Pablo F. Sanz

On the numerical integration of three-invariant elastoplastic constitutive models

We investigate the performance of a numerical algorithm for the integration of isotropically hardening three-invariant elastoplastic constitutive models with convex yield surfaces. The algorithm is based on a spectral representation of stresses and strains for infinitesimal and finite deformation plasticity, and a return mapping in principal stress directions. Smooth three-invariant representations of the Mohr–Coulombmodel, such as the Lade–Duncan and Matsuoka–Nakai models, are implemented within the framework of the proposed algorithm. Among the specific features incorporated into the formulation are the hardening/softening responses and the tapering of the yield surfaces toward the hydrostatic axis with increasing confining pressure. Isoerror maps are generated to study the local accuracy of the numerical integration algorithm. Finally, a boundary-value problem involving loading of a strip foundation on a soil is analyzed with and without finite deformation effects to investigate the performance of the integration algorithm in a full-scale non-linear finite element simulation. 2002 Elsevier Science B.V. All rights reserved.

Mechanical Modeling of Multi-Layer Sedimentary Rock Folding

Sedimentary rock folding results from a number of mechanisms, including buckling due to lateral tectonic compression and slip on thrust faults in the underlying strata. Movements experienced by folded layers are typically very large and may include significant rigid body translation and rotation, considerable straining, and relative slip at the interface between layers. In this paper we present a mechanical model for capturing isothermal ductile folding processes of sedimentary rocks using nonlinear continuum mechanics and finite deformation contact kinematics. Folding of rock layers with distinct mechanical properties may result in relative tangential slip at the interface between them. Of particular interest is the formulation and implementation of a finite deformation frictional contact model to account for relative sliding of two adjacent rock layers. Our method considers a Coulomb friction law that is suitable for geomaterials. The penalty method is used to implement the frictional contact model [1]. The formulation of the model includes a consistent linearization of the weak form of the linear momentum balance to enable optimal convergence for Newton-Raphson iterations. To capture the ductile response of the rock layers, we implement an elastoplastic constitutive model; a three-invariant yield criterion is used to define plastic loading and a non-associated flow rule to control inelastic dilatancy. To integrate the stresses we employ a fully Lagrangian approach along with multiplicative plasticity theory for finite deformations. This work enables us to investigate the relationship among folded shapes, internal stress state, and the occurrence of deformation bands and/or relative slip at the layer interfaces. Supported by U.S. Department of Energy, Grant No. DEFG02- 03ER15454, and U.S. National Science Foundation, Grant No. CMG-0417521.

Ductile Folding of Sedimentary Rocks

This paper deals with numerical simulations of ductile folding of sedimentary rock layers with kilometer-scale dimensions. We use nonlinear continuum mechanics and the finite element method to understand the mechanics of large deformation leading to strain localization. Rock layers are subjected to combined bending and either extension or compression. Depending on the nature of the accompanying lateral deformation (i.e., whether it is extension or compression), localized deformation can manifest itself at different scales in the deforming mass. These studies are useful for integrating the mechanical and geological concepts and principles in order to formulate models constrained by available geological data.