On material forces and finite element discretizations

• Published in: Computational mechanics Vol. 29; no. 1; pp. 52 - 60
• Main Authors: MUELLER, R, MAUGIN, G. A
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01-07-2002; Berlin Springer Nature B.V
• Subjects: Computation; Computational techniques; Discretization; Exact sciences and technology; Finite element method; Finite-element and galerkin methods; Fracture mechanics (crack, fatigue, damage...); Fracture mechanics, fatigue and cracks; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematical methods in physics; Physics; Solid mechanics; Static elasticity; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Finite element method; Eshelby tensor; High strain; Numerical method; Non linear effect; Structural analysis; Crack propagation
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-002-0322-2

The idea of using material forces also termed configurational forces in a computational setting is presented. The theory of material forces is briefly recast in the terms of a non-linear elastic solid. It is shown, how in a computational setting with finite elements (FE) the discrete configurational forces are calculated once the classical field equations are solved. This post-process calculation is performed in a way, which is consistent with the approximation of the classical field equations. Possible physical meanings of this configurational forces are discussed. A purely computational aspect of material forces is pointed out, where material forces act as an indicator to obtain softer discretizations.