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A rate-independent model for geomaterials under compression coupling strain gradient plasticity and damage

Maicol Caponi, Vito Crismale

Abstract

We study a strain gradient-enhanced version of a model for geomaterials under compression by Marigo and Kazymyrenko (2019) coupling damage and small-strain associative plasticity. We prove that the jumps in time of the plastic variable may happen only along jumps of the damage variable. Moreover, we perform a vanishing-viscosity analysis showing existence of Balanced Viscosity quasistatic solutions à la Mielke-Rossi-Savaré.

A rate-independent model for geomaterials under compression coupling strain gradient plasticity and damage

Abstract

We study a strain gradient-enhanced version of a model for geomaterials under compression by Marigo and Kazymyrenko (2019) coupling damage and small-strain associative plasticity. We prove that the jumps in time of the plastic variable may happen only along jumps of the damage variable. Moreover, we perform a vanishing-viscosity analysis showing existence of Balanced Viscosity quasistatic solutions à la Mielke-Rossi-Savaré.
Paper Structure (12 sections, 25 theorems, 332 equations)

This paper contains 12 sections, 25 theorems, 332 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation
  4. Mathematical framework
  5. Global quasistatic evolutions
  6. Definition and preliminary results
  7. Existence of a global quasistatic evoltion
  8. Continuity in time
  9. Approximate viscous evolutions
  10. Discretization in time
  11. Passage to the limit
  12. Balanced viscosity (BV) solutions

Key Result

Lemma 2.5

The functional $\mathcal{H}$ is lower semicontinuous in $L^1(\Omega;\mathbb M^{n\times n}_{\rm sym})$.

Theorems & Definitions (68)

  • Remark 2.1
  • Remark 2.2
  • Remark 2.3
  • Remark 2.4
  • Lemma 2.5
  • proof
  • Remark 2.6
  • Lemma 2.7
  • proof
  • Lemma 2.8
  • ...and 58 more