Computerized deformation analyzer

A method of finite element analysis comprising:

• receiving, at a computer, an elastic deformation range and a plastic deformation range of a material, the elastic deformation range transitioning into the plastic deformation range at a point associated with the yield stress of the material;
• modeling the material with a mesh comprising a plurality of elements, each of the plurality of elements comprising a plurality of nodes;
• for each of a plurality of iterations of the finite element analysis, calculating a stiffness matrix for the each of the plurality of elements, wherein the stiffness matrix is calculated using a modulus of elasticity according to the elastic deformation range when a value of strain calculated from a previously determined element displacement is below the point associated with the yield stress and according to the plastic deformation range when the value of strain is equal to or above the point;
• and
• after calculating the stiffness matrix for the each of the plurality of elements, determining that a displacement of the each of the plurality of nodes is within a predetermined modeling tolerance.

An apparatus for modeling displacement of a material, comprising:

• a software program stored on a computer readable medium and operable, when executed on a processor, to:
• receive an elastic deformation range and a plastic deformation range of the material;
• model a region of the material with a mesh comprising a plurality of elements;
• and
• determine, by performing a finite element analysis on the mesh by the computer, a displacement for at least one point on each of the elements, the displacement resulting from a set of modeled boundary conditions, the finite element analysis including recurrently approximating the modulus of elasticity for each element according to the elastic deformation range and the plastic deformation range based on a value of strain calculated from a previously calculated element displacement.

A system for modeling displacement of a material within a computer-aided analysis environment, comprising:

• a computer system having a display unit, an input device, and a processor;
• a computer readable medium coupled to the computer system, the computer readable medium comprising a software program operable to be executed on the processor and to:
• receive an elastic deformation range and a plastic deformation range of the material;
• model a region of the material with a mesh comprising a plurality of elements;
• and
• determine, by performing a finite element analysis on the mesh by the computer, a displacement for at least one point on each of the elements, the displacement resulting from a set of modeled boundary conditions, the finite element analysis including recurrently approximating the modulus of elasticity for each element according to the elastic deformation range and the plastic deformation range based on a value of strain calculated from a previously calculated element displacement.