Dilatancy; Endochronic soil models; Ground shock; Shear-induced volume change; Stress-strain relations.

A new endochronic theory of plasticity is presented which can accurately describe the mechanical response of hysteretic materials to complex, three-dimensional deformation histories, including cyclic deformation. The theory is based on several new advancements in the endochronic framework, which broaden its predictive scope. Various features of the resulting model are illustrated, including its ability to describe (1) cyclic simple shear of dry sand and wet clay over many cycles of deformation, (2) response of a real soil (McCormick Ranch soil) to the standard laboratory soil tests, and (3) response of McCormick Ranch soil to cyclic triaxial tests. It is believed that this is the first constitutive model that has demonstrated the capability to realistically describe, for a given soil, both standard laboratory tests and cyclic response under three-dimensional loading conditions. The constitutive model presented here should allow more meaningful analyses to be made in many areas of soil response, particularly for ground motion and soil-structure interaction due to to other seimsic disturbances. The proposed model also has wide application to other materials, such as metals, and could provide improved descriptions of the response of various metallic components under transient loads.

A new endochronic theory of plasticity is presented which can predict accurately the mechanical response of hysteretic materials to complex shear straining histories, including cyclic deformation. The theory is based on a new definition of the intrinsic time measure recently introduced into the endochronic framework, which broadens its predictive scope. The present theory is motivated by considering a one-dimensional parallel assembly of basic endochronic elements, each of which consists of a linear elastic spring attached in series to a nonlinear endochronic slider. The extension of the concept to general three-dimensional states is straightforward and is presented herein. Various unique features of the model are described, and the application of the model to the cyclic response of dry sand is illustrated.