Numerical formulation for solving soil/tool interaction problem involving large deformation

Purpose – The aim of this work is to provide a global 3D finite element (FE) model devoted to the modelling of superficial soil ploughing in the large deformation range and for a vast class of soil treatment tools. Design/methodology/approach – We introduced soil constitutive equation in a FE software initially designed for the metal forming. We performed the numerical integration of the non‐linear ploughing problem. Non‐linearities encountered by the problem can be summed up: as soil constitutive equation (idealized with non‐associated compressible plastic law), unilateral frictional contact conditions (with a rigid body), geometrical non‐linearities (the ploughing tool) and large deformation range. To handle such difficulties we performed several numerical methods as implicit temporal scheme, Newton‐Raphson, non‐symmetric iterative solver, as well as proper approximation on stress and strain measures. Findings – Main results deal with the validation of the integration of the non‐linear constitutive equation in the code and a parametric study of the ploughing process. The influence of tool geometric parameters on the soil deformation modes and on the force experienced on the tools had been point out. As well, the influence of soil characteristics as compressibility had been analyzed. Research limitations/implications – This research is devoted to perform a numerical model applicable for a large range of soil treatment tools and for a large class of soil. However, taking into account all kind of soil is utopist. So limitations met are essentially related to the limit of the accuracy of the elasto‐plastic idealization for the soil. Practical implications – In practice the numerical model exposed in the paper can clearly help to improve and optimize any process involving superficial soil submitted to the mechanical action of a rigid body. Originality/value – The original value of the paper is to provide a global and an applicable numerical model able to take into account the main topics related to the ploughing of superficial soils. Industrials in geotechnics, in agriculture or in military purposes can benefit in using such numerical model.

[1]  Jean-Loup Chenot,et al.  Numerical formulations and algorithms for solving contact problems in metal forming simulation , 1999 .

[2]  Pieter A. Vermeer,et al.  Time integration of a constitutive law for soft clays , 1999 .

[3]  Gioacchino Viggiani,et al.  Ground movements around excavations in granular soils: a few remarks on the influence of the constitutive assumptions on FE predictions , 2000 .

[4]  Peter Wriggers,et al.  Non-linear finite element analysis of solids and structures, volume 1: Essentials, M. A. Crisfield, John Wiley. ISBN: 0-471-92956-5 , 1994 .

[5]  J. C. Simo,et al.  Consistent tangent operators for rate-independent elastoplasticity☆ , 1985 .

[6]  P. Wriggers.  Finite element algorithms for contact problems , 1995 .

[7]  W. N. Liu,et al.  A re-formulation of the exponential algorithm for finite strain plasticity in terms of cauchy stresses , 1999 .

[8]  J. C. Simo,et al.  Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory , 1992 .

[9]  Cécile Nouguier,et al.  Simulation des interactions outil-sol. Application aux outils de traitement des sols , 1999 .

[10]  Boris Jeremić,et al.  Line search techniques for elasto‐plastic finite element computations in geomechanics , 2001 .

[11]  Pedro Arduino,et al.  Implicit integration of elastoplastic constitutive models for frictional materials with highly non-linear hardening functions , 1997 .

[12]  Thierry Coupez,et al.  Génération de maillage et adaptation de maillage par optimisation locale , 2000 .

[13]  Augustin Gakwaya,et al.  Modeling of the metal powder compaction process using the cap model. Part II: Numerical implementation and practical applications , 2002 .

[14]  R. de Borst,et al.  A unified approach to the implicit integration of standard, non‐standard and viscous plasticity models , 2002 .

[15]  M. Sofonea,et al.  Stress formulation for frictionless contact of an elastic-perfectly-plastic body , 2004 .

[16]  J. Rice,et al.  Finite-element formulations for problems of large elastic-plastic deformation , 1975 .

[17]  Abdul Mounem Mouazen,et al.  A numerical–statistical hybrid modelling scheme for evaluation of draught requirements of a subsoiler cutting a sandy loam soil, as affected by moisture content, bulk density and depth , 2002 .

[18]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[19]  Ronaldo I. Borja,et al.  Cam-Clay plasticity, part I: implicit integration of elastoplastic constitutive relations , 1990 .

[20]  D. Gee-Clough,et al.  Deformation and Failure in Wet Clay Soil: Part 3, Finite Element Analysis of Cutting of Wet Clay by Tines , 1994 .

[21]  Isam Shahrour,et al.  Use of sparse iterative methods for the resolution of three‐dimensional soil/structure interaction problems , 1999 .

[22]  A. Mouazen,et al.  A review of the finite element modelling techniques of soil tillage , 1998 .

[23]  N. Renon.  Simulation numérique par éléments finis des grandes déformations des sols : application à la scarification , 2002 .

[24]  M. Fortin,et al.  A stable finite element for the stokes equations , 1984 .

[25]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[26]  Jean-Luc Bucaille.  Simulation numérique de l'indentation et de la rayure des verres organniques , 2001 .

[27]  Gary F. Dargush,et al.  Finite-element analysis of time-dependent large-deformation problems , 1992 .

[28]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[29]  Roland W. Lewis,et al.  Finite element simulation for dynamic large elastoplastic deformation in metal powder forming , 1998 .

[30]  Jean-Philippe Ponthot,et al.  Unified stress update algorithms for the numerical simulation of large deformation elasto-plastic and elasto-viscoplastic processes , 2002 .

[31]  M. Abu-Farsakh,et al.  Coupled theory of mixtures for clayey soils , 1997 .

[32]  E. H. Lee,et al.  Finite‐Strain Elastic—Plastic Theory with Application to Plane‐Wave Analysis , 1967 .

[33]  M. Crisfield.  Non-Linear Finite Element Analysis of Solids and Structures, Essentials , 1997 .

[34]  B Cambou,et al.  MODELE DE COMPORTEMENT DES SOLS NON COHERENTS , 1988 .