Modeling cracks and cracking models: Structures, mechanisms, boundary conditions, constraints, inconsistencies and the proper domains of natural laws
type: Item
instance of: scholarly article
title: Modeling cracks and cracking models: Structures, mechanisms, boundary conditions, constraints, inconsistencies and the proper domains of natural laws
zbMATH Open document ID: 1115.74007
author: Jordi Cat
published in: Synthese
publication date: 2006-02-08T00:00:00Z
review text: The paper presents philosophical discussion how much of physics lies beyond the strict domain of laws, basing on examples from micro- and macroscopic physics, shock waves, crack propagation, symmetry breaking, etc. The author focuses on the role of laws in the characterization of models of real systems and phenomena in order to highlight the cognitive value of ''auxiliary'' elements in mathematical representation. He argues that in important cases the physics or physical understanding does not lie either in laws or in their properties such as universality, consistency and symmetry. While the actual domain of application of laws should be seen as much broader, in the broader domain of application their validity, centrality and consistency may be seriously compromised. It is shown that ``anomic'' representational elements, namely boundary conditions, state descriptions, configuration of parts, constraints, limits, structures and mechanisms, reveal themselves as central to the descriptive and explanatory power of theories and models. Based on some examples, it is shown that these elements are often interrelated. The author argues that laws cannot always specify completely and consistently what models should describe and, connectedly, that laws might not be true of the relevant kind of models either. An adequate account of successful science needs notions of models that can accommodate and take seriously the relevant characterization of phenomena or reality that anomic elements offer. Finally, it is shown how the results of the discussion could be applied to representation and explanation of unification, approximation and dispositional properties.
Mathematics Subject Classification ID: 74A45
Mathematics Subject Classification ID: 00A71
zbMATH DE Number: 5005201
reviewed by: Ivan A. Parinov
MaRDI profile type: Publication
full work available at URL: s11229-004-6259-6
OpenAlex ID: W2114823367
cites work: One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation
cites work: In favor of laws that are not \textit{ceteris paribus} after all
cites work: On understanding: Maxwell on the methods of illustration and scientific metaphor
cites work: Hyperbolic systems of conservation laws II
cites work: Are instantaneous velocities real and really instantaneous?: An argument for the affirmative
DOI: 10.1007/S11229-004-6259-6
Recommended article: Laws of crack motion and phase-field models of fracture
Recommended article: Crack Models with Embedded Discontinuities
Recommended article: Analysis of a model of field crack mechanics for brittle materials
Recommended article: Analytical derivation and investigation of the interface crack models
Recommended article: Modelling crack propagation in structures: Comparison of numerical methods
Recommended article: Q3131150
Recommended article: Mathematical and computational analyses of cracking formation. Fracture morphology and its evolution in engineering materials and structures
Recommended article: Crack models based on the extended finite element method
Recommended article: Cracks in Cosserat Continuum—Macroscopic Modeling
description: scientific article; zbMATH DE number 5005201