Hyperelasticity

The deformation gradient tells us how a material point deforms. But how much stress results from that deformation? In this video, we develop the framework of hyperelastic material modeling to answer exactly that question. We introduce the strain energy density function as the central object that links deformation to stress, and explore the physical requirements it must satisfy to produce a physically meaningful material response. We then discuss one of the most widely used hyperelastic models: the Neo-Hookean model. Keywords: engineering, physics, continuum mechanics, solid mechanics, fluid mechanics, deformation gradient, stress tensor, strain tensor, Cauchy stress tensor, first Piola-Kirchhoff stress tensor, second Piola-Kirchhoff stress tensor, hyperelasticity, large deformation, thermodynamics of materials, material frame indifference, objectivity, isotropy, compressible, incompressible, Helmholtz free energy potential, stored energy density potential, strain energy density potential References: Fuhg et al., A Review on Data-Driven Constitutive Laws for Solids (https://link.springer.com/10.1007/s11...) Linden et al., Neural networks meet hyperelasticity: A guide to enforcing physics (https://linkinghub.elsevier.com/retri...) Linka & Kuhl, A new family of Constitutive Artificial Neural Networks towards automated model discovery (https://www.sciencedirect.com/science...) Music: The Palace Gardens - Asher Fulero Variable Circumstance - Dan