[Paper Review] Infeasibility of the nonlocal strain gradient theory for applied Physics

Mohamed Shaat|arXiv (Cornell University)|Nov 27, 2017

Nonlocal and gradient elasticity in micro/nano structures33 references3 citations

TL;DR

This paper challenges the physical validity of the nonlocal strain gradient theory (NSGT) in applied physics, demonstrating that it is inherently inconsistent due to the overlapping physical interpretations of nonlocal and strain gradient effects. It proves that both nonlocal and strain gradient theories independently model hardening and softening behaviors, rendering their combination in a unified theory physically infeasible and contradictory.

ABSTRACT

In this communication, the feasibility of the nonlocal strain gradient theory for fields of applied mechanics is investigated. It is demonstrated that the nonlocal strain gradient theory is physically incorrect. It is proved that each of the nonlocal theory and the strain gradient theory can model, both, hardening and softening behaviors of materials. Moreover, it is proved that the nonlocal theory and the strain gradient theory describe the same physical phenomena, and hence the strain gradient theory cannot be merged with the nonlocal theory in a unified model. This short communication comments on a series of papers in which the nonlocal strain gradient theory was utilized in different areas of applied mechanics.

Motivation & Objective

• To assess the physical feasibility of the nonlocal strain gradient theory (NSGT) in applied mechanics and materials science.
• To investigate whether the nonlocal and strain gradient theories can coherently coexist in a unified model.
• To determine whether NSGT can consistently describe both hardening and softening behaviors in materials.
• To challenge the validity of NSGT as used in recent literature across various applied mechanics fields.
• To clarify the physical distinction—or lack thereof—between nonlocal and strain gradient effects.

Proposed method

• Analytical derivation of the governing equations for both nonlocal and strain gradient theories to compare their physical interpretations.
• Mathematical proof that each theory—nonlocal and strain gradient—can independently model both hardening and softening material responses.
• Demonstration that the two theories describe identical physical phenomena, implying redundancy in their combination.
• Logical analysis of the NSGT framework to expose inconsistencies in its physical assumptions.
• Comparison of theoretical predictions with known mechanical behavior to validate or reject the model.
• Use of symmetry and variational principles to show that the NSGT formulation leads to unphysical results.

Experimental results

Research questions

• RQ1 Can the nonlocal strain gradient theory consistently model both hardening and softening behaviors in materials?
• RQ2 Do the nonlocal and strain gradient theories describe distinct physical phenomena or overlapping effects?
• RQ3 Is it physically valid to merge the nonlocal and strain gradient theories into a single unified model?
• RQ4 Why do recent applications of NSGT in applied mechanics fail to account for its inherent physical inconsistencies?
• RQ5 What are the mathematical and physical contradictions arising from the NSGT formulation?

Key findings

• The nonlocal strain gradient theory is physically infeasible because it combines two theories that describe the same physical phenomena.
• Both the nonlocal theory and the strain gradient theory can independently model both hardening and softening behaviors, undermining the need for their combination.
• The strain gradient theory cannot be meaningfully merged with the nonlocal theory, as they are not complementary but redundant.
• The NSGT framework leads to contradictory physical interpretations, rendering it unsuitable for accurate modeling in applied physics.
• The paper concludes that the use of NSGT in recent literature is fundamentally flawed due to its lack of physical consistency.
• The theoretical foundation of NSGT is invalid, as it fails to distinguish between nonlocal and gradient effects, which are not independent mechanisms.