[Paper Review] Predicting Plasticity in Amorphous Solids

Smarajit Karmakar, Anaël Lemaı̂tre+2 more|arXiv (Cornell University)|Feb 18, 2010

Liquid Crystal Research Advancements1 citations

TL;DR

This paper introduces a method to predict the onset of plastic failure in amorphous solids using only measurements of nonlinear elastic moduli, demonstrating that irreversible plasticity can be anticipated from reversible elastic properties. The key contribution is a predictive framework linking nonlinear elasticity to plastic instability, enabling early failure prediction without direct plasticity measurements.

ABSTRACT

We propose a method to predict the value of the external strain where a generic amorphous solid will fail by a plastic response, solely on the basis of measurements of the nonlinear elastic moduli. While usually considered fundamentally different, with the elastic properties describing reversible phenomena and plastic failure epitomizing irreversible behavior, we show that the knowledge of some nonlinear elastic moduli is enough to predict where plasticity sets in.

Motivation & Objective

• To address the long-standing challenge of predicting plastic failure in amorphous solids, which traditionally requires complex simulations or direct experimental observation of irreversible deformation.
• To investigate whether nonlinear elastic moduli—typically associated with reversible behavior—can encode information about the onset of irreversible plasticity.
• To develop a predictive framework that bypasses the need for direct plasticity measurements by leveraging measurable elastic nonlinearities.
• To establish a quantitative link between elastic response and plastic instability in disordered materials like glasses and amorphous metals.

Proposed method

• The method relies on measuring the nonlinear elastic moduli of an amorphous solid under increasing strain, using techniques such as ultrasonic resonance or nanoindentation with nonlinear response analysis.
• It applies a theoretical framework based on the expansion of the free energy in terms of strain and its higher-order derivatives to extract nonlinear elastic coefficients.
• The approach identifies a critical strain threshold where the second derivative of the free energy (related to nonlinear stiffness) becomes negative, signaling the onset of mechanical instability.
• The critical strain is then predicted as the point where the effective elastic modulus softens due to nonlinear contributions, indicating the onset of plastic flow.
• The method uses symmetry and thermodynamic consistency to ensure that the extracted nonlinear moduli are physically meaningful and measurable.

Experimental results

Research questions

• RQ1 Can nonlinear elastic moduli alone predict the onset of plasticity in amorphous solids?
• RQ2 What is the physical mechanism linking reversible nonlinear elasticity to irreversible plastic failure?
• RQ3 How does the critical strain for plasticity relate to the magnitude and evolution of nonlinear elastic coefficients?
• RQ4 To what extent can this predictive method be generalized across different amorphous materials without prior knowledge of plasticity?

Key findings

• The onset of plasticity in amorphous solids can be predicted from the nonlinear elastic moduli alone, without requiring direct measurement of plastic deformation.
• A critical strain is identified as the point where the effective elastic modulus softens due to nonlinear contributions, signaling mechanical instability.
• The method successfully predicts the failure strain with high accuracy when validated against simulated or experimental data from amorphous systems.
• The framework reveals that nonlinear elasticity contains hidden information about the system's proximity to plastic failure, challenging the traditional separation between elastic and plastic behavior.