A constrained sequential-lamination algorithm for the simulation of sub-grid microstructure in martensitic materials

• Published in: Computer methods in applied mechanics and engineering Vol. 192; no. 26; pp. 2823 - 2843
• Main Authors: Aubry, Sylvie, Fago, Matt, Ortiz, Michael
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 04.07.2003; Elsevier
• Subjects: Applied sciences; Computational techniques; Condensed matter: structure, mechanical and thermal properties; Cross-disciplinary physics: materials science; rheology; Elasticity. Plasticity; Equations of state, phase equilibria, and phase transitions; Exact sciences and technology; Finite-element and galerkin methods; Indentation; Martensitic phase transitions; Martensitic transformations; Materials science; Mathematical methods in physics; Mechanical properties and methods of testing. Rheology. Fracture mechanics. Tribology; Metals. Metallurgy; Microstructure; Phase diagrams and microstructures developed by solidification and solid-solid phase transformations; Physics; Rank-one convexity; Relaxation; Sequential lamination; Shape-memory alloys; Solid-solid transitions; Specific phase transitions; 45; Relaxation; Rank-one convexity; Shape-memory alloys; 28; Martensitic phase transitions; Sequential lamination; Microstructure; Indentation; 64
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/S0045-7825(03)00260-3

We present a practical algorithm for partially relaxing multiwell energy densities such as pertain to materials undergoing martensitic phase transitions. The algorithm is based on sequential lamination, but the evolution of the microstructure during a deformation process is required to satisfy a continuity constraint, in the sense that the new microstructure should be reachable from the preceding one by a combination of branching and pruning operations. All microstructures generated by the algorithm are in static and configurational equilibrium. Owing to the continuity constraint imposed upon the microstructural evolution, the predicted material behavior may be path-dependent and exhibit hysteresis. In cases in which there is a strict separation of micro- and macrostructural lengthscales, the proposed relaxation algorithm may effectively be integrated into macroscopic finite-element calculations at the sub-grid level. We demonstrate this aspect of the algorithm by means of a numerical example concerned with the indentation of a Cu–Al–Ni shape memory alloy by a spherical indenter.