# A mathematical framework for finite strain elastoplastic consolidation. Part 1: Balance laws, variational formulation, and linearization

Borja, Ronaldo I. and Alarcón Álvarez, Enrique (1995). A mathematical framework for finite strain elastoplastic consolidation. Part 1: Balance laws, variational formulation, and linearization. "Computer Methods in Applied Mechanics and Engineering", v. 122 (n. 1-2); pp. 145-171. ISSN 0045-7825. https://doi.org/10.1016/0045-7825(94)00720-8.

## Description

Title: A mathematical framework for finite strain elastoplastic consolidation. Part 1: Balance laws, variational formulation, and linearization Borja, Ronaldo I. Alarcón Álvarez, Enrique Article Computer Methods in Applied Mechanics and Engineering April 1995 0045-7825 122 E.T.S.I. Industriales (UPM) Mecánica Estructural y Construcciones Industriales [hasta 2014] Recognition - No derivative works - Non commercial

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## Abstract

A mathematical formulation for finite strain elasto plastic consolidation of fully saturated soil media is presented. Strong and weak forms of the boundary-value problem are derived using both the material and spatial descriptions. The algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the Kirchhoff pore water pressure. Balance laws are written for the soil-water mixture following the motion of the soil matrix alone. It is shown that the motion of the fluid phase only affects the Jacobian of the solid phase motion, and therefore can be characterized completely by the motion of the soil matrix. Furthermore, it is shown from energy balance consideration that the effective, or intergranular, stress is the appropriate measure of stress for describing the constitutive response of the soil skeleton since it absorbs all the strain energy generated in the saturated soil-water mixture. Finally, it is shown that the mathematical model is amenable to consistent linearization, and that explicit expressions for the consistent tangent operators can be derived for use in numerical solutions such as those based on the finite element method.

Item ID: 15230 http://oa.upm.es/15230/ oai:oa.upm.es:15230 10.1016/0045-7825(94)00720-8 http://www.sciencedirect.com/science/article/pii/0045782594007208 Biblioteca ETSI Industriales 10 May 2013 11:00 21 Apr 2016 15:15

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