A return map algorithm for general isotropic elasto/visco‐plastic materials in principal spaceRosati, Luciano; Valoroso, Nunziante
doi: 10.1002/nme.970pmid: N/A
We describe a methodology for solving the constitutive problem and evaluating the consistent tangent operator for isotropic elasto/visco‐plastic models whose yield function incorporates the third stress invariant . The developments presented are based upon original results, proved in the paper, concerning the derivatives of eigenvalues and eigenprojectors of symmetric second‐order tensors with respect to the tensor itself and upon an original algebra of fourth‐order tensors obtained as second derivatives of isotropic scalar functions of a symmetric tensor argument . The analysis, initially referred to the small‐strain case, is then extended to a formulation for the large deformation regime; for both cases we provide a derivation of the consistent tangent tensor which shows the analogy between the two formulations and the close relationship with the tangent tensors of the Lagrangian description of large‐strain elastoplasticity. Copyright © 2004 John Wiley & Sons, Ltd.
A new path‐following constraint for strain‐softening finite element simulationsLorentz, E.; Badel, P.
doi: 10.1002/nme.971pmid: N/A
The application of strain‐softening constitutive relations to model the failure modes of real‐life structures is faced to numerical difficulties related to instabilities that appear as sharp snap‐backs of the structural response. A path‐following method has to complement the solution algorithm to achieve convergence despite these critical points. Because of the sharpness of the snap‐backs, it is believed essential that the path‐following constraint distinguish between a purely elastic unloading and a dissipative path. For that purpose, a new constraint based on the maximal value of the elastic predictor for the yield function is proposed. As it is highly non linear, a specific solution algorithm is required. The robustness of this constraint is illustrated by three applications: the study of crack propagations by means of a cohesive zone model, the failure of a structure submitted to nonlocal damage and the simulation of a nonlocal strain‐softening plastic specimen. Copyright © 2004 John Wiley & Sons, Ltd.
Multi‐lithology stratigraphic model under maximum erosion rate constraintEymard, R.; Gallouët, T.; Granjeon, D.; Masson, R.; Tran, Q. H.
doi: 10.1002/nme.974pmid: N/A
Non‐linear single lithology or multi‐lithology diffusion models have been widely used by sedimentologists and geomorphologists in the field of stratigraphic basin simulations to simulate the large scale depositional transport processes of sediments. Nevertheless, as noticed by many authors, erosion and sedimentation processes are non‐symmetric. Soil material must first be produced in situ by weathering processes prior to be transported by diffusion. This is usually taken into account through a prescribed maximum erosion rate of the sediments, but no mathematical description of the coupling with the diffusion model has been proposed so far. In this paper, we introduce a new mathematical formulation for the coupling of the weather limited erosion and the multi‐lithology diffusion models, which appears as a non‐standard free boundary problem for a new variable acting as a limitor of the fluxes. One of the main advantages of this formulation, compared to existing discrete coupling models, is to enable the definition of efficient discretization schemes. A finite volume scheme with implicit time integration is introduced which is proved to be unconditionally stable in the l∞ norm for the sediment thickness, the sediment concentrations in the lithologies, and the flux limitor variables. A Newton algorithm with an iterative computation of the saturated constraints is used to solve efficiently the non‐linear system resulting from the discretization. The efficiency of the model and the numerical scheme is illustrated on 2D and 3D basin simulation examples. Copyright © 2004 John Wiley & Sons, Ltd.
Comparative studies of 3D‐constitutive models for concrete: application to mixed‐mode fracturePivonka, P.; Ožbolt, J.; Lackner, R.; Mang, H. A.
doi: 10.1002/nme.975pmid: N/A
This paper focuses on the predictive capabilities of 3D‐constitutive models for concrete when used for the simulation of mixed‐mode fracture in consequence of shear‐tensile loading. For this purpose, two types of constitutive models are chosen. Models belonging to the first type such as the extended Leon model (ELM) and two multi‐surface models are formulated within the framework of plasticity theory. The ELM (J. Eng. Mech. (ASCE) 1994; 120: 1983–2011), a single‐surface model, accounts for the dependence of the concrete strength on the Lode angle. The first multi‐surface model consists of a tension‐cut‐off for the description of tensile cracking of concrete and a Drucker–Prager surface for the description of compressive failure. To improve the description of concrete cracking, in the second multi‐surface model the tension‐cut‐off function is replaced by three Rankine surfaces. The second type of material models considered in the presented investigation is formulated on the basis of the microplane concept. The performance of the material models is investigated on both the constitutive and the structural level. On the constitutive level, re‐analyses of Willam's test are performed. For the assessment of the model performance on the structural level, a double‐edge‐notched concrete specimen is investigated. Copyright © 2004 John Wiley & Sons, Ltd.