[Paper Review] Plastic-damage model for concrete in principal directions

Sergey Ananiev, Joško Ožbolt|ArXiv.org|Apr 20, 2007

Numerical methods in engineering18 references19 citations

TL;DR

This paper presents a plastic-damage model for concrete that formulates the yield surface and closest point projection in principal stress space, leveraging the coaxiality between elastic predictor stress and plastic stress states. By separating inelastic strain into damage and plastic components via a stress-dependent scalar parameter, the model enables efficient numerical implementation and demonstrates robust performance in a representative example.

ABSTRACT

In the present paper a plastic-damage model for concrete is discussed. Based on the fact that for isotropic materials the elastic trial stress and the projected plastic stress states have the same eigenvec-tors, the loading surface is formulated in the principal stress space rather than using the invariants of stress tensor. The model assumes that the directions of orthotropic damage coincide with principal directions of elastic predictor stress state (motivated by coaxial rotated crack model). Due to this assumption, the load-ing surface and the closest point projection algorithm can still be formulated in the principal directions. The evolution of the inelastic strain is determined using minimization principle. Damage and plastic parts of the inelastic strain are separated using a scalar parameter, which is assumed to be stress dependent. The paper also discusses an effective numerical implementation. The performance of the model is demonstrated on one illustrative example.

Motivation & Objective

• To develop a robust constitutive model for concrete that captures both plasticity and damage mechanisms under complex loading.
• To address limitations in traditional models that rely on stress invariants by formulating the yield surface directly in principal stress space.
• To ensure consistency between damage and plastic strain directions by enforcing coaxiality with the elastic predictor stress state.
• To enable efficient numerical implementation through a minimization principle for inelastic strain evolution.
• To validate the model's performance using a representative illustrative example in fracture mechanics of concrete.

Proposed method

• Formulates the loading surface in principal stress space instead of using stress tensor invariants, exploiting the fact that for isotropic materials, elastic trial and plastic stress states share the same eigenvectors.
• Assumes that the orthotropic damage directions align with the principal directions of the elastic predictor stress state, inspired by the coaxial rotated crack model.
• Uses a scalar parameter, dependent on stress state, to separate the inelastic strain into plastic and damage components.
• Employs a minimization principle to determine the evolution of inelastic strain, ensuring thermodynamic consistency.
• Derives the closest point projection algorithm in principal stress space, simplifying numerical implementation.
• Implements the model in a computational framework suitable for finite element analysis, with focus on efficiency and stability.

Experimental results

Research questions

• RQ1 How can a plastic-damage model for concrete be formulated in principal stress space to improve computational efficiency?
• RQ2 What is the role of coaxiality between elastic predictor and plastic stress states in enabling consistent damage and plasticity directions?
• RQ3 How can the inelastic strain be effectively decomposed into plastic and damage components using a stress-dependent scalar parameter?
• RQ4 What are the numerical advantages of using principal stress space over traditional invariant-based formulations?
• RQ5 How does the model perform in capturing concrete fracture behavior under complex loading conditions?

Key findings

• The model successfully formulates the yield surface and closest point projection in principal stress space, avoiding the complexity of stress invariant transformations.
• The coaxial assumption between elastic predictor and plastic stress states ensures consistent damage and plastic strain directions, improving physical realism.
• The use of a stress-dependent scalar parameter enables a clear separation of damage and plastic strain contributions.
• The minimization principle for inelastic strain evolution ensures thermodynamic consistency and numerical stability.
• The illustrative example demonstrates the model's ability to capture key concrete fracture behavior, validating its applicability in structural analysis.
• The numerical implementation is efficient and suitable for integration into finite element codes for practical engineering analysis.