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Comparison between different viewpoints on bulk growth mechanics

Alfio Grillo and Salvatore Di Stefano

Vol. 11 (2023), No. 2, 287–311
Abstract

This work brings together two viewpoints on the mechanics of bulk growth that, in spite of some similarities, originate from different conceptualizations of this phenomenon. Each viewpoint designates a specific approach to growth, identified by the “growth law” that it determines, i.e., the “rule” governing the mass variation in the considered growing medium. In the first approach, which we call the “a priori approach”, the growth law is supplied phenomenologically, is viewed as a constraint, and is appended to the principle of virtual work in order to determine the effective dynamic equations of the growth problem at hand. On the other hand, in the second approach, denominated the “a posteriori approach”, growth is regarded as an unconstrained problem, and the growth law is viewed as a consequence of the medium’s dynamics. To highlight the main differences between these two approaches, we solve numerically a simple benchmark problem, and we compare the simulations obtained for each approach.

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Keywords
growth phenomenology, principle of virtual work, benchmark tests
Mathematical Subject Classification
Primary: 65Z05, 74B20, 74F25, 92B05, 92F99
Milestones
Received: 9 November 2022
Revised: 2 February 2023
Accepted: 4 March 2023
Published: 12 November 2023

Communicated by Francesco dell'Isola
Authors
Alfio Grillo
Dipartimento di Scienze Matematiche “G. L. Lagrange”
Politecnico di Torino
Torino
Italy
Salvatore Di Stefano
Dipartimento di Ingegneria Civile, Ambientale, Edile, del Territorio e di Chimica
Politecnico di Bari
Bari
Italy